Comparison of statistical methods for sequential parallel comparison designs with time-to-event endpoints under non-proportional hazards

The sequential parallel comparison design (SPCD) addresses high placebo response rates by enriching the study population with placebo nonresponders. Prior work established inference for SPCD time-to-event endpoints under proportional hazards, but treatment effects often vary over time, and it is unclear whether standard time-to-event methods retain their properties under SPCD’s two-stage structure when this assumption is violated. We present a systematic evaluation of test statistic robustness under non-proportional hazards in SPCD designs with a time-to-event endpoint, examining the commonly used test statistics based on the Cox proportional hazards model, nonparametric rank based tests, and the restricted mean survival time (RMST) approach. Under proportional hazards, all methods maintain appropriate type I error control, with the weighted log-rank and Cox Wald statistics achieving the highest power. Under non-proportional hazards, performance diverges by treatment effect pattern: the nonparametric Gehan-Wilcoxon statistic shows greater sensitivity to early and diminishing effects, while the RMST approach performs more reliably under crossing hazards with early benefit. These findings highlight the importance of aligning test selection with anticipated treatment dynamics in time-to-event trials designed by using the SPCD.