BLINDED EVALUATIONS OF EFFECT SIZES IN CLINICAL TRIALS ... 2013 Turkoz.pdf · endpoints in addition...

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BLINDED EVALUATIONS OF EFFECT SIZES IN CLINICAL TRIALS COMPARISONS BETWEEN BAYESIAN AND EM ANALYSES

1 Nov 2013

IBRAHIM TURKOZ PhD

Janssen Research amp Development LLC NJ

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Introduction

Background

Literature Review

Objective

Methods

EM Algorithm

Bayesian Approaches

Model Selection

Simulations

Set-up

Results

Application

Discussions and Conclusions

Questions

Outline

Nov 2013 2 Outline

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Clinical trials can have a major impact on public health

Required information for designing a clinical trial is not fully

available

Ongoing monitoring of accumulating data is necessary

Interim analyses are common

Usually costly

Requires unblinding treatment assignments

Statistical implications

We will investigate the use of the accumulated data for purposes

of modifying aspects of the study design IN BLINDED

SETTING

Background

3 Introduction Nov 2013

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Background Motivating Question MDD Trial[1]

4 Introduction

Additional AD Treatment

1 Mahmoud AR Pandina JG Turkoz I Kosik-Gonzalez C Canuso MC Kujawa JM and Gharabawi GM Risperidone for treatment-refractory major depressive disorder

Annals of Internal Medicine 2007 147 593-602

Prior AD Treatment

Nov 2013

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Nov 2013 5 Introduction


RANDOMIZATION for

those who did not respond

6 weeks long but the primary time

point was Week 4

Placebo + AD Treatment as usual Placebo + AD Treatment as usual

Active + AD Treatment as usual



Prior AD Treatment

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RANDOMIZATION for

Patients with Caroll

Depression Score gt20

And CGI-S4


point was Week 4

Outcome Parameters

Clinician Rated Patient Reported

bullHRSD-17 (primary efficacy

scale)

bullCGI-S

bullMost Troubling Symptoms

(MTS) or PaRTS-D

bullPatient Global Impression of

Severity PGIS





Prior AD Treatment

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Background Motivating Question MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

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Background Motivating Question Schizoaffective Trial


Psychosis

Mania Depression

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Psychosis

Mania Depression

PANSS

30-210

YMRS

0-60

HAM-D-21

0-52

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Background Motivating Question Schizoaffective Trial[1]


BL Wk 6

n=95 PBO

n=216 PALI PR 3 - 12 mgd (start at 6 mg flexible)

Study 3002

N=311

Psychosis

Mania Depression

1 Canuso CM Lindenmayer JP Kosik-Gonzalez C Turkoz I Carothers J Bossie CA Schooler NR A randomized double-blind placebo-controlled study of 2 dose ranges of

paliperidone extended-release in the treatment of subjects with schizoaffective disorder J Clin Psychiatry 2010 May71(5)587-98

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Psychosis

Mania

Depression

Changes in PANSS

Total Score at Week 6

YMRS

HAM-D-21

PRIMARY ENDPOINT SECONDARY ENDPOINTS

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Psychosis

Mania

Depression

YMRS

HAM-D-21


FOR REGISTRATION PURPOSES

Changes in PANSS


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Background Motivating Question ADHD Trial 1


1 Wigal SB Wigal T Schuck S Brams M Williamson D Armstrong RB and Starr HL Academic Behavioral and Cognitive Effects of OROSreg Methylphenidate on Older Children

with Attention-DeficitHyperactivity Disorder J Child Adolesc Psychopharmacol 2011 April 21(2) 121ndash131

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Background


It is important to evaluate secondary endpoints to differentiate your

drug from other drugs in market place

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Background




Another symptom

Functionality

Medication Satisfaction

Certain Adverse Reactions

Cognition

Etc

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Background




Another symptom

Functionality



Cognition

Etc

Failure to consider important outcomes can limit the

conclusions of clinical trials

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Background


bull Examination of appropriate statistical methods to test secondary

endpoints requires careful consideration

bull Fixed sequence gate-keeping procedures [1234] are widely used

because of their ease of application and interpretation in many

circumstances

bull These gate-keeping procedures often require prospective ordering

of null hypotheses for secondary endpoints

bull Can we use information that is available to order the null

hypotheses based on interim effect sizes without breaking the

blind

1 Demitrienko A Tamhane A Bretz F Multiple testing problems in pharmaceutical statistics 2010 ChapmanampHallCRC Biostatistics Series

2 Westfall PH Krishen A Optimally weighted fixed sequence and gatekeeper multiple testing procedure J of Statistical Planining and Inference 99 (2001) 25-40

3 Weins B Dmitrienko A (2005) The fallback procedure for evaluating a single family of hypotheses Journal of Biopharmaceutical Statistics 15 929ndash942

4 Bretz F Maurer W Brannath W Posch M A graphical approach to sequentially rejective multiple test procedures Stat in Med 2009 28586ndash604

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Literature Review


bull EM algorithm to estimate the within group variance for sample size re-

estimation without unblinding at interim stages has been suggested [123]

bull Enrollment order of subjects and the randomization block sizes to estimate the

within group variance have also been used [4]

bull Risk of unblinding the treatment effect from blinded inferences based on

knowledge of the randomization block size for continuous and binary

outcomes [5]

bull The recent draft FDA guidance on adaptive designs [6] discusses possible

study design modifications such as selection andor order of secondary

endpoints in addition to sample size re-estimation

bull Blinded treatment effects for survival endpoints[7] were also examined

1Gould AL Shih WJ Sample size re-estimation without unblinding for normally distributed outcomes with unknown variance Communications in Statistics Theory and Methods

1992 21 2833ndash2853

2 Shih WJ Sample size reestimation in clinical trials In Biopharmaceutical sequential statistical applications Peace K (ed) Marcel Dekker New York 1992 285ndash301

3 Shih WJ Sample size reestimation for triple blind clinical trials Drug Information Journal 1993 27 761ndash764

4 Xing B Ganju J A method to estimate the variance of an endpoint from an on-going blinded trial Statistics in Medicine 2005 24 1807-1814

5 Miller F Friede T Kieser T Blinded assessment of treatment effects utilizing information about randomization block length Statistics in Medicine 2009 28 1690-1706

6 Guidance for industry Adaptive design clinical trials for drugs and biologics

httpwwwfdagovdownloadsDrugsGuidanceComplianceRegulatoryInformationGuidancesucm201790pdf

7 Xie J Quan H Zhang J Blinded assessment of treatment effects for survival endpoint in an ongoing trial Pharmaceutical Statistics 2012

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Objective


bull Instead of formal interim analyses on unblinded data use the

information from blinded data

bull Assess the feasibility of estimating magnitude of treatment effect

on various secondary endpoints in ongoing trial

bull Primary objective is to compare posterior ordering of the signal-

to-noise ratios (effect sizes) using available data

points

d

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Model

Nov 2013 Methods 22

( 1 01 12 ) is the response variable for the endpoint from

20 ~ (0 )

th thjijkY i n j k K k j

ijk k k ik ik ijk ky z N i i d

20 0

21 1

0

treatment group on subject

~ ( )

~ ( )

the mean placebo response

magnitude of the treatment effect

latent binary treatment assignment

We assume that lower scores a

i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )

re better and the average effect of the treatment is

k k k k

k

Y N

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Model

Nov 2013 Methods 23

For a two component univariate normal mixture model it is appropriate to specify the

complete likelihood function for a given response in the form

( |p y z

2 20 0 1 1 0

1 0 =p(z 1)

where ( ) ( ) is randomization weight

The signal-to-noise ratio for endpoint ( 1 )

) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2

to compare the EM and Bayesian algorithm induced

posterior ordering of the signal-to-noise ratios of endpoints ( | )kP d d d y

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EM Algorithm

Nov 2013 Methods 24

=p(z 1)

MMLEs are the most common way to estimate parameters of interest however MMLEs

often do not have closed form solutions EM seeks the MMLE by iterativel

1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying

Expectation and Maximizing steps

ˆE-Step log ( | ) |

M-Step the conditional expectation is maximized with respect to This yields the new estimates

tE p y z yθ θ

θ

( 1) ( 1)ˆ for and a distribution for t tz θ

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EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0

Conditional expectation of latent treatment assignment at iteration ( 1) is

ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )

In the M step the mean pa

t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1

ˆˆ ˆrameters and variance parameter at iteration are ( 1)

ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

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Bayesian Approach

Nov 2013 Methods 26

The likelihood function of the mixture distribution and the prior distributions of and z

are combined to obtain the joint posterior distribution which is assumed to contain all the information

abou

θ

t the unknown parameters Using the Bayes theorem the posterior distribution satisfies

where

( | ) is the likelihood

( | ) is the prior probability of latent tre

( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment

( ) is the prior distribution of p θ θ

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Bayesian Approach

Nov 2013 Methods 27

The conditional distribution of the treatment allocation is proportional

this reduces to latent treatment allocation probability in EM

Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s

in order to reduce sensitvity

For simplicity purposes we have

~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

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Bayesian Approach

Nov 2013 Methods 28

Regardless of the structure of the prior distribution the posterior distribution does not have

a simple closed form In order to make inferences about the unknown parameters MCMC

methodologies are em

2 2 20 0 0

2

2 2

ployed to generate samples from the posterior distribution The joint

posterior probability distribution of these parameters satisfies

( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

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Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

Likelihood for treatment

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Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

Likelihood for placebo arm

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Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

Prior for treatment arm

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Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

Prior for Placebo arm

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Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

In computations =3 and small scale hyperparameter ( 001) are assumed

i i

i i

z z

y

y y

s s

Prior for Sigma

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Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12

The posterior conditional distributions of parameters of interest in equation are given by

1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

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Bayesian Approach with Covariate

Nov 2013 Methods 35

We assume a trial with stratified randomization The sample is divided into subsamples on the

basis of stratifaction factor (covariate additional medication usage and groups)

Let denote ti

yes no

g

22

0 2

he known strata membership of the subject 1 if observation belongs to the

strata and 0 if it does not The joint posterior distribution then takes the form

1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

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Nov 2013 Methods 37

202

2 20 02 2

02

Conditional posterior probability treatment assignment at each iteration is given by

1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0

The posterior distribution for parameters of interest are computed to be

( ) ( ) ( )

1~

1 2 1 2

( )

~

i i yes no yes yes no no

i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX

Bayesian Approach with Covariate and a Power Prior

Nov 2013 Methods 39

0

[123]0

0 0

0

Denote the historical data by and current data by

[01] to control the influence of the historical data on the current study

1 approaches full barrowing from

0 approaches no ba

D D

D

0

0

0

rrowing from

The basic idea is to use the power parameter to control the influence of the historical data on the current study

Let assume

( | ) is the past data likelihood

D

L D

0 0 0 0 0

0 0

( | ) is the current data likelihood

( | ) ( | ) ( ) ( ) is the posterior given past likelihood

Then the full likelihood is proportional to ( | ) ( | )

L D

p D L D p p

p D L D

1 Ibrahim J Chen MH Power prior distributions for regression models Statistical Science 2000 1546-60

2 Duan Y Ye K Smith EP Evaluating water quality using power priors to incorporate historical information Environmetrics 2006 17 95-106

3 Hobbs BP Carlin BP Mandrekar S and Sargent DJ Hierarchical commensurate and power prior models for adaptive incorporation of historical information in

clinical trials Biometrics 2011 671047-1056

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Nov 2013 Methods 40

0

0 0

22

0 0 2 2

The joint posterior distribution can be extended to include the prior for

Think of as the historical effective sample size

The result takes the form

1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g

p yes yes yes p yesi

z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s

Prior for Power Parameter

BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1

The posterior distribution of parameters of interest is computed to be

( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no

p yes yes p yes no no p noi i yes no

i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43

By contrast with frequentist analogues Bayesian model comparison distinguishes which likelihood and prior

combinations better fit the data These measures of performance can be used to choose a singl

[1]

e ldquobestrdquo model

or improve estimation via model averaging

The deviance information criterion (DIC) provides a natural measure of performance in this setting

Models with smaller DIC should be preferre

0 0

0 0

d to models with larger DIC

=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D

Expectation over Expectation over

θ θ

1 DJ Spiegelhalter NG Best BP Carlin A Linde Bayesian measures of model complexity and fit (with discussion) Journal of the Royal Statistics

Society Series B (Statistical Methodology)2002 64 583ndash639

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Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0

( )( ) this is a posterior expectation over ( )average after all the iterations

ˆ

ˆ averaged after all the iterations

updates at each iter

0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation

updates at each iteration

treatment assignment at each iteration

ˆˆ( )ˆˆ( ) this is a posterior expectation over it is using averaged parametersˆ

ˆ

i

i

i iz i

i

z latent

y zD E z

2

0

averaged after all the iterations



treatment assignment at each iterationiz latent

BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45

An important feature of the Gibbs sampler is that each simulated posterior parameter value is always accepted

The main drawback of the Gibbs sampler in this setting is the lack of mixing

We employed a Metropolis-Hastings algorithm with an acceptance-rejection sampling

This involved subsampling 10 of the treatment and placebo group observations and proposing a label switch

1) Draw random candidate samples fromfor switching treatment

2) Generate from the Uniform (01) distribution

(1 ( ( 1))3) If make label change otherwise return to s

( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up

Nov 2013 Simulations 46

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up


Sample Size and Power Computations using a Two-Sample t-test with Two-Sided Type I Error=005

BASS XX

Simulation Set-Up


1 2 3

2 treatment arms with a 11 treatment allocation ratio

3 uncorrelated endpoints and

No missing data

For each case 20 data sets are generated ( 1 20)

Different prior for each of

k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1

Generate Input Data Sets

( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20

Without loss of generality we assumed that

10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up


2 20 1 Each true input clinical trial data set is based on ~ (1010 ) and with normal distribution with variance 10

and corresponding mean value to generate effect sizes for a given scenario

Initi

N

20

0

al values of ( ) for simulations are based on the true input data set parameters and the initial

power parameter estimate is given as 025 and 05

Posterior inferences are based on 1000 i

th

terations

The first 200 iterations are considered to be the burn in period for both EM and Bayesian algorithms

Every 4 point after the burn in period is stored for the Bayesian simulations to re

duce correlations

to emulate thinning process

Eight hundred simulation results in EM and 200 results in Bayesian methods are summarized

Posterior parameter estimates are summuarized

Empirical pr

obability of each triplet combination of effect size ordering is examined

In each case for a given data set the last 20 simulation results are kept for effect size orderings

For each of the study data sets a total of 20 20 20 8000 possible triplet combinations of orderings are available

For 20 different study data sets a total of 160000 possible orderings are available

BASS XX

Simulation Results


Posterior Probability of Effect Size Ordering by Scenario

BASS XX

Simulation Results


Posterior Distribution of Effect Sizes by Scenario Averaged Over 20 Data Sets

BASS XX

Simulation Results


Posterior Distribution of Effect Sizes by Scenario

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Simulation Results Scenario 1


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MDD Trial

Nov 2013 Application 66

Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX

MDD Study Simulations


4 6

Decision Rule 1

Calculate the posterior probability that the HRSD 17 effect size at Week 4 is larger than that of Week 6

( ( ) ( ) | )

Decision Rule 2

Calculate 95 Credible Intervals for W

Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4

eek 4 and Week 6 effect sizes

( ) ( ) ( )

( ) ( ) ( )

Priors for HRSD 17 placebo and treatment means at Week 4 ( ) were assumed to be

( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX



Summary of Effect Sizes for HRSD-17 and PaRTS-D

At Week 4 EM Results were Not Available

Posterior Ordering of Effect Sizes

for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX



DIC Scores on HRSD-17 and PaRTS-D

BASS XX

Discussion and Conclusion

Nov 2013 Discussion 72

We investigated whether or not the researchers can obtain reliable estimates of effect sizes

without knowing treatment assignments

Instead of relying on the clinicianrsquos subjective evaluations the

suggested methodologies

provide numerical assistance

We showed how to order secondary null hypotheses while the study is ongoing

without unblinding the treatments

without losing the validity

of the testing procedure

and with maintaining the integrity of the trial

In our simulations we used prior distributions whose hyper parameters reflect the true values

of the model parameters I

n MDD analyses we used prior distributions whose hyper parameters

reflect the original study design elements

BASS XX



The EM algorithm frequently failed to generate posterior parameter estimates

Both the Bayesian and the EM algorithms overestimated treatment differences and

standardized effect sizes

The Bayesian

algorithms performed better than existing EM algorithm counterparts in ordering

the standardized effect sizes

With the Bayesian algorithm the posterior probability for identifying the ground-truth ordering

increased both as a function of the effect size differences and as a function of the sample size

For large sample sizes the proportion of times the true ordering was selected was high (ab ove 35)

and the variability of standardized effect sizes was low

With the EM algorithm the probability for identifying the ground-truth ordering was low

(sometimes near zero) and the variability of

standardized effect sizes was high

BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Introduction

Background

Literature Review

Objective

Methods

EM Algorithm

Bayesian Approaches

Model Selection

Simulations

Set-up

Results

Application

Discussions and Conclusions

Questions

Outline

Nov 2013 2 Outline

BASS XX



available



Usually costly





SETTING

Background


BASS XX


4 Introduction




Prior AD Treatment

Nov 2013

BASS XX




RANDOMIZATION for



point was Week 4





Prior AD Treatment

BASS XX




RANDOMIZATION for



And CGI-S4


point was Week 4

Outcome Parameters



scale)

bullCGI-S


(MTS) or PaRTS-D


Severity PGIS





Prior AD Treatment

BASS XX



Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX



Psychosis

Mania Depression

BASS XX



Psychosis

Mania Depression

PANSS

30-210

YMRS

0-60

HAM-D-21

0-52

BASS XX



BL Wk 6

n=95 PBO


Study 3002

N=311

Psychosis

Mania Depression



BASS XX



Psychosis

Mania

Depression

Changes in PANSS


YMRS

HAM-D-21


BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



available



Usually costly





SETTING

Background


BASS XX


4 Introduction




Prior AD Treatment

Nov 2013

BASS XX




RANDOMIZATION for



point was Week 4





Prior AD Treatment

BASS XX




RANDOMIZATION for



And CGI-S4


point was Week 4

Outcome Parameters



scale)

bullCGI-S


(MTS) or PaRTS-D


Severity PGIS





Prior AD Treatment

BASS XX



Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX



Psychosis

Mania Depression

BASS XX



Psychosis

Mania Depression

PANSS

30-210

YMRS

0-60

HAM-D-21

0-52

BASS XX



BL Wk 6

n=95 PBO


Study 3002

N=311

Psychosis

Mania Depression



BASS XX



Psychosis

Mania

Depression

Changes in PANSS


YMRS

HAM-D-21


BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX


4 Introduction




Prior AD Treatment

Nov 2013

BASS XX




RANDOMIZATION for



point was Week 4





Prior AD Treatment

BASS XX




RANDOMIZATION for



And CGI-S4


point was Week 4

Outcome Parameters



scale)

bullCGI-S


(MTS) or PaRTS-D


Severity PGIS





Prior AD Treatment

BASS XX



Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX



Psychosis

Mania Depression

BASS XX



Psychosis

Mania Depression

PANSS

30-210

YMRS

0-60

HAM-D-21

0-52

BASS XX



BL Wk 6

n=95 PBO


Study 3002

N=311

Psychosis

Mania Depression



BASS XX



Psychosis

Mania

Depression

Changes in PANSS


YMRS

HAM-D-21


BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX




RANDOMIZATION for



point was Week 4





Prior AD Treatment

BASS XX




RANDOMIZATION for



And CGI-S4


point was Week 4

Outcome Parameters



scale)

bullCGI-S


(MTS) or PaRTS-D


Severity PGIS





Prior AD Treatment

BASS XX



Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX



Psychosis

Mania Depression

BASS XX



Psychosis

Mania Depression

PANSS

30-210

YMRS

0-60

HAM-D-21

0-52

BASS XX



BL Wk 6

n=95 PBO


Study 3002

N=311

Psychosis

Mania Depression



BASS XX



Psychosis

Mania

Depression

Changes in PANSS


YMRS

HAM-D-21


BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX




RANDOMIZATION for



And CGI-S4


point was Week 4

Outcome Parameters



scale)

bullCGI-S


(MTS) or PaRTS-D


Severity PGIS





Prior AD Treatment

BASS XX



Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX



Psychosis

Mania Depression

BASS XX



Psychosis

Mania Depression

PANSS

30-210

YMRS

0-60

HAM-D-21

0-52

BASS XX



BL Wk 6

n=95 PBO


Study 3002

N=311

Psychosis

Mania Depression



BASS XX



Psychosis

Mania

Depression

Changes in PANSS


YMRS

HAM-D-21


BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX



Psychosis

Mania Depression

BASS XX



Psychosis

Mania Depression

PANSS

30-210

YMRS

0-60

HAM-D-21

0-52

BASS XX



BL Wk 6

n=95 PBO


Study 3002

N=311

Psychosis

Mania Depression



BASS XX



Psychosis

Mania

Depression

Changes in PANSS


YMRS

HAM-D-21


BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



Psychosis

Mania Depression

BASS XX



Psychosis

Mania Depression

PANSS

30-210

YMRS

0-60

HAM-D-21

0-52

BASS XX



BL Wk 6

n=95 PBO


Study 3002

N=311

Psychosis

Mania Depression



BASS XX



Psychosis

Mania

Depression

Changes in PANSS


YMRS

HAM-D-21


BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



Psychosis

Mania Depression

PANSS

30-210

YMRS

0-60

HAM-D-21

0-52

BASS XX



BL Wk 6

n=95 PBO


Study 3002

N=311

Psychosis

Mania Depression



BASS XX



Psychosis

Mania

Depression

Changes in PANSS


YMRS

HAM-D-21


BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BL Wk 6

n=95 PBO


Study 3002

N=311

Psychosis

Mania Depression



BASS XX



Psychosis

Mania

Depression

Changes in PANSS


YMRS

HAM-D-21


BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



Psychosis

Mania

Depression

Changes in PANSS


YMRS

HAM-D-21


BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



Psychosis

Mania

Depression

YMRS

HAM-D-21



Changes in PANSS


BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX





BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX





BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Background




BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Background




Another symptom

Functionality



Cognition

Etc

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Background




Another symptom

Functionality



Cognition

Etc



BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Background






circumstances





blind





BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Literature Review








outcomes [5]






1992 21 2833ndash2853








BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Objective








points

d

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Model

Nov 2013 Methods 22


20 ~ (0 )



20 0

21 1

0


~ ( )

~ ( )





i k k k

i k k k

k

k

ik

i

Y N

Y N

z

y

21 0~ ( )


k k k k

k

Y N

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Model

Nov 2013 Methods 23



( |p y z

2 20 0 1 1 0

1 0 =p(z 1)



) ( | ) (1 ) ( | )

Our objective is

k k kk d k K

p y p y

1 0

θ θ

θ θ θ

1 2



BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

EM Algorithm

Nov 2013 Methods 24

=p(z 1)



1 0( | ) ( | ) (1 ) ( | )p y z p y p y 1 0θ θ θ

( )

y applying




tE p y z yθ θ

θ


BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

EM Algorithm

Nov 2013 Methods 25

( ) ( ) 2( )( 1) ( ) 0

( ) ( )( ) 2( ) 2( )0 0


ˆˆ ˆ( | )ˆ( 1| )

ˆˆ ˆ ˆ ˆ( | ) (1 ) ( | )


t t tt t

i t tt t t

t

N yP z y

N y N y

θ

20

( 1) ( 1) ( 1)( ) ( )0

( 1) ( 1)1 10

( 1) ( 1)( ) ( )

1


ˆ ˆ ˆ( 0 | ) ( 1| )( )

ˆˆ

ˆ ˆ( 0 | ) ( 1| )

n nt t tt t

i ii it ti i

nt tt t

i i

i i

t

P z y y P z y y

P z y P z y

θ θ

θ θ

1)

1

( 1) ( 1) ( 1) ( 1)( ) 2 ( ) 21 0

2(t 1

ˆ ˆˆ ˆ( 1| )( ) ( 0 | )( )

ˆ

n

nt t t tt t

i ii i

i

P z y y P z y y

n

θ θ

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Bayesian Approach

Nov 2013 Methods 26



abou

θ


where



( | ) ( | ) ( | ) ( )

p y z

p z

p z y p y z p z p

θ

θ

θ θ θ θ

atment assignment


BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Bayesian Approach

Nov 2013 Methods 27



Prior Distribution

( | ) ( | ) ( | ) ( )

( | ) ( | )

p z y p y z p z p

p z y p y z

θ θ θ θ

θ θ

20 0 0

21 0 1 1

2

s



~ ( )

~ ( )

~ ( )

( )

j N

N y s

N y s

Gamma

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Bayesian Approach

Nov 2013 Methods 28




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Bayesian Approach

Nov 2013 Methods 29




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Bayesian Approach

Nov 2013 Methods 30




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Bayesian Approach

Nov 2013 Methods 31




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Bayesian Approach

Nov 2013 Methods 32




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2

i i

i i

z z

y

y y

s s


BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Bayesian Approach

Nov 2013 Methods 33




2 2 20 0 0

2

2 2



( | ) ( | ) ( ) ( )

1 1exp (

2

n

p z y p y z p z p

y

2 20 02

1 0

12 220 1 0 0

2 2 21 0

1) exp ( )

2

( ) ( ) 1exp exp exp( )

2 2


i i

i i

z z

y

y y

s s

Prior for Sigma

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Bayesian Approach

Nov 2013 Methods 34

0 12 2 2

0 110

2 2 2 2 2 20 1 0 1

0

1 0 12


1~

1 1 1 1

( )

~

i i

i

i i

i

y z y y

s sN

n n

s s s s

y zy

sN

21

1 12 2 2 2

1 1

20

2 12

3

1

1 1

( )

~

i i

i i

i i

i

n

z z

s s

y z

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX


Nov 2013 Methods 35



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX


Nov 2013 Methods 36



Let denote ti

yes no

g

22

0 2



1( | ) e

i

n

yes no

i g yes

p z y

202

1 01

2 20 12 0 0

02 2 21 00 01

12

2

1xp ( )

2

( ) ( )1exp ( ) exp exp

2 2 2

1exp( )

i

i i

i i

i i

i g

z g

g gi

z g

y

y yy

s s

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX


Nov 2013 Methods 37

202

2 20 02 2

02


1exp ( )

2 Yes strata

1 1exp ( ) exp ( )

2 2

( 1)

1exp (

2

i yes

i yes i

i

i

y

y y

P z

y

2

2 20 02 2

)

No strata1 1

exp ( ) exp ( )2 2

no

i no iy y

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX


Nov 2013 Methods 38

1 102 2 2

0 110

2 2 2 2 2 20 1 0 1

0


( ) ( ) ( )

1~

1 2 1 2

( )

~


i

i

yes

y z y yy

s sN

n n

s s s s

y

N

0

1 1 0 1 1 2 0 1

2 2 2 21 1

1 1 1 1 1 2 1 2

2 2 2 2 2 2 2 21 1 1 1

20 0

2

( )

1 1 ~

1 1 1 1

( ) (

~

i i i

i g yes i g no

noi i i i

i g i g i g i g

i i yes i i

z y zy y

s sN

z z z z

s s s s

y z y z

2

1 1 1 2

23

)

no

i g i g

n

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX


Nov 2013 Methods 39

0

[123]0

0 0

0




0 approaches no ba

D D

D

0

0

0

rrowing from


Let assume


D

L D

0 0 0 0 0

0 0




L D

p D L D p p

p D L D





BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX


Nov 2013 Methods 40

0

0 0

22

0 0 2 2




1 1( | ) exp (

2

n

y n

n

p z y y

0 0

0 0

0

20

1

21 0 1 1 2

02 21 10

21 0 1 1

21 1

0 0 0

0

)

( )1exp ( ) exp

2 2

( )exp

2

( )exp

i

i

i g

z g


z

p no no no p no

p

n y ny

s s

n y n

s s

n y

s

0

2 10 2

2 20

1 10 0

1exp( )

2

(1 )

p

a b

n

s


BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX


Nov 2013 Methods 41

0

0

1 2 20 0 0 1 1 12

0 00 2 20 1

0 1


( ) ( )(1 ) exp

2

( ) exp

2

aop yes yes p yesb

no no

y n y n

s s

y

0 0 0

0 0 0 0

21

21

0 0 1 1 1 1

2 2 20 11

00 1 0 1

2 2 2 2 2 20 1 0 1

( ) ( )( )

1~

p no


i

p p p p

n

s

y n y n y ny z

s sN

n n n nn n

s s s s

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX


Nov 2013 Methods 42

0

0 0

0

0 1 1 1 1

2 21

1 1 1 1 1 1

2 2 2 21 1


( )( )

1~

(

~

i i

yes p yesi g

yesi i

p yes p yesi g i g

no

y zy n

sN

z zn n

s s

y

N

0

0 0

0

0 1 1 1 2

2 21

1 1 1 2 1 2

2 2 2 21 1

2 20 0

1 1 1 22

23

)( )

1

( ) ( )

~

i i

no p noi g

i i

p no p noi g i g

i i yes i i no

i g i g

n

zy n

s

z zn n

s s

y z y z

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Model Selection

Nov 2013 Methods 43



[1]





0 0

0 0


=2 ( ) since ( )

ˆˆ =2 ( ) ( )

ˆˆ 2 ( ) ( )

d

d

DIC p D

D D p D D

D D


θ θ



BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Model Selection

Nov 2013 Methods 44

0

20

0 021

2

0


ˆ



0 0ˆˆ2 ( ) ( )

i i

i

y zD E

DIC D D

20

0 21

ation




ˆ

i

i

i iz i

i

z latent

y zD E z

2

0





BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

MCMC Gibbs Sampling

Nov 2013 Methods 45








( 1)

i i

i i

u

p zu

p z

tep 1

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Simulation Set-Up


Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt ~0 170

4 10 gt 05 gt ~0 72

5 10 gt 05 gt ~0 468

1d 3d2d

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Simulation Set-Up



BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Simulation Set-Up


1 2 3



No missing data



k y y y

l l

the endpoints

20 0 0

21 0 1 1

2

2 20 0 1


( ) ~ ( )

( ) ( ) ( ) ~ ( )

~ ( ) 123 1 20


10 10

k k

k k

k k

k k k

k l N Y s

k l k l k l N Y s

IG b k l

Y s s

Scenario N

1 05 = 05 = 05 170

2 08 gt 05 gt 03 170

3 10 gt 05 gt 0 170

4 10 gt 05 gt 0 72

5 10 gt 05 gt 0 468

2d 3d1d

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Simulation Set-Up




Initi

N

20

0




th

terations



duce correlations




Empirical pr





BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Simulation Results



BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Simulation Results



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

MDD Trial


Primary Time Point

Week 4 or Week 6

Primary Endpoint

HRSD-17 or PaRTS-D

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

MDD Trial Results


BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

MDD Trial Results


BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX



4 6

Decision Rule 1


( ( ) ( ) | )

Decision Rule 2


Wk WkP d H d H

Y

4 4 4

6 6 6

4

2 204 4 0 0

14 4


( ) ( ) ( )

( ) ( ) ( )


( ) ~ ( 15 7 )

( ) ~

Wk Wk Wk

Wk Wk Wk

Wk

Wk

Wk

d H d H d H

d H d H d H

H

H N Y s

H

2 21 1( 12 7 )N Y s

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX






for HRSD-17

Week 4 Week 6

EM 00 1000

Bayesian 477 523

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX




BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

















BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX






The Bayesian










BASS XX

Discussion


THANK YOU

QUESTIONS

BASS XX

Discussion


THANK YOU

QUESTIONS

BLINDED EVALUATIONS OF EFFECT SIZES IN CLINICAL TRIALS ... 2013 Turkoz.pdf · endpoints in addition...

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Transcript of BLINDED EVALUATIONS OF EFFECT SIZES IN CLINICAL TRIALS ... 2013 Turkoz.pdf · endpoints in addition...