R. Sridhara, G. Chen, K. He, G.Y.H. Chi Division of Biometrics 1 OB, OPaSS, CDER, FDA

1. PROBLEM OF ALPHA ADJUSTMENT IN STUDIES WITH MULTIPLE PRIMARY ENDPOINTS – EVALUATION OF RELATIONSHIP BETWEEN ENDPOINTS R. Sridhara, G. Chen, K. He, G.Y.H. Chi Division of Biometrics 1 OB, OPaSS, CDER, FDA MCP2002

2. Disclaimer This talk is not an official FDA guidance or policy statement. No official support or endorsement by the FDA is intended or should be inferred. MCP2002

3. Outline • Example • The Problem • Literature • Challenges • Illustration • Summary MCP2002

4. Example Oncology Clinical Trials Comparing Two Treatment Groups for Efficacy: • Primary Endpoint: Overall Survival (OS) – Gold Standard • Secondary Endpoint: Time to Progression (TTP) – Commonly Selected Endpoint • Test of Hypothesis: Using Log-rank Test Statistic in both cases • Generally all the alpha is spent in testing OS • Drug Approval is based on Primary Endpoint Comparison MCP2002

5. The Problem • OS not significant, but TTP significant • After progression treatment changed to: (1) standard care or (2) patients in both groups receive new treatment, or (3) patient entered into a new study • OS = TTP + TPD, where TPD = Time from progression to death • TPD is a random variable • Strength of relationship between OS and TTP depends on TPD – Treatment received after progression P D 0 MCP2002

6. Literature • Boneferroni: Reject Hi if Pi /n • Holm (1979): Reject Hi if Pi /(n-i+1) • Simes (1986): Reject H(i) if P(i) i/n • Hochberg (1988): Reject H(i)if P(i) /(n-i+1) MCP2002

7. Literature • Westfall & Young (1989): Prmax {|Ti| > C} =  • Westfall & Young (1993): Resampling-based approach • Jin & Chi (1998): Primary and Secondary endpoints - Bootstrap approach • Moye (2000): primary & experimental alpha • D’Agostino; Koch; O’Neill MCP2002

8. Literature • Gong J, et. al. (2000): Test for primary and secondary endpoints using partial Boneferroni correction • Bender & Lange (2001): Review MCP2002

9. BUT…Drug APPROVAL Based on Primary Endpoints ONLY If an Endpoint is so Important it should be evaluated as Primary Endpoint MCP2002

10. OS and TTP Co-primary Endpoints H0: HROS = 1 and HRTTP = 1 HA: HROS 1 or HRTTP 1 ProbH0 (|X| > Cz/2 or |Y| > Cz/2) =  = 0.05, Where X is the log-rank statistic for OS and Y is the log-rank statistic for TTP MCP2002

11. Possible Scenarios • Significant differences between treatments with respect to both OS and TTP • No Significant differences between treatments with respect to both OS and TTP • Significant difference between treatments with respect to OS but not TTP • Significant difference between treatments with respect to TTP but not OS MCP2002

12. Options to control overall Type I error • Boneferroni Adjustment - Simple, Conservative • Gate Keeping – Up front ordering required • Global Test – Evaluation of correlation • Bootstrap MCP2002

13. Simplistic View Test Statistics for OS and TTP are jointly asymptotically normally distributed: (Z1, Z2) be the limit of the bivariate log-rank statistics (X, Y) Under Ho of no treatment differences for both endpoints, (Z1, Z2) will be bivariate normal with mean zero, variance 1 (without loss of generality) and correlation co-efficient  MCP2002

14. Under these Assumptions… Alpha Inflation (Simulations using S-Plus PMVNORM function) MCP2002

15. Challenges • To estimate , correlation co-efficient between the log-rank statistics, several studies have to be conducted or monte carlo simulations can be used •  is a random variable with unknown distribution • Point estimate of  will inflate error particularly if the distribution is skewed • Some M% confidence limit may be used as the estimate MCP2002

16. More Difficulties • Correlation between OS and TTP = 1 • Correlation between OS and TTP in placebo arm is same as correlation between OS and TTP in treatment arm ? • 1 ~ F • Correlation between test statistics X and Y = 2 • Adjustment of type I error can be considered • 2 ~ G • What Is The Relationship between F and G ? MCP2002

17. Illustration using Re-sampling Method • Original Data on 916 patients randomly assigned to Treatment A and Treatment B • 662/916 patients had progression • 308/916 patients had died • This data was re-sampled with replacement 50 times (using bsample in Stata software) • Correlation between OS and TTP within each of the 50 data sets were computed. The mean of the 50 correlation coefficients was 0.52 (s.d. 0.02) • Log-rank Statistics for TTP (X1,…,X50) and OS (Y1,…,Y50) for each of the 50 data sets were computed. The correlation between and X & Y was 0.64 MCP2002

18. Summary • Pre-specification of the decision rule in the evaluation of efficacy is important • When Co-primary endpoints are considered: • Boneferroni adjustment - conservative if correlated • Gate Keeping - specification of ordering required • Global Test - evaluation of correlation is challenging (ongoing research) • Bootstrap - sample data or distributional assumptions required • Two-stage Approach - ongoing research MCP2002

19. References • Holm S (1979) Scand. J. Statist. 6, 65-70 • Simes RJ (1986) Biometrika 73, 751-754 • Hochberg Y (1988) Biometrika 75, 800-802 • Westfall PH, Young SS (1989) JASA 84, 780-786 • Westfall PH, Young SS (1993) Resampling-based multiple testing, Jon Wiley & Sons. • Jin K, Chi GYH (1998) ASA proceedings, Biopharm. Sec. • Moye LA (2000) Stat. Med. 19, 767-779 • D’Agostino, Sr RB (2000) Stat. Med. 19, 763-766 • Koch GG (2000) Stat. Med. 19, 781-784 • O’Neill RT (2000) Stat. Med. 19, 785-793 • Gong J, Pinheiro JC, DeMets DL (2000) Cont. Clin. Trials 21, 313-329 • Bender R, Lange S (2001) J. Clin. Epi. 54, 343-349 • Pocock SJ (1997) Cont. Clin. Trials 18, 530-545 • Zhang J, Quan H, Ng J, Stephanavage ME (1997) Cont.Clin.Trials 18, 204-221 MCP2002