Clinical Trial Simulation P3_Optimizing... · would like the modeling & simulation work conducted...

Clinical Trial SimulationSociety for Clinical Trials Workshop

Seth Berry, PharmDRussell Reeve, PhD

May 18th, 2014

Copyright © 2013 Quintiles

Outline

• Models> Your simulations are only as good as the data and models going into the simulation

• Simulations> Trial Design

- Fixed vs. Adaptive Designs> Simulated Patients

- Virtual Subjects vs Re-samplingVirtual Subjects vs. Re sampling- Multivariate Distribution Sampling- Disease Progression Models

> Inclusion / Exclusion Criteria> Drug Model> Drug Model

- Dose-Response- PK-PD (1-CMT)

> Study ConductC li- Compliance

- Sampling> Study Statistical Analysis> Replicates for Scenario / Sensitivity Testing

2

> Controlled vs. Un-controlled Variables (Tamaguchi Design)> Maximizing Probability of Success (ie, Power), Efficiencies, Utility Indices, and Minimizing the

Type 1 Error RateCopyright 2014 - Quintiles12 May 2014

Motivation for Trial Simulation

• Need to design a trialg• Standard methods are inadequate

> Consider the usual back of the envelope calculation N = 2(zβ − z1−α/2)2Δ2/σ2.

> Do we know Δ? σ?- Regional treatment effects?

> What about dropouts? Missing observations? Effects of imputation?p g p> What distribution of responses? AEs?> Effect of inclusion/exclusion criteria?> Timing of observations?

3Copyright 2014 - Quintiles12 May 2014

Example: Anakinra in RA

Anakinra Model

0.5

0.6

Treatment effect varies

0.3

0.4

AC

R20

with time.

Note that placebo

0.1

0.2

Note that placebo response drops back to baseline gradually beyond about week 15

10 20 30 40 50

Time (weeks)

beyond about week 15.

4


Other factors to be considered

• Placebo effect varies with the number of treatmentParticular true in CNS but also true in other areas• Particular true in CNS, but also true in other areas> For example, RA

Plot of Predictors for E0 and Emax

1

max

m

m

mm

m

m0

EmaxE0

-10

Pre

dict

or fo

r E0

or E

m

mm mm

0

0

0

00

0 00

0

1 0 1 5 2 0 2 5 3 0 3 5 4 0

-2

5

1.0 1.5 2.0 2.5 3.0 3.5 4.0

Number of Treatment Arms

Copyright 2014 - Quintiles12 May 2014

Fixed vs Adaptive Designs


Fixed vs Adaptive

• Similarities> Both type of designs benefit from trial simulation> Patient recruitment Treatment Randomization Drug Effect (PK/PD) Trial level statistical

analysis Adjusting trial design parameters to optimize• Differences

> Cannot get away with back-of-envelope calculations in adaptive trials> Interim analyses create more complex statistical issuesy p

- Recruitment rate, center (or nation or region) by treatment interaction- More operating characteristics to worry about

» Fixed: Power function, Type I error rate (power under null)» Adaptive: Power function Type I error rate expected sample size probability of success» Adaptive: Power function, Type I error rate, expected sample size, probability of success

• Our Focus Today> Due to limited amount of time, we will discuss simulations of fixed designs today> Can talk with us after the class about adaptive design simulations


Modeling & SimulationS ft

Software Use Platform

SAS 9.2 Statistical Programming and T diti l St ti ti l A l

Virtual Machine

Software

Traditional Statistical Analyses, Trial Simulations

R 3.0.3 and S+ 6.2 Advanced Statistical Analyses, Trial Simulations, Graphical Analyses

Virtual Machine, HPC Cloud

Analyses

NONMEM 6.2 Population PK-PD Modeling and Simulation

Internal Web-Based Server Cluster

Pharsight Trial Simulator Clinical Trial Simulation Internal Server

Phoenix WinNonlin Non-compartmental PK Analysis Local Desktops

OpenBUGS Bayesian Analysis Virtual Machine

WinBUGS – PKBUGS PK Bayesian Analysis Virtual Machine

WinPOPT D-Optimal Sampling Design Virtual Machine

ADDPLAN and FACTS Adaptive Trial Design Virtual Machine

8

ADDPLAN and FACTS Adaptive Trial Design Virtual Machine


Simulation ToolsE h h th i t th

• Pharsight’s Phoenix Trial Designer (Trial Simulator)> Graphical User Interface makes programming a simulation easy and explaining to

Each has their own strength

> Graphical User Interface makes programming a simulation easy, and explaining to others straightforward

> Can create quite complicated designs, and features the full trial behavior (recruitment, compliance, input/output, data analysis, etc.)

> Expensive and needs a good computing environment- Not particularly good on virtual machines

> Don’t save too much of the intermediate data, as it is stored in Microsoft’s Access> Sometimes difficult to analyze properly scenarios unless you export the data> Sometimes difficult to analyze properly scenarios unless you export the data

• SAS> Preferred language of statisticians> Data step fairly powerful for simulation, with many distributions built-inData step fairly powerful for simulation, with many distributions built in> Requires a modular building of code, that is often counterintuitive and confusing> For large simulations, can be difficult to explain to others, and to document and

debug even for experienced statisticians

9

> SAS sells a version that works in their parallelized cloud (very fast)


Simulation ToolsE h h it t th

• R or S-PLUS> Growing in popularity for simulation projects

Each has its own strengths

> Growing in popularity for simulation projects> Functions are very convenient for plugging in modules

- Might have input/output function, another for compliance model, etc.> Very flexible, and can build the simulation from the inside/outy ,> All of the new statistics students know this language> Revolution Analytics has a version that works in a parallel computing environment

(very fast, but with limited parallelization built into functions)B t i l ti t ll li ith t ll f ti b i- But simulations are easy to parallelize even without all functions being parallelized

• FACTS> Stands for Fixed and Adaptive Clinical Trial SimulationStands for Fixed and Adaptive Clinical Trial Simulation> Very good for a wide variety of pre-canned adaptive designs> Only simulates the decision algorithm in conjunction with the recruitment rate

- Recruitment much more an issue in adaptive designs than fixed

10

> Pretty easy to use, even if the output displays are a bit confusing


High Performance ComputingT d TiTurnaround Time

“If faced with a pending development decision on Friday, would like the modeling & simulation work conducted overwould like the modeling & simulation work conducted over

the weekend and the results available on Monday morning.” - Dennis Gillings, Quintiles CEO

• Scalable Cloud Computational Resourceso Case Study using R

- Revolution Analytics / Microsoft Azure Cloud Computing

- Implemented up to 1000 computational cores simultaneously

- Reduced modeling & simulation computational time from 2 months down to approximately 1 hour.

- Linear relationship between number of cores and timeLinear relationship between number of cores and time savings

- Successful deployed on critical trial simulation for client for design of Bayesian trial


Simulation Planning


Begin with the End in MindO i f t i l i l ti

• Assess effect of study parameters on operating characteristicsCalculate operating characteristics (power etc)

Overview of trial simulation process

• Calculate operating characteristics (power, etc)• Statistically analyze endpoints of interest• What endpoints are we collecting, and when?

Ho are endpoints affected b dosing (PK/PD relationship)• How are endpoints affected by dosing (PK/PD relationship)> What about compliance? Will need a drop out model.

• What treatment arms?> Any modification to those treatment arms (e g sample size change> Any modification to those treatment arms (e.g., sample size change,

additions/subtractions, randomization changes)• What population are drawing from?

F l d i b ild h f thFor complex designs, build each of these components modularly so that you can modify later.

B ild l th i d f

13

Build only those pieces you need for your question.


Overview of Plan

> Dose-response (exposure, etc.)> Measurements

- Efficacy, safety> Population of interest

S b t b d i t- Subset based on covariates> Timing of dosing/interventions, measurements> Drop outs, other noncompliance> Data analysis modelData analysis model> Variations in design parameters

- Effect of changing timing, dosing, sample size, treatment effect size, etc.


Dose-Response (exposure)• Model linking dose to clinical

0.5

Drug Effect vs Exposure for Different Population Markers

gendpoint> Efficacy> SafetyOf

0 5

0

rom

bas

elin

e

No Poly

Obs 369

• Often use the Hill model> Y = a + d/(K + (x/c)b)

• If PK models available, then can use exposure parameters

-1

-0.5al

load

Cha

nge

fr Obs 369

Obs 370

Obs 369, 370

Pred None

Pred 369

can use exposure parameters> AUC, Cmax> If you have PK model, can use

that to generate drug

-2

-1.5

0 20 40 60 80

log

Vira Pred 370

Pred 369, 370concentrations

See http://aquaticpath.umd.edu/appliedtox/module1.html

15

0 20 40 60 80Drug Concentrationfor more information


Measurements

• Measurements are outcomes that are measured• In TS, these are scheduled

> Dialog box for that> Can be missed at random> Lot of flexibility on probability of miss or hazard

function• In SAS and R, can program in missingness

> Good way to assess impact on MAR or MNAR> Good way to assess impact on MAR or MNAR> Create model for AE that yield drop outs

• Measurements can have measurement error• Can simulate measurements but ignore for laterCan simulate measurements but ignore for later

analysis if changes are needed

16


Population

• For a given trial/indication, there are many relevant covariates that could g yinfluence treatment outcome/disease progression.

• Want to specify distribution models for covariates that approximate real world patients.

• If you have a large sampling of patients, can sample with replacement from the list, OR create distributions and generate purely in silico participants


Randomization and Sample Size

• Randomization> What if randomization is not balanced?

- Dunnett’s: Optimal if ratio is close to k1/2 : 1 : 1: … : 1> Can investigate effect of treatment x center interaction (especially for adaptive

where we have staggered starts and recruitment rates across centers)where we have staggered starts and recruitment rates across centers)> Effect of multiple populations

- Already on DMARD vs DMART-naïve• Sample SizeSample Size

> Can investigate range of sample size to characterize power function, other performance metrics of the trial


Timing (Protocol scheduled times)

• Patients are scheduled a series of treatment. For example, taking drug once p g gdaily for 2 months.

• Patients are scheduled for multiple follow-ups so that treatment effect be observed.

• Want to set up trial protocol: treatment and observation schedules.


Noncompliance• Trial protocol could be violated: missing dose, missing follow-up, missing p g g p g

patients, etc.• Want to set up models for noncompliance

• Easiest: P{ dropping out on visit t } = p• What is effect if dropouts are dose-dependent?

> P{ dropping out on visit t } = p0 + p1 I{ treatment = active }


Data Analysis Model• Simulated data is only useful with proper analysis.y p p y• Want to specify analysis method (based on protocol), for each replicate or

each scenario of the simulation.

• Good place to investigate:> Effects of adding covariates to the analysis (may not be as useful in categorical as

you would hope)> Missing data strategies (i e LOCF vs MMR etc )> Missing data strategies (i.e., LOCF vs MMR, etc.)> Multiple comparison strategies


Simulation Design• The point of simulation is to explore different scenarios.p p• Want to specify many scenarios based on design parameters (sample size,

treatment effect size, variability of effect size, etc) and their combinations.

• Central Composite Design for optimizing responses (eg, Power)


Modeling & SimulationBasic Concepts


Defining Modeling and Simulation

Modeling: “Looking backward”D l th ti l d l t d ib d l i b ti• Develop mathematical models to describe and explain observations

Modeling

Simulation: “Looking forward” • Using a model to predict outcomes based on “what if” assumptionsg p p

Simulation

F Bi h M&S i i di d t t d l d i l t l ti hi

24

For Biopharma: M&S is using diverse data sources to model and simulate relationships between drug exposure, response, and patient characteristics


The Learn and Confirm CycleA It ti A hAn Iterative Approach

Model Answer

DesignDataQuestion es g

Execute

ataQuestion

Execute

25Derived from Sheiner LB, Clin Pharmacol Therap 1997, 61:275-291

The Learn and Confirm ParadigmA li d t th D D l t PApplied to the Drug Development Process

Phase I Phase II Phase III

Model Model Model

Design

E

Data Design

Execute

Data Design

Execute

Data

Execute Execute Execute


The Learn and Confirm ParadigmN L Ph I II d IIINo Longer Phase I, II, and III

Learning Confirm

Model ModelModel

Design

E

Data Design

Execute

DataDesign

Execute

Data

Execute ExecuteExecute


PK-PD Principles


The Causal ChainF D t Cli i l E d i t

• Represents the basic amount of drug being administered to a patientOft t ti i t th t d t h ti

From Dose to Clinical Endpoint

Dose• Often a static assignment that does not change over time

• The amount of drug that is observed in the body

Concentration

g y• Varies within a subject over time due to the effect of absorption, distribution, metabolism, and

elimination (ADME) of the drug• Additionally can vary between subjects due to differences in the ADME

Response

• In basic clinical pharmacology receptor theory, the effect the drug has on the body.• Varies within a subject over time due to the concentration of drug available to elucidate an effect• Additionally can vary between subjects due to differences in the receptors / genetics• Is not always quantifiable

Clinical

• The observed patient outcome or assessment.• Can vary both within and between patients over time.

29

Endpoint


Dose vs Concentration ResponseD i d A l i

• Dose-Response

Design and Analysis

DX

D1

D2

O (Pl b )

R X

O (Placebo)D1 D2O

• Concentration-Response

C1X

C2

O (Placebo)

R X

30

( )C1 C2O


Dose vs Concentration ResponseI li ti f L Ph ki ti V i bilit

• Low PK Variability = No Confounding & Little Overlap

Implications of Low Pharmacokinetic Variability

R

C D D

R

D

D D

C

D

D1 D2 D3

D1 D2 D3

R

31

C


Dose vs Concentration ResponseI li ti f Hi h Ph ki ti V i bilit

• High PK Variability = Confounding Overlap

Implications of High Pharmacokinetic Variability

RR

D2 D3D1C D2 D3D1

D1 D2 D3

R

32

C


Dose vs Concentration ResponseThe Confounding Effect of High Correlation Between Pharmacokinetics

• Dose-Response

The Confounding Effect of High Correlation Between Pharmacokinetics and Response

DD1

D2

O (Pl b )

R

• Concentration-Response> C t ti R P t t A i t Di d Ph ki ti

O (Placebo)C

> Concentration-Response Protects Against Disease and Pharmacokinetic Confounders That Cause the Down Bias

C1

C2

O (Placebo)

R

33

( )C


Case StudyR d i d D C t ti C t ll d Cli i l T i lRandomized Dose vs. Concentration Controlled Clinical Trials

34Source: Reeve, R and M Hale (1994) Results and efficiency of Bayesian dose adjustment in a clinical trial with a binary endpoint. Proceedings of the Biopharmaceutical Section of the ASA 1994

ExposureT i lTerminology

Poor Metric Best Metric

Dose Cmax or AUC Concentration

Due to the potential confounding that causes the down bias


Pharmacokinetic ModelsEstimating Exposure ParametersEstimating Exposure Parameters

• Well-Stirred Pharmacokinetics Model • Physiologically Based Pharmacokinetics (PBPK)(PBPK)

Lungs

Right Heart

Left Heart

Peripheral Lungs

Upper Body

Peripheral Compartment

LiverIntestine

Spleen

Central C t t

Lower Body

KidneysCompartment


Variability ModelsE ti ti th V i bilitEstimating the Variability

O erall VariabilitOverall Variability

Between Subject Variability Within Subject Variability(Inter Subject Variability) (Intra Subject Variability)

True WSV Residual Error(Measurement Error)

37

(Measurement Error)


Population PK ModelsN li Mi d Eff t M d liNonlinear Mixed Effects Modeling

• Create Basic Structural Model1 2 3 C t t> 1-, 2-, 3-Compartment

> Route of Administration (Oral, IV)> Estimate PK Parameters 500

600

- Absorption Rate Constant- Volume of Distribution- Clearance

300

400

ncen

tratio

n (m

g/L)

• Create Error Model> Between Subject Variability

- Exponential Error Model100

200Con

Exponential Error Model> Within Subject Variability

- Proportional Error ModelAdditive Error Model

0 6 12 18 24 30 36 42 48Time After Dose (hr)

0

38

- Additive Error Model

Source: Example developed from analysis of a large, proprietary, de-identified illustrative data set.

Population PK ModelsN li Mi d Eff t M d li

> Evaluate Covariate Relationships40

Nonlinear Mixed Effects Modeling

- Weight Adjusted Dosing- Renal / Hepatic Impairment Adjustment- Concomitant Medication Drug-Drug

Interaction Signal10

20

30

Cle

aran

ce (L

/hr)

Interaction Signal

> Variability Estimates in Patients

- ExposureR

40 60 80 100 120 140Weight (kg)

0

10

- Response

> Justify Dose / Labeling30

40

(L/h

r)

0

10

20

Cle

aran

ce

39

0 50 100 150 200Creatinine Clearance (mL/min)


Population PK-PD ModelsN li Mi d Eff t M d liNonlinear Mixed Effects Modeling

• Create Basic Structural ModelLi P E Si id l 0 9

1.0600

Pharmacokinetics Pharmacodynamics

> Linear, Power, Emax, SigmoidalEmax, Hysteresis

> Estimate PK ParametersB li

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Effe

ct

100

200

300

400

500

Con

cent

ratio

n (m

g/L)

- Baseline- Maximum Effect (Emax)- Effective Concentration (EC50)

10-1.0 100.0 101.0 102.02 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 89

Concentration (mg/L)

0.0

0.1


0

Ph ki ti Ph d i• Create Error Model> Between Subject Variability

- Proportional Error 0.7

0.8

0.9

1.0

Pharmacokinetics - Pharmacodynamics

p- Additive Error

> Within Subject Variability- Proportional Error Model 0.2

0.3

0.4

0.5

0.6Ef

fect

40

Proportional Error Model- Additive Error Model


0.0

0.1


Disease Progression Models

• Basic Disease Progression ModelAdditive Symptomatic Model

> Alzheimer’s> Parkinson’s (UPDRS)

A is

Additive Symptomaticwith Tolerance

> Anemia> Diabetes> Thromboembolic Disorders

Partially

Fully Protective

ase

Sta

tus

• Time-To-Event Models

> Myocardial Infarction> Stroke

Partially Protective

Dis

ea

Natural Progression Stroke

TimeStartTreatment


Population PK-PD ModelsM d l V lid ti

• Re-Sampling Techniques

Model Validation

• Internal • Inputs

Stability Predictability Sensitivity

Re Sampling Techniques

> Bootstrap: Random

Sampling with

Internal

> Visual & Numerical

Predictive Checks

Inputs

> Vary Covariates

> Vary Observations

Replacement

> Jack-Knife: N-1

> Condition Number

> Posterior Predictive

Checks

• External

> Vary Independent

Variable

• Exclusions

> Data Splitting

> Comparison with

Exclusions

> Observations

> SubjectsSeparate Study / Data


Protocol Deviations and Execution Models


Protocol Deviations and Execution ModelsO i

• The evaluation of variation in the conduct of clinical study designs to identify the strengths and weaknesses of a specific design

Overview

the strengths and weaknesses of a specific design• Examples:

> Adherence to Dosing Regimen

- Wrong or Extra Doses

- Improper Timing of Doses / Dosing Holiday

> Dropout ModelsDropout Models

- Time Patient Discontinues Study Procedures

- Time to Switch to Different Medication (eg, Rescue Medication)


Adherence ModelingC ll ti Adh D tCollecting Adherence Data

• John Urquhart’s Rule of 6’sq

• Pill Bottle Caps or Blister Packs

• Uses microprocessor in cap to collect date and time data on when doses aredate and time data on when doses are taken

• LCD Readout or Wireless Scanner

• Drawbacks• Drawbacks

> Only solid dosage forms

> Cost : $274/patient for 6 months

> Limited acceptance

> Multiple dose removal and setting dose aside

45

• Eg MEMSCap™ Medication Even Monitoring System by Aardex


Adherence ModelingE ti ti Adh M k Mi d Eff t R i M d lEstimating Adherence – Markov Mixed Effects Regression Model

46Source: Girard, et. al. “A Markov Mixed Effect Regression Model for Drug Compliance”, Statistics in Medicine.. Vol 17, pgs 2313-2333. (1998)

Adherence ModelingP di ti Adh M k Mi d Eff t R i M d lPredicting Adherence – Markov Mixed Effects Regression Model

47Source: Girard, et. al. “A Markov Mixed Effect Regression Model for Drug Compliance”, Statistics in Medicine.. Vol 17, pgs 2313-2333. (1998)

Adherence ModelingI t EImpact on Exposures

• Adherence holidays can drop concentration levels below a threshold for therapeutic efficacyefficacy

• Non-compliance with administration (eg, double dosing) can also raise dos g) ca a so a seconcentration levels above toxicity thresholds, leading to potential adverse events

48Source: Comté, et. al. “Estimation of the comparative therapeutic superiority of QD and BID dosing regimens, based upon integrated analysis of dosing history and pharmacokinetics”, Journal of Pharmacokinetics and Pharmacodynamics. Vol 34, pgs 549-558. (2007)

Dropout ModelingH d M d lHazard Models

• Assuming the time to a specified discontinuation event u follows a distribution function F, then the probability of the event occurring is:, p y g

where the hazard λ is defined as the probability the event happens given it has not h d t ifi d ti t d i th i d f th t d T

⋅⋅= ⋅−T u dueufp0

)()( λθ

happened at a specified time t during the period of the study T

Placebo Disease

Drug PK Biomarker

Clinical Outcome

DropoutAdherence Therapy PK Biomarker

Adverse Event

DropoutAdherence

49Source: Kimko & Duffull. Simulation for Designing Clinical Trials.: A Pharmacokinetic-Pharmacodynamic Modeling Perspective. Marcel Dekker, New York, NY. 2003

Placebo

Additional Slides


Use in Early Drug Development

• Biomarkers/Surrogate Endpoints/Clinical Markers

> Early Start on Proof of Concepty p> Early Read on Establishing Variability in PK / PD> Helpful for Selection of Doses for Phase 2

(Dose Ranging Studies)> ExamplesExamples

- CD4 counts / viral load- Serum Glucose- CT / MRI / PET- Genomics -> CYP2D6 Metabolizers- QTc- Blood Pressure

INR- INR- Cure / No Cure


Additional ResourcesB kBooks


Simulation


Clinical Trial Simulation

• Clinical Trial Simulation> Protocol Design> Protocol Deviation

- Adherence / Compliance- Drop-out

> Covariate Distribution / CorrelationD / Ph ki ti /> Dose / Pharmacokinetic /Pharmacodynamic Model

> Data Analysis Plan> Results> Results> Simulation Scenarios

54Figure courteous of Pharsight Trial Simulator

Trial Design


Trial DesignPl thi i Ad

• Dosing schedulesTiming of endpoints

Plan this in Advance

• Timing of endpoints• Parallel, crossover, extension phase?


Simulated Patients


Covariate Distribution Model

• Specify subject covariates distributions.p y j> Trial simulator set up covariates before entering the subject loop.> Population covariates cannot be assigned values during the simulation.

• Discrete and continuous distributions.> Tip: Try to use nominal values for discrete distributions. Example, use male and

female for Race instead of 0 and 1.• Covariates can be used as study inclusion and exclusion criteria during

enrollment and to stratify subjects during assignment to treatment groupsenrollment, and to stratify subjects during assignment to treatment groups. • Covariate distributions may vary across a number of sub-populations, the

covariate distribution model can model sub-population and center effects. • Variability in the covariate distribution model can be enabled or disabledVariability in the covariate distribution model can be enabled or disabled

separately from that in the drug model.


Simulated PatientsVi t l S bj t R li

• Virtual subjects much easier to create> Just need distribution

Virtual Subjects vs. Re-sampling

Brainard and Burmaster (1992) Risk Analysis

For the U.S. population, we fit bivariate distributions > Just need distribution> Keep in mind that many covariates will be

correlated- Difficult to maintain direct correlation

p pto estimated numbers of men and women aged 18-74 years in cells representing 1 in. intervals in height and 10 lb intervals in weight. For each sex separately, the marginal histogram of height is well fit by a normal distribution. For men and women, respectively, the

i l hi t f i ht i ll fit damong covariates> Distribution of age and weight

marginal histogram of weight is well fit and satisfactorily fit by a lognormal distribution. For men, the bivariate histogram is satisfactorily fit by a normal distribution between the height and the natural logarithm of weight. For women, the bivariatehistogram is satisfactorily fit by two superposed

1 0 0

histogram is satisfactorily fit by two superposed normal distributions between the height and the natural logarithm of weight. The resulting distributions are suitable for use in public health risk assessments

http://www.ncbi.nlm.nih.gov/pubmed/15023742 0

4 0

6 0

8 0

Wei

ght (

kg)

• Re-sampling from an existing database

0 1 0 2 0 3 0 4 0 5 0 6 0A g e (y r)

0

2 0

60

more realistic> Based on actual patients


Simulated PatientsDi P i M d l

• Example

Disease Progression Models

• P{ TS | t } = a + b[1−exp(−kt)]

Correlation among time points• Correlation among time points in the data, despite its binary-ness, though it typically does not affect results

• Useful when you may need to y yinvolve many time points in your analysis, or if you are investigating time points to use as the primary

61

as the primary


Simulated PatientsDi P i M d lDisease Progression Models

Usef l to get realistic ariation• Useful to get realistic variation among molecules

• Expected treatment effects can be estimatedestimated

• Prior for model parameters can be constructed


Inclusion / Exclusion Criteria


Inclusion/Exclusion

• Apply IE criteria against simulated patientspp y g p> Chiefly for covariates that affect response

• Could have large effect on study performance• Match up to you TPP


The Drug Model(s)


Drug Model (Input/Output)

• Drug model is the most important part of the trial design.g p p g• Scheduled events: Formulations, Responses, Actions and Events


Pharmacokinetic – Pharmacodynamic ModelI t ti I t Cli i l T i l Si l tiIntegration Into Clinical Trial Simulation

• Inputs to Dose-PK-PD Model> Protocol Deviation> Protocol Deviation

- Adherence / Compliance- Drop-out

> Model Parameters Adjusted jBased Upon Virtual Patient Covariates

• Outputs from Dose-PK-PD Model> Exposures for Scenario Testing

of Sampling Design> Response> Response

- Efficacy- Safety

67Figure courteous of Pharsight Trial Simulator

Drug ModelD R M d l

• Two models that fit most situations> Linear

Dose-Response Model

> Linear> Hill (alias Emax, logistic, Michaelis-Menten)

Two forms of same equation:R = E0 + Emax xγ/(Kγ + xγ) + e

R E E /{ 1 [ b(l ) ] }

69

Thompson et al (2013)

R = E0 + Emax/{ 1 + exp[ −b(log x − c) ] }


Drug ModelPh ki ti Ph d i M d l

• Think in steps> Dose PK PD

Pharmacokinetic – Pharmacodynamic Models

> Dose PK PD

• C(t) = (D/V)[ exp(−(CL/V)t) − exp(-kat) ] PK ModelInput: Dose, tp ,Output: C(t)

• Instant effect> R = E0 + Emax C(t)γ/(K γ + C(t)γ )> QT prolongation is often modeled this wayQ p g y

• Delayed effect> R = E0 + Emax C(t)γ/(K γ + C(t − tdelay)γ )

PD ModelInput: C(t), t

Output: Response

70

0 max ( ) ( γ ( delay) )


Models of Study Conduct


Models of Study ConductT diti l S i l (D O ti l) S PK S li Wi dTraditional Serial vs. (D-Optimal) Sparse PK Sampling Windows

Traditional Serial Sampling D-Optimal Design Sparse Sampling Windows600

600

300

400

500

atio

n (m

g/L)

300

400

500

ntra

tion

(mg/

L)

100

200Con

cent

ra

0

100

200Con

cen

• Typical sampling scheme for Phase 1 Studies• Intensive, rigid sampling difficult for patients

• Sparse sampling more common in Phase 2/3• Limited sampling windows offer flexibility for

0 2 4 6 8 10 12 14 16 18 20 22 24Time After Dose (hr)

0 0 2 4 6 8 10 12 14 16 18 20 22 24Time After Dose (hr)

• Good for descriptive statistics, not as informative for modeling

clinic and patients, but can also be too flexible• More informative for modeling• Need a priori information (ie, the PK model)• Reduce cost associated with redundant sampling• Optimizing sampling can help strengthen study

72

Optimizing sampling can help strengthen study outcomes and can be evaluated by looking at various sampling scenarios


Models of Study ConductAdh ( k C li )

• Simple Adherence Models (1-coin vs. 2-coin)> 1-coin model: The likelihood a patient will take a

Adherence (aka, Compliance)

medication on any given day> 2-coin model: The likelihood a patient will take a

medication today, depending if they took the previously prescribed medication.

> n coin model: Expandable out to n doses> n-coin model: Expandable out to n doses• Advanced Adherence Models

> Correlation Between Adherence and Dose Frequency- High rates for QD dosing- Lower rates for BID, TID, QID

> Correlation Between Adherence and Dose Timing- Different adherence rates for morning dose

vs lunch vs evening> Correlation Between Adherence and Duration of

Treatment- Decreases out over time for chronic therapies- Decrease of Efficacy (Tolerance) or Development of

73

Adverse Events> Feedback Loop dependent upon Efficacy and Safety

Endpoints


Study Statistical Analysis


Statistical AnalysisNow is the time to plan for effects of analysis on study operating

• Build simple statistical analyses into your simulation to begin wthFactors you may wish to investigate:

Now is the time to plan for effects of analysis on study operating characteristics

• Factors you may wish to investigate:> Covariate adjustment: Help or hurt?> Effect of categorization of endpoint> Effect of different time pointsEffect of different time points

- Azheimer’s: Treatment effect broadens over time» Interplay between length of study and N

> Treatment of missing data- LOCF, MMRM, etc.

> Endpoint summarization- Slope, AUEC, change from baseline

> Analysis populations> Analysis populations- ITT: Variability in mean difference due to imputation method and dropouts- PP: Variability in sample size due to dropouts

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Scenario & Sensitivity Testing


Scenario & Sensitivity TestingObj ti d M th d

• Objective: Investigate the effects of design parameters on design performance metrics

Objectives and Method

parameters on design performance metrics• Looking for: Design with adequate power,

appropriate Type I error rate, adequate estimation precision, and robust against gfactors we cannot control> Cannot control ED50, but there may be uncertainty

in it, so want trial that gets “correct” decision most of the time regardless of ED50 valueof the time regardless of ED50 value

• Design parameters: Vary by design• Replicates: Repeatedly run trial to get

distribution> Common to see 10,000 replicates

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Scenario & Sensitivity TestingC t ll d U t ll d V i bl (T hi D i )

• Example:> Dose adaptive design to estimate best dose for

Controlled vs. Un-controlled Variables (Tamaguchi Design)

Factorial Design of> Dose adaptive design to estimate best dose for Phase III in Alzheimer’s

> What can we vary?- Sample size (N), time to endpoint, number of

N Time Num Doses IA Point Trt Effect300 6 mo 2 50% Vary this

Factorial Design of Simulation

doses, point of interim analysis- Have estimate of effect size with uncertainty

» Based on last study, our prior on treatment effect is Normal(3 2 12)

500 6 mo 2 50%300 12 mo 2 50%500 12 mo 2 50%300 6 mo 4 50%500 6 mo 4 50%300 12 4 50%effect is Normal(3, 2.1 )

• Two approaches to handling treatment effect> Tamaguchi design

300 12 mo 4 50%500 12 mo 4 50%300 6 mo 2 70%500 6 mo 2 70%300 12 mo 2 70%500 12 mo 2 70%

g g- Another factor in the design, to be controlled

> Bayesian approach- Random variable, and to get power we average

conditional power across all values of treatment

500 12 mo 2 70%300 6 mo 4 70%500 6 mo 4 70%300 12 mo 4 70%500 12 mo 4 70%

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conditional power across all values of treatment effect

Scenario & Sensitivity TestingM i i i P b bilit f S (i P ) t

Design 1 Design 2

Overall Prob Pick Arms Overall Prob Pick Arms

Maximizing Probability of Success (ie, Power), etc

Param 1 Param 2 Power Best Dose Dropped N / arm Power Best Dose Dropped N / arm

djus

ted

alph

a 0.

05

0 0 11.3% 0.887 0 xx 0.126 0.874 3.521 xx1 78.4% 0.586 0 xx 0.605 0.47 2.259 xx2 100.0% 0.873 0 xx 0.996 0.98 1.444 xxFactorial design for

parameters including 2Many types of design characteristics can be

Bonf

erro

ni a = 0 1 0 14.3% 0.857 0 xx 0.139 0.861 3.584 xx

1 100.0% 0.135 0 xx 1 1 0.924 xx2 100.0% 0.068 0 xx 1 1 0.634 xx

n = 1000 trials

parameters, including 2 design options

characteristics can be investigated

Design 1 Design 2

Volume DoseOverall Power

Prob Pick Best Dose

Arms Dropped N / arm

Overall Power

Prob Pick Best Dose

Arms Dropped N / Arm

5 0 0 13 8% 86 2% 0 xx 0 213 0 787 4 91 xx

Stat analysis included in

simulation design

uste

d al

pha

= 0.

05 0 0 13.8% 86.2% 0 xx 0.213 0.787 4.91 xx1 76.4% 55.6% 0 xx 0.812 0.628 3.641 xx2 100.0% 86.5% 0 xx 1 0.987 2.599 xx

1 0 15.3% 84.7% 0 xx 0.228 0.772 4.933 xx1 100 0% 17 2% 0 xx 1 1 1 623 xx

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Una

dju 1 100.0% 17.2% 0 xx 1 1 1.623 xx

2 100.0% 7.1% 0 xx 1 1 1.032 xx

Work through Specific Examples


Outcome Optimization


Case StudyCli i l T i l Si l ti O t O ti i ti

Challenge Solution ResultsChallenge Solution ResultsChallenge Solution ResultsChallenge Solution Results

• Methodology: • No weight-based PTZ dose

Clinical Trial Simulation - Outcome Optimization

• Background Methodology:> Monte Carlo Simulations using

Pharsight® Trial Simulator™2.2.2

> Using a previously developed PTZ Population PK model with

No weight based PTZ dose adjustments are required in obese population

• Validates the use of extended-infusion regimens in both the

Background> Treatment:

- Piperacillin / Tazobactam (PTZ)

> Problem: PTZ Population PK model, with covariates normal and obese individuals- Obtain Probability of target

attainment (PTA) > MIC for more than 50% of the dosing interval

- Identify if dosing needs to b dj t d i th bbe adjusted in the obese population (including adjustments for CrCL)

- Compare traditional vsextended – infusion dosing regimens

(%)

regimens

82Source: TP Dumitrescu, R Kendrick, H Calvin, and NS Berry. “Using Monte Carlo Simulations to Assess Dosing Regimen Adjustments of Piperacillin/Tazobactam in Obese Patients with Varying Renal Functions.” Journal of Pharmacokinetics and Pharmacodynamics. May 2013

Bi i l ithBioequivalence with Sample Size Re-estimationestimation


Basic SetupObj ti d P i K l d

• Generic drug, but want to compare with 2 existing on-market products• Very long half-life (>2 weeks), so will do a parallel design

Objectives and Prior Knowledge

• Toxicity not an issue• Will be comparing AUC and Cmax• Standard statistical analysis

> log AUC and log Cmax modeled independently> If 90% confidence interval for log AUC1/log AUC2 is between 0.8 and 1.25, then

bioequivalent (BE); otherwise, fail to be BE> Comparison must be made to both comparators> Comparison must be made to both comparators

• CV of AUC = 0.3 (based on literature of N=20 patients in a different population)

• No data on Cmax variability but we think smaller than AUCNo data on Cmax variability, but we think smaller than AUC

• Decided to do a sample size re-estimation> But when?

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But when?• Of interest: Type I and Type II error rates• We will program this in SAS

Flow Chart for SimulationWill b d i SASWill be programmed in SAS

SAS code to Simulate log(Cmax)

Simulate log(Cmax)

For ease of programming, create all data, and will drop

data phase1;input CV DOrate InterimPoint;do iter = 1 to &NumIter;

NumDays = &TargetN / &PatientsPerDay;those not used in analysis

Do Interim Analysis

do patient=1 to &MaxN;day = floor((patient-1)/6) + 1;trt = mod(patient-1, 3) + 1;if patient<=&TargetN then PlannedGroup=1;

else PlannedGroup=0;if patient<=&TargetN*InterimPoint then ForInterim=1;Recalculate n using only

first ninterim subjects, and keep n subjects overall

if patient<=&TargetN*InterimPoint then ForInterim=1; else ForInterim=0;

logCmax = normal(0)*CV;if uniform(0) <= DOrate then DO=1; else DO=0;if trt=1 then logCmax = logCmax + 0.05; lastPK = day + &ADAPKtime;

Final Analysis

Calculate confidence intervals, and from that

power

lastPK day &ADAPKtime;output;

end;end;

cards;0.33 0 0.333

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power Etc.


SAS code to calculate new sample size, but first need to calculate the coefficient of variation from the blinded data, so we do not do a fancy mixed model but a simple CV

Simulate log(Cmax)


so we do not do a fancy mixed model, but a simple CV calculation ignoring the treatment effect

those not used in analysis

Do Interim Analysisproc sql;

create table BlindedInterimResults asselect CV DOrate InterimPoint iter N(DO) as NsoFarRecalculate n using only

first ninterim subjects, and keep n subjects overall

select CV, DOrate, InterimPoint, iter, N(DO) as NsoFar, mean(DO) DORateObs, std(logCmax) as CVhat,

max(lastPK)+&PKanalysisTime+&AssayTime as StartAdditionalCohortfrom phase1where ForInterim=1group by CV, ADArate, InterimPoint, iter;

Final Analysis


power

group by CV, ADArate, InterimPoint, iter;

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power


SAS code to calculate new sample size, based on results from the PROC SQL on last slide

Simulate log(Cmax)


data Predicted;set BlindedInterimResults;NumEvaluable = (1-ADARateObs)*&Cohort*&NumCohort/3;if NumEvaluable < 60 then MaxN=10; else MaxN=8;

from the PROC SQL on last slide

those not used in analysis

Do Interim Analysis

if NumEvaluable < 60 then MaxN=10; else MaxN=8;

*** Calculate Sample Size ***;CVpt1 = 0.25; CVpt2 = 0.275; CVpt3 = 0.3;SS1 = 36; SS2 = 43; SS3 = 50;array CVpt {*} CVpt1-CVpt12;

Recalculate n using only first ninterim subjects, and

keep n subjects overall

y p { } p p ;array SS {*} SS1-SS12;

if CVhat <= CVpt1 then SSarm = SS1;else

do i=2 to 12;if CV t{i 1} CVh t CV t{i} th SS SS{i}Final Analysis


power

if CVpt{i-1} < CVhat <= CVpt{i} then SSarm = SS{i};end;

Recruit = SSarm/(1-ADARateObs); ** Per arm sample size **;Recruit = 3*Recruit; ** Sample size total **;Recruit = ceil(max(NsoFar, Recruit)); ** Keep what we already have **;

run;

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power run;


SAS code to Calculate CI and Power: Analyze complete data, and then determine whether BE criteria are met (and in what proportion of in silico trials

Simulate log(Cmax)


ods listing close;ods output Estimates=estimates;proc mixed data=FinalData(where=(DO=0));

by CV ADArate InterimPoint iter;those not used in analysis

Do Interim Analysis

by CV ADArate InterimPoint iter;class trt;model logCmax = trt;estimate 'TrtDiff 1 vs 2' trt 1 -1 0 / cl alpha=0.1;estimate 'TrtDiff 1 vs 3' trt 1 0 -1 / cl alpha=0.1;estimate 'TrtDiff 2 vs 3' trt 0 1 -1 / cl alpha=0.1;

Recalculate n using only first ninterim subjects, and

keep n subjects overall

prun;ods listing;

data CIinLimits;set estimates;if l (0 8) l d l (1 25) th I Li it 1Final Analysis


power

if log(0.8) <= lower and upper <= log(1.25) then InLimits=1;else InLimits=0;

run;

proc sql;select CV ADArate InterimPoint mean(AnyIn) as AnyInRate mean(AllIn) as AllInRate

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power select CV, ADArate, InterimPoint, mean(AnyIn) as AnyInRate, mean(AllIn) as AllInRatefrom TrialResultsgroup by CV, ADArate, InterimPoint;

Dose Ranging Study ith O I t i twith One Interim to

Drop Doses

Dose-Response Model

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Basic SetupObj ti d P i K l d

• New molecular entity entering Phase II in a debilitating, progressive disease with no alternative treatment

Objectives and Prior Knowledge

• We have 4 doses to investigate, plus placebo• Endpoint is continuous, measured at baseline, 3 mo, 6 mo, 9 mo, and 12 mo• Phase I data indicates

> Toxicity> Linear dose-response curve, linear time-response curve

• We want to drop doses as fast as possible in non-efficacious dose groupsPh I i di t t i it> Phase I indicates toxicity

• Generated this in RGenerated this in R• Will not have complete code, but will have key pieces• Advantage to R in this context

> Can create sub-modules as functions which we can then alter as assumptions

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> Can create sub modules as functions, which we can then alter as assumptions change

Onion Approach to Building Si l tiSimulation

S i

Summary: What is the power of each parameter set, what sample size yields acceptable power etcSummarize

overall results

Generate many

size yields acceptable power, etc

Generate trials: Need to replicate to calculate power, while varying key parameters (sampleGenerate many

trials, varying assumptions

varying key parameters (sample size, type of design, etc.)

Generate trial data: Generate in silico patients and get their resultsGenerate trial

datasilico patients and get their results

Subject data: Based on modeling of Phase I data

SubjectTest is superiority over

placebo, so

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Power = Prob{ p-value < α }

Response for a Given SubjectC t d f ti th t t t th ff tCreated as function so that we can use arguments to vary the effect

subject.data <- function(dose=300, dose.effect){

weeks <- c(4, 8, 12, 16, 24)n <- length(weeks) Create dose- and time-response

function. Based on prior data, is linear eta <- rnorm(1, 0, 10)epsilon <- rnorm(n, 0, 10)

if(dose==0){

p ,is both dose and time. Potentialldifferent model for placebo than for treated.

val <- 0 - xxxxxx*dose*dose.effect + eta + epsilon}else{

val <- 0 + eta + epsilon}}

result <- data.frame(week=weeks, val=val)result

}

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Trial SimulationC ll f ti bj t d tCalls function subject.data

run.trial <- function(sample.size, dose.effect, design){

des2 < design[design$status 1 ]des2 <- design[design$status == 1,]DesignPts <- dim(des2)[1]NumRep <- trunc( sample.size/DesignPts ) + 1doses <- rep(design$dose1, sample.size)[1:sample.size]

data.out <- data.frame(

Set up data structures needed for output (

dose1=doses,Response=rep(0,length(doses)),dose=as.factor(doses),volume=as.factor(volume)

)

for(i in 1:dim(data.out)[1]){

subj <- subject.data(dose=data.out[i,"dose1"], dose.effect)row <- subj$week==24data out[i "Response"] < subj[row 3]

Simulate data for a trial

data.out[i,"Response"] <- subj[row,3]}

trial.lm <<- lm(Response~dose-1, data=data.out)pvalues <- summary(trial.lm)$coefficients[,4]pvalues[summary(trial.lm)$coefficients[,1]>0] <- 1

Perform data analysis, and return result of t i l

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p y $pvalues

}

trial

Vary ParametersO ti Ch t i ti f T i l d Diff t S iOperating Characteristics of Trial under Different Scenarios

i ll f i (i 1 d d (0 1 2 0 1 2) l h 0 05)sim.all <- function(iter=1, dose.cond=c(0, 1, 2, 0, 1, 2), alpha=0.05) {

##### Set everything upfixed.power <- function(output){

output[(length(output)-2):length(output)]

Set up basic structure in which results will be deposited

output[(length(output) 2):length(output)]}

K <- length(dose.cond)power.curve <- data.frame(P560=rep(0,K), overall=rep(0, K),

best.dose=rep(0, K))

##### Vary the parameters, and call the simulation functionfor(i in 1:K){

fixed.output <- fixed.design(iter, sample.size=180, d ff t d d[i]

Make.design2() function returns

Simulate each scenario

dose.effect=dose.cond[i], alpha=0.05, make.design2()

)power.curve[i,] <- fixed.power(fixed.output)

}cbind(data.frame(n=rep(iter, K), dose=dose.cond, volume=vol.cond), power.curve)

function returns the parameters to

be varies

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cbind(data.frame(n rep(iter, K), dose dose.cond, volume vol.cond), power.curve)} Return results to user

CNS phase III trial simulation

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BackgroundP hi t d i l ti bj ti

• Preparing for Phase III for NME> Have data from earlier phases to produce models

Program history and simulation objective

> Have data from earlier phases to produce models> Phase I: Dose-ascending study with dense PK data, but no PD data> Phase II: Have both sparse PK, and clinical endpoint

- Phase II clinical endpoint (standard questionnaire endpoint for this indication) will p ( q p )carry into Phase III as the primary

- Dose ranging, endpoint at 3 months

Di i l l i di th t lti t l lt i d th• Disease is a slowly progressive disease that ultimately results in death> Instrument will be modeled as a linear decay over time

• Significant unmet need

• Simulation objectives> Determine best sample size, time of endpoint, and probability of success

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Design basicsPh III t d d d i

• Will have up to 2 dose groups + placebo groupParallel randomized double blind

Phase III standard design

• Parallel, randomized, double-blind• We expect treatment to gradually benefit the patients, or at least slow the

progression of the disease> Treatment is symptomatic relief> Treatment is symptomatic relief> Would we change design if it were possibly disease modifying?

• Follow patients up to at least 1 year, but primary time point may be earlier

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Our Onion

S iSummarize overall results

Generate many

Start with building models for what we know, and fill in the remainder with assumptions. Effect of assumptions can beGenerate many

trials, varying assumptions

Effect of assumptions can be assessed in the simulation.

Let’s start with the subject model (input/output)Generate trial

data(input/output).

Subject

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Subject ModelD D E Cli i l O t

• Pharmacokinetics> Build model from Phase I which has the best data

Dose Drug Exposure Clinical Outcomes

> Build model from Phase I, which has the best data> 2 compartment model is best fit

- Constructed population model in NONMEM- Advantages of population model here: Estimates of variability of parametersg p p y p

Source Central Sinkka

kel

Alternatives for ka

Peripheral

ka = ka,tv exp(η2)ka = ka,tv exp(θ W)

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Peripheral

Efficacy ResponseD D E Cli i l O t

• Response (change from baseline) at month 3 modeled as function of dose> Can modify this function

Dose Drug Exposure Clinical Outcomes

> Can modify this function> Assume linear effect over time> Can modify treatment effect estimates to establish power curve

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Patient ModelP i d l b ildi

• From Phase I: PK Model, steady state version (since out at 3 months or beyond)

Progress in model building

beyond)> Cpt = (D/V) exp(−ka t)/(1 − exp(− ka t )) + ω

- ka and V has subject-level random variables in them

Will need a covariate model

• From Phase II: PD Model for efficacy> E{Y} = β0 + β1ALT + β2 AST + β3 Age + β4 Sex + β5 log(Cpt)

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{ } β0 β1 β2 β3 g β4 β5 g( pt)> Variability estimates come from the model as well as mean structure

Adherence ModelH d bl ith thi i li t i l

• Adverse events related to drug concentration> P(constipation) = logit(γ + γ C )

Had problems with this in earlier trialsCONSTIPATION

NS

TIP

ATI

ON

0.6

0.8

1.0

> P(constipation) = logit(γ 0+ γ1 Cpt)> Will increase drop out hazard function> Include in missed dose hazard function?

- h(t) = h1 exp(AEconst)

Pro

babi

lity

of C

ON

0.0

0.2

0.4

0

0 16.67 33.33 50 66.67 83.33( ) 1 p( const)

• Patients drop out as study progresses> Hazard of drop out increases over time, and is

Max(concentration) P-value= 0.058

treatment dependent> These are phase II patients, maybe phase III will

be more committed? Can modify hazard during scenario building.g

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Covariate Model BuildingA t l D t Lit t R i Alt ti

• Best alternative would be data already in hand for the existing patient population> Can construct multivariate models

Actual Data or Literature Review Alternative

> Can construct multivariate models• Literature review can also give some

guidance• Alternative source of dataAlternative source of data

> NAMCS

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Source: Stragnes et al (2004) Body Fat Distribution, Relative Weight, and Liver Enzyme Levels: A Population-Based Study, Hepatology, Vol 39, Issue, pp 754-763 (http://onlinelibrary.wiley.com/doi/10.1002/hep.20149/pdf)

Design Options—ScenariosP ibiliti t I ti tPossibilities to Investigate

StandardScenarios

Interim analysis with possibility of stopping for

Standard deviation of differences

among means N / armFirst Futility Sample Size (fraction f)

5 50 15 (30%)of stopping for futility 50 25 (50%)

50 35 (70%)100 30 (30%)

No interim analysis

( )100 50 (50%)100 70 (70%)

10 50 15 (30%)50 25 (50%)50 35 (70%)100 30 (30%)

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( )100 50 (50%)100 70 (70%)

Scenario AnaylsisO ti i i th d i

• Design was factorial, so our analysis is straightforwardOften “surprising” (i e outside of consensus) information is gleaned

Optimizing the design

• Often surprising (i.e., outside of consensus) information is gleaned

1.0

Probability of Futility - Null Case

N=50 0

N Savings Pr Fut

0.4

Pr Succ

0

Pr SS PhaseIII

Comparing Update Frequencies: Every Week(Black), Every 2 Weeks(Red), and Every 4 Weeks(Green)

0.2

0.4

0.6

0.8

Pro

babi

lity

of F

utili

ty N=1000.

000.

100.

20

Nul

lcas

e

50 100

0.0

0.2

0.4

50 100

0.0

0.1

0.2

0.3

50 100

0.30

0.40

0.50

50 100

0.0

Fraction f

.3 .5 .7

1.0

Probability of Futility - Expected Case

00.

100.

20

Expe

cted

00.

100.

20

50.

70.

9

50.

70.

9

0.2

0.4

0.6

0.8

1

Pro

babi

lity

of F

utili

ty

N=50N=100

0.0

50 100

0.20

aped

0.0

50 100

100.

20

0.5

50 100

0.9

0.5

50 100

0.9

105

0.0

0

Fraction f

P

.3 .5 .7 0.00

0.10

Ush

a

50 100

0.00

0.1

50 100

0.5

0.7

50 100

0.5

0.7

50 100

Take Home Message

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Conclusions

• Timing> Simulations don’t have to be perfect but they do have to be timely> Simulations don t have to be perfect, but they do have to be timely

• Quality of Predictions> PK-PD Example > Retrospective CNS discussed aboveRetrospective CNS discussed above

- Simulation results predicted outcome of study- Analysis indicated probability of success to be low, and indeed the study failed to

show statistical significance for efficacy> Mofetil example

- MMF is a drug to reduce organ rejection episodes. - The drug is excreted renally. - In prior trials for kidney transplantation there was an inverse relationship between- In prior trials for kidney transplantation, there was an inverse relationship between

drug concentration in blood and probability of rejection.- Trial was simulated in SAS.

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Mycophenolate mofetil RCCTC l i

• MMF is a drug to reduce organ rejection episodes. The drug is excreted renally

Conclusions

• The drug is excreted renally. • In prior trials for kidney transplantation, there was an inverse relationship

between drug concentration in blood and probability of rejection.• Randomized Concentration-Controlled Trial (RCCT) was proposed Was• Randomized Concentration-Controlled Trial (RCCT) was proposed. Was

designed using simulation

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MMF ResultsT i l R lt d I f ti Gl d f Si l ti

• Information gleaned from the simulations> Effects of dose adjustments

Trial Results and Information Gleaned from Simulations

> Effects of dose adjustments> Effects of maximum dose> Power and Type I error rate

- Nonstandard null hypothesisyp> Ability to discriminate among doses> Distribution of doses

- Needed for manufacturing- Save several million dollars off the cost of the trial just on this finding

> Trial ResultLogistic regression analysis showed a highly statistically significant relationship- Logistic regression analysis showed a highly statistically significant relationship between median ln(MPA AUC) and the occurrence of a biopsy-proven rejection (P<0.001)

Van Gelder et al (1999) A randomized double-blind, multicenter plasma concentration controlled study of the safety

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and efficacy of oral mycophenolate mofetil for the prevention of acute rejection after kidney transplantation, Transplantation, 68(2) pp 261-66.

Take Home MessageG l C id ti

• Powerful tool to support trial designUnderstanding what you know and what you don’t know

General Considerations

• Understanding what you know and what you don t know> Your models and simulations are only as good as the data and assumptions that go

into them> Creating the model is just as beneficial as conducting the simulationsg j g

• You don’t have to have all of the different pieces to do trial simulation.> Just work with what you have> If need be make assumptions and test them

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Clinical Trial Simulation P3_Optimizing... · would like the modeling & simulation work conducted...

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Transcript of Clinical Trial Simulation P3_Optimizing... · would like the modeling & simulation work conducted...