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

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

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**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**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**Outline**• Example • The Problem • Literature • Challenges • Illustration • Summary MCP2002**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**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**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**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**Literature**• Gong J, et. al. (2000): Test for primary and secondary endpoints using partial Boneferroni correction • Bender & Lange (2001): Review MCP2002**BUT…Drug APPROVAL Based on Primary Endpoints ONLY If an**Endpoint is so Important it should be evaluated as Primary Endpoint MCP2002**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**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**Options to control overall Type I error**• Boneferroni Adjustment - Simple, Conservative • Gate Keeping – Up front ordering required • Global Test – Evaluation of correlation • Bootstrap MCP2002**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**Under these Assumptions…**Alpha Inflation (Simulations using S-Plus PMVNORM function) MCP2002**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**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**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**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**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