The Choice of a Randomization Procedure in Survival Studies with Nonproportional 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 nonproportional 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 nonproportional 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.