Keywords: Group sequential, Interim analysis, priary endpoint, secondary endpiont, Type I error
In clinical trials with multiple endpoints, a hierarchical testing strategy with pre-specified order is often used to ensure the strong control of the family wise error rate (FWER). We consider a clinical trial with a primary endpoint (E1) and a secondary endpoint (E2) where E2 is tested only if E1 is significant. In the fixed sample size design, testing of E2 at a nominal level a after rejection of E1 at a level will strongly control FWER at a level. However, this hierarchical testing strategy may not control FWER in group sequential (GS) setting (Hung et al (2007)). Hung et al investigated three strategies for testing the secondary endpoint in GS design and concluded that a strategy in which the same rejection boundary at a level for E1 is used to test E2 can control FWER; however, it may be overly conservative. They suggested a more powerful strategy in which a boundary value corresponding to a/2 level is used to test E2. Glimm et al (2010) and Tamhane et al (2010) further researched this topic and evaluated different combinations of rejection boundaries for testing E1 and E2. As a result, a recommended strategy is to use O’Brien-Fleming (OF) boundary for E1 and Pocock (PO) boundary for E2. One potential limitation in these papers is that the information fractions at interim analyses are assumed to be the same for primary and secondary endpoints. Our research is motivated by a phase 3 oncology trial in which E1 is overall survival (OS) and secondary endpoints (E2s) include progression-free survival (PFS) and objective response rate (ORR). The timing of interim analysis is determined based on the information fraction of E1 and the maturity of E2s at interim analysis is different from that of E1. We will use simulations to evaluate how rejection boundaries based on endpoint-specific information fractions of E1 and E2s impact overall type I error rate and power under different scenarios of treatment effect of E1 and correlation of endpoints.