Simulation-based comparative performance of survival methods in the case of non-proportional hazards

Abstract

A popular choice in cancer research when comparing survival between treatments is to consider the log-rank test. It has been well-established that it is the most powerful non-parametric test to compare survival functions when the hazards are proportional over time. However, in the case of non-proportional hazards, the log-rank test may no longer be optimal. While a number of statistical approaches have been invertigated to compare treatment effects on survival when the hazards are not proportional, they are still underused. This lack of application can be explained by the fact that it is currently unclear which approach should be used to design and analyze studies comparing cancer treatments. In this study, a particular focus is on immunotherapy treatments. The issue of how to compare treatment effects when the hazards are likely non-proportional is of major interest for contemporary cancer research due to the groundbreaking achievements of immunotherapy, which is typically characterized by a delayed treatment effect. The aim of this present master thesis was to compare the classical logrank test and methods designed to deal with non-proportional hazards. We reviewed the statistical properties of different approaches to deal with non-proportional hazards including the logrank test, methods based on the restricted mean survival time, generalized pairwise comparison, weighted log-rank and weighted Kaplan-Meier tests. We also performed an extensive simulation study to investigate their size under various scenarios. Finally, all methods are illustrated on the real EORTC 18991 trial outcome data.