Intensity Adjusted Log-Rank Test

Wu Y and Huag X

Published on: 2025-10-09

Abstract

The log-rank test is a widely used nonparametric method for comparing survival distributions between groups. However, its power diminishes when the proportional hazards condition does not hold, which is common in practice. To address this limitation, we propose the intensity-adjusted log-rank test-a novel extension that adapts to non-proportional hazards while maintaining the simplicity and enhancing the interpretability of the original test. Our approach incorporates time-varying adjustment factors that automatically account for changing hazard ratios, thereby eliminating the need (and the associated bias) for weight specification required by weighted log-rank tests. Simulation studies and a data example demonstrate that the intensity-adjusted log-rank test achieves significant power gains over the standard log-rank test (up to a 55% improvement) under non-proportional hazards, while preserving Type I error control. We introduce a general class of log-rank type tests that includes both the standard log-rank test and our proposed method as specific cases. This new method provides researchers with a flexible, robust, and more powerful tool for survival comparisons when hazards are non-proportional, effectively addressing key limitations of traditional log-rank and weighted log-rank tests.