Higher criticism for rare and weak non-proportional hazard deviations in survival analysis

TL;DR

This paper introduces a higher criticism-based method for detecting rare and weak non-proportional hazard differences in survival data, outperforming traditional tests like the log-rank test in power and sensitivity.

Contribution

The paper presents a novel higher criticism approach tailored for survival analysis, effectively identifying rare and weak hazard deviations that previous methods struggle to detect.

Findings

Outperforms log-rank test in power for rare hazard differences

Effective in detecting non-proportional hazards in gene expression data

Theoretically characterizes the phase transition of test power

Abstract

We propose a method for comparing survival data based on the higher criticism of p-values obtained from multiple exact hypergeometric tests. The method accommodates non-informative right-censorship and is sensitive to hazard differences in unknown and relatively rare time intervals. It attains much better power against such differences than the log-rank test and its variants. We demonstrate the usefulness of our method in detecting rare and weak non-proportional hazard differences compared to existing tests, using simulations and actual gene expression data. Additionally, we analyze the asymptotic power of our method and other tests under a theoretical framework describing two groups experiencing failure rates that are usually identical over time, except in a few unknown instances where one group's failure rate is higher. Our test's power undergoes a phase transition across the plane of rarity and intensity parameters that mirrors the phase transition of higher criticism in two-sample settings with rare and weak normal and Poisson means. The region of the plane in which our method has asymptotically full power is larger than the corresponding region for the log-rank test.