Statistical Analysis for Two-stage Seamless Design with Different Study Endpoints Shein-Chung Chow, Duke U, Durham, NC, USA Qingshu Lu, U of Science and Technology of China Siu-Keung Tse, City U of Hong Kong, Hong Kong Presented at ICSA 2007 Applied Symposium – JP Hsu Memorial Session Raleigh, North Carolina June 4, 2007

Outline Adaptive seamless design Practical issues Statistical methods Sample size calculation Concluding remarks

Definition There is no universal definition. Adaptive randomization, group sequential, and sample size re-estimation, etc. Chow, Chang, and Pong (2005) PhRMA (2006) 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), 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.

Types of adaptation Prospective adaptation Adaptive randomization Interim analysis Stopping trial early due to safety, futility, or efficacy Sample size re-estimation etc. Concurrent adaptation Trial procedures Retrospective adaptation Statistical procedures

Adaptive designs Adaptive randomization design Adaptive group sequential design N-adjustable design Drop-the-loser design Adaptive dose-escalation design Biomarker-adaptive design Adaptive treatment-switching design Adaptive-hypotheses design Adaptive seamless phase II/III trial design Any combinations of the above (multiple adaptive design)

Seamless design A seamless trial design is referred to a program that addresses within a single trial objectives that are normally achieved through separate trials of clinical development

Adaptive seamless design An adaptive seamless design is a seamless trial design that would use data from patients enrolled before and after the adaptation in the final analysis.

Adaptive seamless trial design Characteristics Combine two separate trials into a single trial The single trial consists of two phases Learning phase Confirmatory phase Opportunity for adaptation based on accrued data at the end of learning phase

Advantages of adaptive seamless design Opportunities for saving Stopping early for futility Stopping early for 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

Seamless phase II/III design A seamless phase II/III trial design is referred to a program that addresses within a single trial objectives that are normally achieved through separate trials in phase IIb and phase III of clinical development

Adaptive seamless phase II/III design An adaptive seamless phase II/III design is a seamless phase II/III trial design that would use data from patients enrolled before and after the adaptation in the final analysis.

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

Comparison of powers 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

Comparison Traditional Approach Seamless Design Significance level 1/20 * 1/201/20 Power0.8 * Lead time6 m – 1 yrReduce lead time Sample sizen1+n2n3

Multiple-stage design An adaptive seamless trial design is a multiple-stage design Adaptations Stop the trial early for futility/efficacy Drop the losers Sample size re-estimation etc

Multiple-stage design Statistical approaches Hypotheses testing Stopping rules Decision rules

Hypotheses testing Null hypothesis where is the null hypothesis at the kth stage

Stopping rules Let be the test statistic associated with the null hypothesis Stop for efficacy if Stop for futility if Continue with adaptations if Where and

Test based on individual p-values This method is referred to as method of individual p-values (MIP) Test statistics For a two-stage design, we have

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 For a two-stage design, we have

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 For a two-stage design, we have

Stopping boundaries based on MPP

Practical issues Similar but different study objectives Learning phase is to select optimal dose for confirmatory phase Confirmatory phase is to evaluate efficacy of the treatment Different study endpoints Same study endpoints with different duration Different study endpoints, e.g., biomarker (surrogate) versus clinical Moving target patient population Protocol amendments

Statistical method 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.

Assumptions and and can be related by where is an error term with zero mean and variance

Weighted-mean approach Graybill-Deal estimator where

Sample size For simplicity, let. Then the total sample size For testing the hypothesis of equality, it can be verified that an approximate formula for n is given as where and

Concluding remarks The usual sample size calculation for an adaptive two-stage design with different study endpoints needs adjustment. Key assumptions in the above derivation are (i) there is a well-established relationship between the endpoints and (ii) the responses are continuous. When there is a shift in patient population (e.g., as the result of protocol amendments), the above method needs to be modified.