A generalized Kruskal-Wallis test for comparing K samples subject to unequal patterns of censorship

TLDR

The authors introduce a generalized Kruskal‑Wallis test for K samples with arbitrary right censoring, extending Gehan’s Wilcoxon generalization, and propose an alternative statistic for the case of equal censoring distributions. The method permits censoring distributions to differ among populations and derives statistics that follow asymptotic chi‑square distributions under the null, whether censoring variables are treated as random or fixed. The paper presents asymptotic power and efficiency analyses and demonstrates the test’s performance through numerical examples.

Abstract

A generalization of the Kruskal-Wallis test, which extends Gehan's generalization of Wilcoxon's test, is proposed for testing the equality of K continuous distribution functions when observations are subject to arbitrary right censorship. The distribution of the censoring variables is allowed to differ for different populations. An alternative statistic is proposed for use when the censoring distributions may be assumed equal. These statistics have asymptotic chi-squared distributions under their respective null hypotheses, whether the censoring variables are regarded as random or as fixed numbers. Asymptotic power and efficiency calculations are made and numerical examples provided.