lifelines-hc: Higher Criticism testing for sparse non-proportional hazard departures in Python

2026-10-05

AI Summary

This study addresses the limited power of standard tests in survival analysis for detecting sparse non-proportional hazards differences at unknown time points. We propose a novel detection method based on Higher Criticism that requires no prespecified temporal pattern of hazard deviation. By leveraging hypergeometric p-values to effectively accommodate right-censored data, this approach overcomes key limitations of traditional weighted log-rank tests and is implemented as an open-source Python package. Across four clinical research applications, our method successfully identified sparse hazard differences overlooked by both the log-rank test and MaxCombo, demonstrating superior detection sensitivity and practical utility.

Abstract

The log-rank test is the standard tool for two-sample survival comparison and has good power against proportional-hazards alternatives, but it loses power against sparse hazard departures, in which the hazard difference is concentrated in a small number of time intervals whose locations along the follow-up are unknown a priori (Kipnis, Galili and Yakhini, Biometrika 2026). Weighted log-rank tests -- Gehan-Wilcoxon, Tarone-Ware, Peto-Prentice, Fleming-Harrington -- each impose a pre-specified temporal emphasis. Combination procedures such as MaxCombo and the Yang-Prentice short-term/long-term hazard-ratio model relax that choice, but still scan only a small dictionary of global temporal shapes and remain insensitive to sparse departures occurring outside them. We introduce lifelines-hc, a Python package extending the lifelines survival library with the HCHG test: Higher Criticism applied to per-interval hypergeometric p-values. HCHG applies to right-censored two-sample data and detects sparse hazard departures at unknown locations without committing to any temporal pattern. Across four clinical case studies -- CheckMate 057 PFS (n=582), COMET-1 OS (n=1028), AZURE DFS (n=3359), and the Copenhagen Study Group for Liver Diseases cirrhosis trial (n=446, fully public individual patient data) -- HCHG achieves p <= 0.014 in every dataset, while the log-rank test is non-significant throughout (p >= 0.26). MaxCombo and the Yang-Prentice adaptive log-rank test detect the delayed-benefit crossing in CheckMate 057 (p < 0.001) but are non-significant on the remaining three (p >= 0.24), where the departure is sparse or multi-window rather than a smooth short-term/long-term hazard-ratio pattern. lifelines-hc is freely available under the MIT license at https://github.com/alonkipnis/lifelines-hc and via pip install lifelines-hc.

Problem

• survival analysis
• sparse hazard departures
• log-rank test
• non-proportional hazards
• Higher Criticism

Innovation

• Higher Criticism
• sparse hazard departures
• survival analysis
• hypergeometric test
• right-censored data