# $K$-sample omnibus non-proportional hazards tests based on right-censored data

## TL;DR

This paper introduces new, powerful statistical tests for comparing non-proportional hazard functions in right-censored data, overcoming key challenges posed by censoring and unequal group distributions, with demonstrated superior performance.

## Contribution

The paper develops invariant, consistent tests for non-proportional hazards that address censoring and unequal distributions, extending existing methods to censored data.

## Key findings

- Proposed tests outperform existing methods in simulations under non-proportional hazards.
- The tests are invariant and consistent, suitable for right-censored data.
- Implementation available in R package KONPsurv.

## Abstract

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 {https://github.com/matan-schles/KONPsurv