Familywise error for multiple time-to-event endpoints in a group sequential design

We investigate the familywise error rate (FWER) for time-to-event endpoints evaluated using a group sequential design with a hierarchical testing procedure for secondary endpoints. We show that, in this setup, the correlation between the log-rank test statistics at interim and at end of study is not congruent with the canonical correlation derived for normal-distributed endpoints. We show, both theoretically and by simulation, that the correlation also depends on the level of censoring, the hazard rates of the endpoints, and the hazard ratio. To optimize operating characteristics in this complex scenario, we propose a simulation-based method to assess the FWER which, better than the alpha-spending approach, can inform the choice of critical values for testing secondary endpoints.