An Alpha-Exhaustive Parametric Multiple Comparison Procedure for Clinical Trials with Planned Evaluation of Treatment Effect in Pre-Defined Subgroups and Interim Analyses
In the era of precision medicine, it is often of interest to conduct clinical trials to evaluate treatment effect in the overall population as well as one or more pre-defined subgroups. Furthermore, long-duration confirmatory trials commonly have interim analyses. Parametric multiple comparison procedures, which take into account the correlations between test statistics, can be particularly useful as a testing strategy for these clinical trials. In this presentation, we consider clinical trials with a survival endpoint and derive an approximation formula for the pairwise correlation between stratified log-rank test statistics, thus allowing the construction of such parametric procedures. To ensure strong control of overall type I error and to maximize statistical power, we utilize the closure principle with exact level α tests for testing each intersection hypothesis in the closed family and refer to the resulting multiple comparison procedures as α-exhaustive parametric procedures. In particular, we propose and illustrate the construction of an α-exhaustive parametric procedure that maintains a fixed alpha allocation ratio between the hypotheses and applies the same error spending function to all primary endpoints. The performance of this proposed α-exhaustive parametric procedure in regard to type I error control and statistical power is evaluated via simulations.