Adaptive Design Methods in Clinical Trials Shein-Chung Chow, PhD Department of Biostatistics and...

Adaptive Design Methods in Clinical Trials

Shein-Chung Chow, PhD

Department of Biostatistics and BioinformaticsDuke University School of Medicine

Durham, North Carolina

Presented atThe 2011 MBSW, Muncie, Indiana

May 23, 2011

Lecture 1 - Outline

What is adaptive design? Type of adaptive designs

Possible benefits Regulatory perspectives Protocol amendments

What is adaptive design?

There is no universal definition. Adaptive randomization, group sequential,

and sample size re-estimation, etc. PhRMA (2006) FDA (2010)

Adaptive design is also known as Flexible design (EMEA, 2002, 2006) Attractive design (Uchida, 2006)

PhRMA’s definition

PhRMA (2006). J. Biopharm. Stat., 16 (3), 275-283.

An adaptive design is referred to as a clinical trial design that uses accumulating data to decide on how to modify aspects of the study as it continues, without undermining the validity and integrity of the trial.

PhRMA’s definition

Characteristics Adaptation is a design feature. Changes are made by design not

on an ad hoc basis. Comments

It does not reflect real practice. It may not be flexible as it means

to be.

FDA’s definition

US FDA Guidance for Industry – Adaptive Design Clinical Trials for Drugs and Biologics Feb, 2010

An adaptive design clinical study is defined as a study that includes a prospectively planned opportunity for modification of one or more specified aspects of the study design and hypotheses based on analysis of data (usually interim data) from subjects in the study

FDA’s definition Characteristics

Adaptation is a prospectively planned opportunity.

Changes are made based on analysis of data (usually interim data).

Does not include medical devices? Comments

It classifies adaptive designs into well-understood and less well-understood designs

It does not reflect real practice (protocol amendments)

It is not a guidance but a document of caution

Adaptation

An adaptation is defined as a change or modification made to a clinical trial before and during the conduct of the study.

Examples include Relax inclusion/exclusion criteria Change study endpoints Modify dose and treatment duration

etc.

Types of adaptations Prospective adaptations

Adaptive randomization Interim analysis Stopping trial early due to safety, futility, or efficacy Sample size re-estimation

etc. Concurrent adaptations

Trial procedures Implemented by protocol amendments

Retrospective adaptations Statistical procedures Implemented by statistical analysis plan prior to

database lock and/or data unblinding

Adaptive trial designs Adaptive randomization design Group sequential design Flexible sample size re-estimation design Drop-the-losers (play-the-winner) design Adaptive dose finding design Biomarker-adaptive design Adaptive treatment-switching design Adaptive-hypotheses design Seamless adaptive trial design Multiple adaptive design

Adaptive randomization design A design that allows modification of

randomization schedules Unequal probabilities of

treatment assignment Increase the probability of

success Types of adaptive randomization

Treatment-adaptive Covariate-adaptive Response-adaptive

Comments

Randomization schedule may not be available prior to the conduct of the study.

It may not be feasible for a large trial or a trial with a relatively long treatment duration.

Statistical inference on treatment effect is often difficult to obtain if it is not impossible.

Group sequential design

An adaptive design that allows for prematurely stopping a trial due to safety, efficacy/futility, or bothbased on interim analysis results

Sample size re-estimation Other adaptations

Comments Well-understood design without

additional adaptations Overall type I error rate may not be

preserved when there are additional adaptations

(e.g., changes in hypotheses and/or study endpoints)

there is a shift in target patient population

Flexible sample size re-estimation An adaptive design that allows for

sample size adjustment or re-estimation based on the observed data at interim blinding or unblinding

Sample size adjustment or re-estimation is usually performed based on the following criteria variability conditional power reproducibility probability

etc.

Comments

Can we always start with a small number and perform sample size re-estimation at interim?

It should be noted sample size re-estimation is performed based on estimates from the interim analysis.

A flexible sample size re-estimation design is also known as an N-adjustable design.

Drop-the-losers design

Drop-the-losers design is a multiple stage adaptive design that allows dropping the inferior treatment groups

General principles drop the inferior arms retain the control arm may modify or add additional arms

It is useful where there are uncertainties regarding the dose levels

Comments

The selection criteria and decision rules play important roles for drop-the-losers designs.

Dose groups that are dropped may contain valuable information regarding dose response of the treatment under study.

How to utilize all of the data for a final analysis?

Some people prefer pick-the-winner.

Adaptive dose finding design A typical example is an adaptive dose

escalation design. A dose escalation design is often used

in early phase clinical development to identify the maximum tolerable dose (MTD), which is usually considered the optimal dose for later phase clinical trials adaptation to the traditional “3+3”

escalation rule continual re-assessment method (CRM) in

conjunction with the Bayesian’s approach

Comments How to select the initial dose? How to select the dose range

under study? How to achieve statistical

significance with a desired power with a limit number of subjects?

What are the selection criteria and decision rules?

What is the probability of achieving the optimal dose?

Biomarker-adaptive design A design that allows for adaptation

based on the responses of biomarkers such as genomic markers for assessment of treatment effect.

It involves qualification and standard optimal screening design establishment of predictive model validation of the established

predictive model

Comments A classifier marker usually does not

change over the course of study and can be used to identify patient population who would benefit from the treatment from those do not. DNA marker and other baseline marker for

population selection

A prognostic marker informs the clinical outcomes, independent of treatment.

A predictive marker informs the treatment effect on the clinical endpoint. Predictive marker can be population-specific.

That is, a marker can be predictive for population A but not population B.

Comments Classifier marker is commonly used in

enrichment process of target clinical trials Prognostic vs. predictive markers

Correlation between biomarker and true endpoint make a prognostic marker

Correlation between biomarker and true endpoint does not make a predictive biomarker

There is a gap between identifying genes that associated with clinical outcomes and establishing a predictive model between relevant genes and clinical outcomes

Adaptive treatment-switching design A design that allows the investigator

to switch a patient’s treatment from an initial assignment to an alternative treatment if there is evidence of lack of efficacy or safety of the initial treatment

Commonly employed in cancer trials In practice, a high percentage of

patients may switch due to disease progression

Comments Estimation of survival is a

challenge to biostatistician. A high percentage of subjects

who switched could lead to a change in hypotheses to be tested.

Sample size adjustment for achieving a desired power is critical to the success of the study.

Adaptive-hypotheses design A design that allows change in

hypotheses based on interim analysis results often considered before database

lock and/or prior to data unblinding Examples

switch from a superiority hypothesis to a non-inferiority hypothesis

change in study endpoints (e.g., switch primary and secondary endpoints)

Comments

Switch between non-inferiority and superiority The selection of non-inferiority margin Sample size calculation

Switch between the primary endpoint and the secondary endpoints Perhaps, should consider the switch from

the primary endpoint to a co-primary endpoint or a composite endpoint

Seamless adaptive trial design A seamless adaptive (e.g., phase II/III)

trial design is a trial design that combines two separate trials (e.g., a phase IIb and a phase III trial) into one trial and would use data from patients enrolled before and after the adaptation in the final analysis Learning phase (e.g., phase II) Confirmatory phase (e.g., phase III)

Comments Characteristics

Will be able to address study objectives of individual (e.g., phase IIb and phase III) studies

Will utilize data collected from both phases (e.g., phase IIb and phase III) for final analysis

Questions/Concerns Is it efficient? How to control the overall type I error rate? How to perform power analysis for sample size

calculation/allocation? How to perform a combined analysis if the

study objectives/endpoints are different at different phases?

Multiple adaptive design

A multiple adaptive design is any combinations of the above adaptive designs very flexible very attractive very complicated statistical inference is often difficult,

if not impossible to obtain

Multiple adaptive design

A multiple adaptive design is any combinations of the above adaptive designs very flexible very attractive very complicated statistical inference is often difficult,

if not impossible to obtainvery painful

Possible benefits

Correct wrong assumptions Select the most promising option

early Make use of emerging external

information to the trial React earlier to surprises (positive

and/or negative) May speed up development process

Possible benefits May have a second chance to re-design

the trial after seeing data from the trial itself at interim (or externally)

Sample size may start out with a smaller up-front

commitment of sample size More flexible but more problematic

operationally due to potential bias

Regulatory perspectives May introduce operational bias. May not be able to preserve type I error

rate. P-values may not be correct. Confidence intervals may not be reliable. May result in a totally different trial that is

unable to address the medical questions the original study intended to answer.

Validity and integrity may be in doubt.

Protocol amendments

On average, for a given clinical trial, we may have 2-3 protocol amendments during the conduct of the trial.

It is not uncommon to have 5-10 protocol amendments regardless the size of the trial.

Some protocols may have up to 12 protocol amendments

Protocol amendments

Rationale for changes Clinical Statistical

Review process Internal protocol review IRB Regulatory agencies

Ad hoc adaptations Inclusion/exclusion criteria (slow

enrollment) Changes in dose/dose regimen or

treatment duration (safety concern) Changes in study endpoints (increase

the probability of success) Increase the frequency of data

monitoring or administrative looks Others

Concerns

Protocol amendments may result in a similar but different target patient population

Protocol amendments (with major changes) could result in a totally different trial that is unable to address the questions the original trial intended to answer.

Target patient population

Has the disease under study Inclusion criteria to describe the

target patient population Exclusion criteria to remove

heterogeneity Subpopulations may be defined

based on some baseline demographics and/or patient characteristics

Target patient population Denote target patient population by

, where and are population mean and standard deviation, respectively.

After a modification made to the trial procedures, the target patient population lead to the actual patient population of

( , )

( , )C ( , )Actual Actual


,

1 /

Actual

Actual C

whereC


is usually referred to as the effect

size The effect size after the

modification made is inflated or reduced by the factor of .

“Clinically meaningful difference” may have been changed after the modification (adaptation) is made.


is referred to as a sensitivity index.

When (i.e., there are no impact on the target patient population after the modifications made). In this case, we have =1 (i.e., the sensitivity index is 1).

0 1and C

Sensitivity index

A shift in mean of the target patient population may be offset by the inflation (or reduction) of the variability, e.g., A shift of 10% (-10%) in mean could be

offset by a 10% inflation (reduction) of variability

may not be sensitive due to the masking effect between and C.

Moving target patient population

Under the moving target patient population, the effect size is the original effect size times the sensitivity index, that is

How will this impact statistical inference?

Actual

Actual

Two possible approaches Adjustment for covariate

Assuming that change in population can be linked by a covariate

Chow SC and Shao J. (2005). J. Biopharm. Stat., 15, 659-666.

Assessment of the sensitivity index Assuming that the shift and/or scale parameter

is random and derive a unconditional inference for the original patient population

Chow SC, Shao J, and Hu OYP (2002). J. Biopharm. Stat., 12, 311-321.

Adjustment for covariate - motivation

An asthma trial (Chow and Shao, 2005)

Primary endpoint: FEV1 change from

baseline

Adaptation: inclusion criteria (slow

enrollment) Range of Baseline FEV1 in Inclusion Criterion

Number of

Patients

Mean of FEV1

Change

Standard Deviation

of FEV1 Change

1.5~2.0 9 0.31 1.86

1.5~2.5 15 0.42 2.30

1.5~3.0 16 0.54 2.79

Adjustment for covariates The idea is to relate the means before

and after protocol amendments by means of some covariates. In other words,

where and are the mean and the corresponding covariate after the protocol amendment, is a given function (linear or non-linear), and is the number of protocol amendments.

,,...,1),( mkxf kk

k kxkth

fm

An example - summary statistics

Range of Baseline FEV1 In Inclusion Criterion

Number of

Patients

Mean ofFEV1

Change

S.D. of FEV1 Change

Mean of Baseline

FEV1

Test drug

1.5~2.0 9 0.31 0.14 1.86

2.0~2.5 15 0.42 0.14 2.30

2.5~3.0 16 0.54 0.16 2.79Placebo 1.5~2.0 8 0.16 0.15 1.82

2.0~2.5 16 0.19 0.13 2.29

2.5~3.0 16 0.20 0.14 2.84

Results of the proposed method

P-value was obtained based on testing for one-sided hypothesis. Classical method ignoring shift in patient population tends to overestimate the

treatment effect.

Estimate for Test Drug

Estimate for Placebo

Difference

Estimated SE

P-value

Covariate-adjusted method

0.33 0.17 0.16 0.057 0.0021

Classical method

0.44 0.19 0.25 0.066 0.0116

Example for sample size calculation

Without

adjustment AdjustmentAdjustme

ntFactor

RHypothesesTotal Each

treatmentTotal Each

treatment

Superiority 200 100 312 156 1.56

Non-inferiority 109 55 170 85 1.56

Equivalence 275 138 431 216 1.56 Note: Two protocol amendment is considered; δ is chosen as

3%.

Endpoint

Goal Model Estimation

Conti.

The WLS method is used to estimate , then

Binary

The ML method is used to estimate , then

: the test treatment : the control treatment

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Summary

Assessment of the sensitivity index

The sensitivity index can be estimated by

where

C

ˆ/ˆ1ˆ

ˆˆˆ Actual

ˆ/ˆˆActualC

Assessment of the sensitivity index There are four scenarios for assessment

of sensitivity index(i) both and are fixed

(ii) is random and is fixed (iii) is fixed and is random (iv) both and are random In addition

The sample size between two protocol amendments is random

The sample size between two protocol amendments is random

Actural ActualActual

ActuralActural Actual

Actural Actual

Sample size adjustment – random location shift

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Lecture 2 - Outline

Adaptive dose finding Algorithm-based design Model-based design Design selection

Seamless adaptive design? Relative advantages and limitations Types of two-stage adaptive design Statistical analysis An example

Concluding remarks

Dose finding trials

Fundamental questions Is there any drug effect? What doses exhibit a response

different from control? What is the nature of the dose-

response relationship? What is the optimal dose?

Dose response trial

Response = f(Dose)or

Dose = g(Response)

Dose response trials

ICH E4 (1994) Guideline on Dose-response Information to Support Drug Registration

Randomized parallel dose-response designs Crossover dose-response design Forced titration design

Dose escalation design Optimal titration design

Placebo-controlled titration to endpoint

Dose response relationship

Null hypothesis Alternative

hypotheses

KH ...: 100

KjiaH .........: 0

KKaH 110 ...:

KiaH ......: 0

KaH ....: 10

KiaH ......: 10

KKiaH 10 .......:

KiaH ......: 10

KKiaH 10 ......:

Dose escalation trial Primary objectives

Is there any evidence of the drug effect?

What is the nature of the dose-response?

What is the optimal dose? Principles

Less patients to be exposed to the toxicity

More patients to be treated at potential efficacious dose levels

Dose escalation trial Algorithm-based design

Traditional dose escalation (TER) rule The “3+3” TER The “a+b” TER

Model-based design Continual reassessment method

(CRM) CRM in conjunction with Bayesian

approach

Dose escalation trial Dose limiting toxicity (DLT)

DLT is referred to as unacceptable or unmanageable safety profile which is pre-defined by some criteria such as Grade 3 or greater hematological toxicity according to the US National Cancer Institute’s Common Toxicity Criteria (CTC)

Maximum tolerable dose (MTD) MTD is the highest possible but still

tolerable dose with respect to some pre-specified DLT.

Dose escalation trial The “3+3” TER

The traditional escalation rule is to enter three patients at a new dose level and then enter another three patients when a DLT is observed.

The assessment of the six patients is then performed to determine whether the trial should be stopped at the level or to escalate to the next dose level.

Traditional escalation rule Basically, there are two types of

escalation rules Traditional escalation rule (TER)

Does not allow dose de-escalation Strict traditional escalation rule (STER)

Allow dose de-escalation if two of three patients have DLTs

The “3+3” TER can be generalized to the “a+b” design with and without dose de-escalation.

Continual reassessment method For the method of CRM, the dose-

response relationship is continually reassessed based on accumulative data collected from the trial. The next patient who enters the trial is then assigned to the potential MTD level Dose toxicity modeling Dose level selection Reassessment of model parameters Assignment of next patient

Dose toxicity modeling

Assumptions There is monotonic relationship

between dose and toxicity The biologically inactive dose is lower

than the active dose, which is in turn lower than the toxic dose

Model The logistic model is often considered

Dose toxicity modeling Model

where is the probability of toxicity associated with dose , and and are positive parameters to be determined.

Then, the MTD can be expressed as

where is the probability of DLT at MTD

1)]exp(1[)( axbxp

)1

ln(1

b

aMTD

)(xp

x a b

Dose toxicity modeling Remarks

For an aggressive tumor and a transient and non-life-threatening DLT, could be as high as 0.5

For persistent DLT and less aggressive tumors, could be as low as 0.1 to 0.25

A commonly used value for is somewhere between 0 and 1/3=0.33Crowley (2001)

Dose level selection

General principles It should be low enough to avoid severe

toxicity It should be high enough for observing

some activity or potential efficacy in humans

The commonly used starting dose is the dose at which 10% mortality occurs in mice

)( 10LD


The subsequent dose levels are usually selected based on the following multiplicative set

where is called the dose escalation factor

11 iii xfx ),...,2,1( ki

if


Remarks The highest dose level should be

selected such that it covers the biologically active dose, but remains lower than the toxic dose.

In general, CRM does not require pre-determined dose intervals.

Reassessment of model parameters

The key is to estimate the parameter in the response mode An initial assumption or prior

about the parameter is necessary in order to assign patients to the dose level based on the toxicity relationship

The estimate of is continually updated based on cumulative data observed from the trial

a

a

Reassessment of model parameter Remarks – the estimation method

could be a frequentist or Bayesian approach

Frequentist approachMaximum likelihood estimate or least square estimate are commonly considered

Bayesian approach- It requires a prior distribution about the parameter- It provides posterior distribution and predictive probabilities of MTD

Assignment of next patient

The updated dose-toxicity model is usually used to choose the dose level for the next patient. In other words, the next patient enrolled in the trial is assigned to the current estimated MTD based on dose-response model

Assignment of next patient

Remarks Assignment of patient to the most

updated MTD leads to majority of the patients assigned to the dose levels near MTD, which allows a more precise estimate of MTD with a minimum number of patients

In practice, this assignment is subject to safety constraints such as limited dose jump and delayed response

Criteria for design selection

Number of patients expected Number of DLT expected Toxicity rate

Probability of observing DLT prior to MTD Probability of correctly achieving the MTD Probability of overdosing Others

Flexibility of dose de-escalation

An example – radiation theraphy Small size cohort for lower dose levels

Minimize the number of patients at lower dose groups

Majority patients near the MTD Ideally, the last two dose cohorts under study

Flexibility for dose de-escalation Limited dose jump if CRM is used Higher probability of reaching the MTD Lower probability of overdosing Also take moderate AE into consideration

Example - clinical trial simulation Simulation runs = 5,000 Initial dose = 0.5 mCi/kg Dose range is from 0.5 mCi/kg to 4.5 mCi/kg #of dose levels = 6 Modified Fibonacci sequence is considered. That

is, dose levels are 0.5, 1, 1.6, 2.5, 3.5, and 4.7. Maximum dose de-escalation allowed = 1 (for

STER) DLT rate at MTD is assumed to be 1/3=33% Logistic toxicity model is assumed for the CRM Uniform prior is assumed for the CRM #of doses allowed to skip = 0

Summary of Simulation Results (based ob 5,000 simulation runs)

Design

# patients expected (N)

# of DLT expected

Mean MTD (SD)

Prob. of selecting correct MTD

“3+3”TER

15.23 2.8 1.94 (0.507) 0.392

“3+3”STER*

17.59 3.2 1.70 (0.499) 0.208

CRM** 13.82 3.2 2.33 (0.451) 0.696

* Allows dose de-escalation

** Uniform prior was used

What is seamless adaptive design?

A seamless trial design is defined as a design that combines two separate (independent) trials into a single study.

The single study is able to address the study objectives that are normally achieved through the conduct of the two trials.

Seamless adaptive trial design

A seamless adaptive trial design is referred to as a seamless design that applies adaptations during the conduct of the trial.

A seamless adaptive design would use data collected from patients enrolled before and after the adaptation in the final analysis.

Characteristics Combine two separate trials into a

single trial It is also known as a two-stage

adaptive design The single trial consists of two

stages (phases) Learning (exploratory) phase Confirmatory phase

Opportunity for adaptations based on accrued data at the end of learning phase

Advantages Opportunity for saving

Stopping early for safety and/or futility/efficacy

Efficiency Can reduce lead time between the

learning and confirmatory phases Combined analysis

Data collected at the learning phase are combined with those data obtained at the confirmatory phase for final analysis

Limitations (regulatory’s concerns) May introduce operational bias

Adaptations relate to dose, hypothesis and endpoint etc.

May not be able to control the overall type I error rate When study objectives/endpoints are

different at different stages Statistical methods for combined

analysis are not well established Complexity depends upon the

adaptations apply

An example

Two-stage phase II/III study Learning (exploratory) phase

Dose finding Confirmatory phase

Efficacy confirmation

Comparison of type I errors

Let and be the type I error for phase II and phase III studies, respectively. Then the alpha for the traditional approach is given by if one phase III study is required if two phase III studies are

required In an adaptive seamless phase II/III

design, the actual alpha is The alpha for a seamless design is actually

times larger than the traditional design

II III

IIIII IIIIIIII

III II/1

Comparison of power Let and be the power for phase

II and phase III studies, respectively. Then the power for the traditional approach is given by if one phase III study is required if two phase III studies are required

In an adaptive seamless phase II/III design, the power is The power for a seamless design is actually

times larger than the traditional design

IIPower IIIPower

IIIII PowerPowerPower *

IIIIIIII PowerPowerPowerPower **

IIIPowerPower IIPower/1

Comparison

Traditional Approach

Seamless Design

Significance level

1/20 * 1/20 1/20

Power 0.8 * 0.8 0.8

Lead time 6 m – 1 yr Reduce lead time

Sample size

1 2n n n ?m n

Seamless adaptive designs

In practice, a seamless adaptive design may combine two separate (independent) trials with similar but different study objectives into a single trial, e.g., A phase II trial for dose selection and a

phase III study for efficacy confirmation In some cases, the study endpoints

considered at the two separate trials may be different, e.g., A biomarker or surrogate endpoint versus

a regular clinical endpoint


Category I - SS Same study objectives Same study endpoints

Category II - SD Same study objectives Different study endpoints

Category III - DS Different study objectives Same study endpoints

Category IV - DD Different study objectives Different study endpoints

Categories of two-stage seamless adaptive designs

Study endpoints at different

stages

S D

Study objectives at

different stages

S I=SS II-SD

D III=DS IV=DD


Category I - SS Similar to typical group sequential design

Category II - SD Biomarker (or surrogate endpoint or clinical

endpoint with shorter duration) versus clinical endpoint

Category III - DS Dose finding versus early efficacy

Category IV - DD Treatment selection with biomarker (or

surrogate endpoint or clinical endpoint with different treatment duration) versus efficacy confirmation with regular clinical endpoint

Frequently asked questions How to perform power analysis for sample

size calculation/allocation? How to control the overall type I error rate

at a pre-specified level of significance? Especially when the study objectives at

different stages are different How to combine data collected from both

stages for a valid final analysis? Especially when the study objectives

and study endpoints at different stages are different

Statistical analysis for Category I – SS designs

Similar to group sequential trial design with planned interim analyses Can be treated as a multiple-stage trial

design with adaptations Adaptations

Stop the trial early for futility/efficacy Drop the losers Sample size re-estimation

etc

Hypotheses testing

Consider a K-stage design and suppose we are interested in testing the following null hypothesis

where is the null hypothesis at the kth stage

KHHHH 002010 ...:

kH 0

Stopping rules

Let be the test statistic associated with the null hypothesis

Stop for efficacy ifStop for futility ifContinue with adaptations if Where and

kT

,kkT ,kkT

,kkk T

)1,..,1( Kkkk KK

Test based on individual p-values

This method is referred to as method of individual p-values (MIP)

Test statistics

For K=2 (a two-stage design), we have

KkpT kk ,...,1,

)( 1121

Stopping boundaries based on MIP

Test based on sum of p-values

This method is referred to as the method of sum of p-values (MSP)

Test statistic


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for

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21

Stopping boundaries based on MSP

Test based on product of p-values

This method is known as the method of products of p-values (MPP)

Test statistic


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121

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for

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21

Stopping boundaries based on MPP

Practical Issues Based on MIP, MSP, or MPP, sample size calculation

for achieving the desire power by controlling the overall type I error rate at a pre-specified level of significance can be obtained Statistical methodology was derived under the

assumptions of category I – SS designs Did not address the issue of sample size allocation.

The target patient population may have been shifted after adaptations How do we preserve type I error rate?

Adaptations are made based on “estimates” How this will affect the power?

More adaptations will result in a more complicated adaptive design

Statistical analysis for Category II – SD designs

Let be the data observed from stage 1 (learning phase) and stage 2 (confirmatory phase), respectively.

Assume that there is a relationship between and , i.e., .

The idea is to use the predicted values of at the first stage for the final combined analysis.

),( yx

x y )(xfy y

Assumptions

and and

and can be related by

where is an error term with zero

mean and variance

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2

x y

Weighted-mean approach

Graybill-Deal estimator

where21 )ˆ1(ˆˆˆ yyGD

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smsn

sn

.1

1

1

1)ˆ1(ˆ41

//

1)ˆ(

22

21

mnsmsnVar GD

Sample size allocation

Let and be the sample sizes at the first and second stages, respectively.

Also, let . Then the total sample size

where is referred to as the allocation factor.

nm

(1 )N n fn

n m

1/ f

Sample size allocation

For testing the hypothesis of equality, we have

where

and

0

10

)1(

)1(811

)(2 Nrr

Nn

222/

20 /)( zzN

2221 /r

Remarks

Following similar idea, formulas for sample size calculation/allocation for testing the hypothesis of superiority, non-inferiority, and equivalence can also be derived.

Similar idea can be applied to count data (binary responses) and time-to-event data assuming that there is a well-established relationship between the two study endpoints at different stages.

Category II – SD designsCategory II – SD designs (continuous and binary endpoints)(continuous and binary endpoints)

Hypotheses Testing

Continuous Endpoint Binary Response

Equality

Non-inferiority(δ < 0)

Superiority(δ > 0)

Equivalence

11

1(1 1 8(1 ) )

2n AB A C

11

1(1 1 8(1 ) )

2n BD D C

11

1(1 1 8(1 ) )

2n DB D C

11

1(1 1 8(1 ) )

2n EB E C

2 222 1 1 2 2

1 22 1

( ) ( ( ) ( ))

( )

z zn

2 221 1 2 2

1 22 1

( ) ( ( ) ( ))

( )

z zn

2 221 1 2 2

1 22 1

( ) ( ( ) ( ))

( )

z zn

2 221 1 2 2

1 22 1

( ) ( ( ) ( ))

( | |)

z zn

Category II – SD designsCategory II – SD designs (time-to-event data)(time-to-event data)

Hypotheses Testing

Weibull Distribution Cox’s Proportional Hazard Model

Equality

Non-inferiority(δ < 0)

Superiority(δ > 0)

Equivalence

2 12

1 2

( ) ( )

( )T R

T R

z zn

M M

2 1

21 2

( ) ( )

( )T R

T R

z zn

M M

2 1

21 2

( ) ( )

( )T R

T R

z zn

M M

2 1

21 2

( ) ( )

(| | )T R

T R

z zn

M M

1 1 1 1

22

1 2 21 2

( )

( )T R T R

z zn

b p p u p p u

2

1 2

( ) ( <0)

( )

z zn

e b K

2

1 2

( ) ( 0)

( )

z zn

e b K

22 2

1 2

( )

( | |)

z zn

e b K

Note

The definitions of the notations given in the previous slides can be found in following reference

ReferenceChow, S.C. and Tu, Y.H. (2008). On two-stage seamless adaptive design in clinical trials. Journal of Formosan Medical Association, 107, No. 12, S51-S59.

Remarks

One of the key assumptions in the proposed method is that there is a well-established relationship between the endpoints Biomarker vs clinical endpoint Same clinical endpoint with different

durations When there is a shift in patient population,

the proposed method needs to be modified Protocol amendments

An example – the HCV study

Study objectives – to evaluate the safety and efficacy of a test treatment for treating patients with hepatitis C virus (HCV) genotype 1 infection Dose selection (phase II) Efficacy confirmation (phase III)

Study design A two-stage phase II/III seamless adaptive

design Subjects are randomly assigned to five

treatments (4 active and one placebo)


Characteristics Study objectives are similar but different Study endpoints are different

Study endpoints First stage – early virologic response

(EVR) at week 12 Second stage – sustained virologic

response (SVR) at 72 week (i.e., 24 weeks after 48 weeks of treatment)

Adaptations considered Two planned interim analyses

The first interim analysis will be performed when all Stage 1 subjects have completed study Week 12.

The second interim analysis will be conducted when all Stage 2 subjects have completed Week 12 of the study and about 75% of Stage 1 subjects have completed Stage 1 treatment.

The O’Brien-Fleming type of boundaries are applied.

Criteria for dose selection at Stage 1

Dose selection is performed based on the precision analysis. Based on EVR, the dose with

highest confidence level for achieving statistical difference (i.e., the observed difference is not by chance alone) as compared to the control arm is selected.


Notations : treatment effect of the ith dose group at

the jth stage based on surrogate endpoint : treatment effect of the ith dose group at

the

jth stage based on regular clinical endpoint

i=1,…, k (dose group)

j=1,2 (stage)

jiE ,

ji ,

Study design of the HCV study

Two-stage seamless adaptive design

Stage 1 Stage 2

Multiple stage design

1st interim analysis

Decision-making

End of Stage 1

2nd interim analysis

Sample size re-estimation

End of study

Stage 1 Stage 2 Stage 3 Stage 4


This two-stage seamless design can then be viewed as a 4-stage design

Hypotheses of interest

kiH

kiH

i

i

,,1,0:

,,1,0:

2,2,0

1,1,0

An example – the HCV study Testing procedure

Stage 1 If , then stop the trial. If , then treatment will proceed

to Stage 2, where Stage 2

If , then

stop the trial. If but then move to Stage

3.

11,ˆmax ci

2,21*, ci 1,21,2 cT

1,22*,21

21*,

21

11,2

ˆˆ cnn

n

nn

nT ii

1,1

ˆmaxarg* iki

i

*iE11,

ˆmax ci

An example – the HCV study Stage 3

If

,

stop the trial; otherwise move to Stage 4. Stage 4

If

,

reject .

32*,21

21*,

21

12,3 ˆˆ c

nn

n

nn

nT ii

2,0H

42*,321

22,3

321

12,4 ˆ c

nnn

nT

nnn

nT i

Controlling type I error rate

It can be shown that the maximum

probability of wrongly rejecting is

achieve when

and .

Denote and the two vectors. Then we

have

2,0H

k 1

}){}{}ˆ({

)(

42,432,32,21*,

2,0),(

cTcTcP

HrejectP

i

01 k

Sample size calculation

Power can be evaluated at and

Denote and the two vectors. Then we have

2111 , kk

*2111 , kk

*

1

),ˆ,*}{}{}ˆ({

),ˆ,*(

)(

1,21,211*,42,432,32,21*,*)*,(

1,21,211*,*

2,0*)*,(

cTckicTcTcP

cTckiP

HrejectP

ii

i

Sample size calculation

Let N be the total number. Then

Similar to Thall, Simon and Ellenburg (1988), we can choose the parameters such that

is minimized.

),ˆ,,ˆ(2

)ˆ(2)1()(

32,32,21*,1,21,211*,3

11*,21

cTccTcPn

cPnnkNE

ii

i

*)*,(2

1),(

2

1** NENE

Remaining issues

How about sample size allocation? Is the usual O’Brien-Fleming type of

boundaries appropriate? How to combine data collected

from both stages for a valid final analysis?

What if there is a shift in target patient population?

Can clinical trial simulation help?

Remarks

The usual sample size calculation for a two-stage design with different study objectives/endpoints needs adjustment.

One of the key assumptions is that there is a well-established relationship between different endpoints. This relationship may not exist or cannot be

verified in practice. When there is a shift in patient population

(e.g., as the result of protocol amendments), the above method needs to be modified.

Future perspectives Well-understood design

Group sequential design Less well-understood design

Adaptive group sequential design Adaptive dose finding Two-stage seamless adaptive design

For less well-understood designs, they should be used with caution

Future perspectives

Design-specific guidances are necessarily developed Misuse Abuse

Statistical methods need to be derived Validity Reliability

Monitoring of adaptive trial design Integrity

Concluding remarks Clinical

Adaptive design reflects real clinical practice in clinical development.

Adaptive design is very attractive due to its flexibility and efficiency.

Potential use in early clinical development. Statistical

The use of adaptive methods in clinical development will make current good statistics practice even more complicated.

The validity of adaptive methods is not well established.

Concluding remarks

Regulatory Regulatory agencies may not realize but

the adaptive methods for review/approval of regulatory submissions have been employed for years.

Specific guidelines regarding different types of less-well-understood adaptive designs are necessary developed.

Selected references

[1] Special issues at Biometrics, Statistics in Medicine, Journal of Biopharmaceutical Statistics, Biometrical Journal, Pharmaceutical Statistics, etc.

[2] Gallo, P., et al. (2006). Adaptive design in clinical drug development – an executive summary of the PhRMA Working Group (with discussions). Journal of Biopharmaceutical Statistics, 16, 275-283.

[3] Chow, S.C. and Chang, M. (2006). Adaptive Design Methods in Clinical Trials. Chapman Hall/CRC Press, Taylor & Francis, New York, NY.

[4] Chow, S.C. and Chang, M. (2008). Adaptive design methods in clinical trials – a review. The Orphanet Journal of Rare Diseases, 3, 1-11.

[5] Pong, A. and Chow, S.C. (2010). Handbook of Adaptive Design In Pharmaceutical Research and Development. Chapman Hall/CRC Press, Taylor & Francis, New York, NY.

Adaptive Design Methods in Clinical Trials Shein-Chung Chow, PhD Department of Biostatistics and...

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Transcript of Adaptive Design Methods in Clinical Trials Shein-Chung Chow, PhD Department of Biostatistics and...