Most statistical tests for treatment effects used in randomized clinical
trials with survival outcomes are based on the proportional hazards assumption,
which often fails in practice. Data from early exploratory studies may provide
evidence of non-proportional hazards which can guide the choice of alternative
tests in the design of practice-changing confirmatory trials. We study a test
to detect treatment effects in a late-stage trial which accounts for the
deviations from proportional hazards suggested by early-stage data. Conditional
on early-stage data, among all tests which control the frequentist Type I error
rate at a fixed $\alpha$ level, our testing procedure maximizes the Bayesian
prediction of the finite-sample power. Hence, the proposed test provides a
useful benchmark for other tests commonly used in presence of non-proportional
hazards, for example weighted log-rank tests. We illustrate the approach in a
simulations based on data from a published cancer immunotherapy phase III
trial.