Testing Independence of Bivariate Censored Data using Random Walk on Restricted Permutation Graph

TL;DR

This paper introduces a novel rank-based test for independence in bivariate censored data using a Markov chain Monte Carlo approach to handle the restricted permutation space, applicable to various censoring types.

Contribution

It develops a new MCMC-based method to evaluate Kendall's tau under censorship, enabling a generic independence test for diverse censoring scenarios.

Findings

Effective in handling different censoring types

Provides accurate null distribution approximation

Outperforms existing methods in real data applications

Abstract

In this paper, we propose a procedure to test the independence of bivariate censored data, which is generic and applicable to any censoring types in the literature. To test the hypothesis, we consider a rank-based statistic, Kendall's tau statistic. The censored data defines a restricted permutation space of all possible ranks of the observations. We propose the statistic, the average of Kendall's tau over the ranks in the restricted permutation space. To evaluate the statistic and its reference distribution, we develop a Markov chain Monte Carlo (MCMC) procedure to obtain uniform samples on the restricted permutation space and numerically approximate the null distribution of the averaged Kendall's tau. We apply the procedure to three real data examples with different censoring types, and compare the results with those by existing methods. We conclude the paper with some additional discussions not given in the main body of the paper.