Computation of the Mann–Whitney Effect under Parametric Survival Copula Models

The Mann–Whitney effect is a measure for comparing survival distributions between two groups. The Mann–Whitney effect is interpreted as the probability that a randomly selected subject in a group survives longer than a randomly selected subject in the other group. Under the independence assumption of two groups, the Mann–Whitney effect can be expressed as the traditional integral formula of survival functions. However, when the survival times in two groups are not independent of each other, the traditional formula of the Mann–Whitney effect has to be modified. In this article, we propose a copula-based approach to compute the Mann–Whitney effect with parametric survival models under dependence of two groups, which may arise in the potential outcome framework. In addition, we develop a Shiny web app that can implement the proposed method via simple commands. Through a simulation study, we show the correctness of the proposed calculator. We apply the proposed methods to two real datasets.