Kendall's Tau for Two-Sample Inference Problems

TL;DR

This paper introduces a Kendall's tau-based method for two-sample inference that is applicable to both censored and uncensored data, providing an alternative to hazard ratio-based tests with solid theoretical backing.

Contribution

The paper develops a new two-sample comparison procedure using Kendall's tau, including a weighted log-rank statistic for censored data, with theoretical properties and practical applications.

Findings

The proposed estimator reduces to the Wilcoxon-Mann-Whitney statistic when no censoring is present.

The method effectively handles right censored data with adapted weights.

Applications demonstrate the method's utility on real datasets.

Abstract

We consider a Kendall's tau measure between a binary group indicator and the continuous variable under investigation to develop a thorough two-sample comparison procedure. The measure serves as a useful alternative to the hazard ratio whose applicability depends on the proportional hazards assumption. For right censored data, we propose a weighted log-rank statistic with weights adapted to the censoring distributions and develop theoretical properties of the derived estimators. In absence of censoring, the proposed estimator reduces to the WMW statistic. The proposed methodology is applied to analyze several data examples.