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Most statistical tests for treatment effects used in randomized clinicaltrials with survival outcomes are based on the proportional hazards assumption,which often fails in practice. Data from early exploratory studies may provideevidence of non-proportional hazards which can guide the choice of alternativetests in the design of practice-changing confirmatory trials. We study a testto detect treatment effects in a late-stage trial which accounts for thedeviations from proportional hazards suggested by early-stage data. Conditionalon early-stage data, among all tests which control the frequentist Type I errorrate at a fixed $\alpha$ level, our testing procedure maximizes the Bayesianprediction of the finite-sample power. Hence, the proposed test provides auseful benchmark for other tests commonly used in presence of non-proportionalhazards, for example weighted log-rank tests. We illustrate the approach in asimulations based on data from a published cancer immunotherapy phase IIItrial.

Optimality of testing procedures for survival data