A comparative study to alternatives to the log-rank test

TL;DR

This study compares traditional and new statistical tests for survival analysis, especially under non-proportional hazards, using extensive simulations to recommend the most robust methods.

Contribution

It provides an updated comparison of various survival tests, including recent omnibus and mean survival time methods, under diverse realistic scenarios.

Findings

Omnibus tests show higher robustness against non-proportional hazards.

New methods based on restricted mean survival time perform well in varied settings.

Traditional log-rank test is optimal only under proportional hazards.

Abstract

Studies to compare the survival of two or more groups using time-to-event data are of high importance in medical research. The gold standard is the log-rank test, which is optimal under proportional hazards. As the latter is no simple regularity assumption, we are interested in evaluating the power of various statistical tests under different settings including proportional and non-proportional hazards with a special emphasize on crossing hazards. This challenge has been going on for many years now and multiple methods have already been investigated in extensive simulation studies. However, in recent years new omnibus tests and methods based on the restricted mean survival time appeared that have been strongly recommended in biometric literature. Thus, to give updated recommendations, we perform a vast simulation study to compare tests that showed high power in previous studies with these more recent approaches. We thereby analyze various simulation settings with varying survival and censoring distributions, unequal censoring between groups, small sample sizes and unbalanced group sizes. Overall, omnibus tests are more robust in terms of power against deviations from the proportional hazards assumption.