1 Keaven Anderson, Ph.D. Amy Ko, MPH Nancy Liu, Ph.D. Yevgen Tymofyeyev, Ph.D. Merck Research Laboratories June 9, 2010 Information-Based Sample Size Re-estimation for Binomial Trials

2 Objective: Fit-for-purpose sample-size adaptation Examples here restricted to binary outcomes Wish to find sample size to definitively test for treatment effect  ≥  min  Minimum difference of clinical interest,  min, is KNOWN  May be risk difference, relative risk, odds-ratio  Do not care about SMALLER treatment differences Desire to limit sample size to that needed if  ≠  min Control group event rate UNKNOWN Follow-up allows interim analysis to terminate trial without ‘substantial’ enrollment over-running

3 Case Study 1 CAPTURE Trial (Lancet, 1997(349): )  Unstable angina patients undergoing angioplasty  30-day cardiovascular event endpoint  Control event rate may range from 10%-20%  Wish 80% power to detect  min = 1/3 reduction (RR)

4 Case Study 2 Response rate study  Control rate may range from 10% to 25%   min = 10% absolute difference

5 Can we adapt sample size? Gao, Ware and Mehta [2010] take a conditional power approach to sample size re-estimation  Presented by Cyrus Mehta at recent KOL lecture  Would presumably plan for null hypothesis  0 >  min and adapt sample size up if interim treatment effect is “somewhat promising” Information-based group sequential design 1.Estimate statistical information at analysis (blinded) 2.Do (interim or final) analysis based on proportion of final desired information (spending function approach) 3.If max information AND max sample size not reached –If desired information likely by next analysis, stop there –Otherwise, go to next interim –Go back to 1.

6 Fair comparison? The scenarios here are set up for information-based design to be preferred  Other scenarios may point to a conditional power approach  Important to distinguish your situation to choose the appropriate method!  Scenarios where the information-based approach works well are reasonably common  Blinded approaches such as information-based design are considered “well-understood’’ in the FDA draft guidance

7 Information-based approach Enroll patients continuously Estimate current information Analyze data Estimate next analysisGo to final (may adapt) Go to next IA Stop if done Stop enrollment

8 Example adaptation Target Information is re-scaled Adapted up to finish

9 Estimating information: Notation

10 Variance of (Note:  =proportion in Arm E) General formula Absolute difference (  = p C – p E ) Relative risk (  = log(p E / p C ))

11 Estimating variance and information Event rates estimated  Assume overall blinded event rate  Assume alternate hypothesis  Use MLE estimate for treatment group event rates (like M&N method) Use these event rates to estimate Statistical information

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15 CAPTURE information-based approach Plan for maximum sample size of 2800 Analyze every 350 patients At each analysis  Compute proportion of planned information  Analyze  Adapt appropriately

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19 Case Study 2 Response rate study  Control rate may range from 10% to 25%   min = 10% absolute difference

20 Execution of the IA Strategy: Conditional power approach of Gao et al Interim Analysis, calculate: Rate Difference Stop for futility Diff<3.86% † 3.86% ≤ Diff<16.7% Stop for efficacy Diff ≥16.7% ‡ † Corresponding to a CP of 15%; ‡ Corresponding to a P< Continue Re- estimate Sample Size CP ≤ CP ≤ 0.85 Compute Conditional Power

21 Overall Power of the Study IA without SSR and IA with SSR Initial sample size is 289 in each case. Maximum possible sample size is 578 (2 times of 289, cap of the SSR) NSAIDS Response Rate DrugA Response Rate gsDesign (Efficacy, Futility) Adaptive (gsDesign+SSR) E(N) † /Group Power E(N) † /Group Power 10%20% 15%25% 20%30% 25%35% † E(N) = expected sample size, which is the average of the sample size for such a design. The actual sample size the study might end up with varies. 90.0% 92.4% %78.2%73.3%86.8%81.9%78.0%

22 Information-based approach

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24 Information-based approach Maximum sample size of 1100 Plan analyses at 200, 400, 600, 800, 1100 Adapt assume target  min =.10  Absolute response rate improvement

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27 Some comments Computations performed using gsDesign R package  Available at CRAN  For CAPTURE example, 10k simulations were performed for a large # of scenarios –Parallel computing was easily implemented using Rmpi (free) or Parallel R (REvolution Computing)  For smaller # of scenarios used for 2 nd case study, sequential processing on PC was fine  My objective is to produce a vignette making this method available Technical issues  Various issues such as over-running and “reversing information time” need to be considered

28 Objective: Fit-for-purpose sample-size adaptation Examples here restricted to binary outcomes Wish to find sample size to definitively test for treatment effect  ≥  min  Minimum clinical difference of interest,  min, is KNOWN  May be risk difference, relative risk, odds-ratio  Do not care about SMALLER treatment differences Desire to limit sample size to that needed if  ≠  min Control group event rate UNKNOWN Follow-up allows interim analysis to terminate trial without ‘substantial’ enrollment over-running

29 Summary Information-based group sequential design for binary outcomes is  Effective at adapting maximum sample size to power for treatment effect  ≥  min  Group sequential aspects terminate early for futility, large efficacy difference Results demonstrated for absolute difference and relative risk examples If you can posit a minimum effect size of interest, this may be an effective adaptation method