This work presents novel and powerful tests for comparing non-proportional hazard functions, based on sample-space partitions. Right censoring introduces two major difficulties, which make the existing sample-space partition tests for uncensored data non-applicable: (i) the actual event times of censored observations are unknown and (ii) the standard permutation procedure is invalid in case the censoring distributions of the groups are unequal. We overcome these two obstacles, introduce invariant tests, and prove their consistency. Extensive simulations reveal that under non-proportional alternatives, the proposed tests are often of higher power compared with existing popular tests for non-proportional hazards. Efficient implementation of our tests is available in the R package KONPsurv, which can be freely downloaded from CRAN.
Keywords: Combined test; consistent test; crossing hazards; non-parametric test; permutation test; right censoring; sample–space partition; versatile test.