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

Kosuke Nakazono, Yu-Cheng Lin, Gen-Yih Liao, Ryuji Uozumi and Takeshi Emura ()
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Kosuke Nakazono: Research Center for Medical and Health Data Science, The Institute of Statistical Mathematics, Tokyo 190-8562, Japan
Yu-Cheng Lin: Department of Information Management, Chang Gung University, Taoyuan 33302, Taiwan
Gen-Yih Liao: Department of Information Management, Chang Gung University, Taoyuan 33302, Taiwan
Ryuji Uozumi: Department of Industrial Engineering and Economics, Tokyo Institute of Technology, Tokyo 152-8552, Japan
Takeshi Emura: Research Center for Medical and Health Data Science, The Institute of Statistical Mathematics, Tokyo 190-8562, Japan

Mathematics, 2024, vol. 12, issue 10, 1-22

Abstract: 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.

Keywords: censoring; copula; Hand’s paradox; Mann–Whitney effect; potential outcome; stress–strength model; survival analysis; survival function; treatment effect; two-sample comparison (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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