Sensitivity Analysis of The Mann-Whitney Effect under Parametric Survival Copula Models

Abstract

In medical research, the Mann-Whitney effect is often used to compare the survival distributions between two independent groups. It is given by the probability that a random subject from the treatment group survives longer than an independent random subject from the control group. In general, researchers examine whether the effect deviates from the null, 1/2. When two survival times are independent of each other, the Mann-Whitney effect can be estimated using Efron's classical method with marginal survival functions. However, under the independence assumption, the Mann-Whitney effect cannot be estimated using the Efron method. To address this, we use parametric copulas to model the bivariate survival function and review the computation procedure for the Mann-Whitney effect under the dependence assumption (Nakazono et al. (2024)). In this article, we introduce Nakazono et al. (2024) and re-examine the behavior of the Mann-Whitney effect estimator in correlated survival data by providing more detailed theoretical explanations and numerical evaluations, including an additional copula (the t-copula). Furthermore, we describe how to implement our proposed method in SAS and R and introduce our web application (https://nkosuke.shinyapps.io/shiny_survival/).