Two-Sample Problems for Survival Time—A Copula-Based Approach for Dependent Censoring—

Abstract

The Mann-Whitney test is a nonparametric test for detecting the difference of two groups, which can be estimated by right-censored survival data. However, the traditional test based on Efron's estimator is invalid when the independent censoring assumption fails to hold. Recently, researchers discuss “dependent censoring”, where the independence assumption is violated. In this article, we review a method for studying the asymptotic bias of Efron's estimator under a copula-based dependent censoring model. We also review an asymptotically unbiased (consistent) estimator of the Mann-Whitney effect, which adopts the copula-graphic estimator to adjust for the effect of dependent censoring. This leads to a valid two-sample test when the structure of dependent censoring is correctly specified by a copula. We also derive the asymptotic distribution of the copula-based estimator under possible misspecification on an assumed copula. The method is illustrated by analyzing a real dataset. We provide the R code to reproduce the data analysis results.