The choice of a randomization procedure in survival studies with non-proportional hazards

The susceptibility of a clinical trial to allocation bias is related to the randomization procedure used to allocate patients to treatments. Consequently, the choice of a suitable randomization procedure is a crucial part of the trial design. For the unweighted log-rank test with proportional hazards, a trial-specific evaluation model for the selection of a suitable randomization procedure exists. However, the assumption of proportional hazards is often not fulfilled as treatment effects change over time. To increase statistical power in the situation of non-proportional hazards, weighted versions of the log-rank test and combination tests haven been suggested. We describe two semiparametric models to reflect the presence of allocation bias in a two-arm parallel group trial with a survival outcome and non-proportional hazards. Based on these, we study the impact of allocation bias on the type I error rate if treatments are compared using a (weighted) log-rank test or a max-combo test. It is shown that the type I error rates depend on the randomization procedure, the allocation bias model, and the statistical test. We conclude that our bias model offers a simple tool with clinically meaningful interpretation for choosing a suitable randomization procedure that reduces the risk of bias.