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

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.

Accepted for publication at Biometrika

References in corpus (13)

• Higher criticism for detecting sparse heterogeneous mixtures
• Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism
• Innovated higher criticism for detecting sparse signals in correlated noise
• Goodness-of-fit tests via phi-divergences
• Higher Criticism for Large-Scale Inference, Especially for Rare and Weak Effects
• Properties of higher criticism under strong dependence
• On the exact Berk-Jones statistics and their p-value calculation
• Feature selection by Higher Criticism thresholding: optimal phase diagram
• Hypothesis testing for high-dimensional sparse binary regression
• False discovery rate control for multiple testing based on p-values with càdlàg distribution functions
• $K$-sample omnibus non-proportional hazards tests based on right-censored data
• Higher Criticism to Compare Two Large Frequency Tables, with sensitivity to Possible Rare and Weak Differences
• Anomaly Detection for a Large Number of Streams: A Permutation-Based Higher Criticism Approach