Parametric inference for the Mann–Whitney effect under survival copula models

Kosuke Nakazono (), Ryuji Uozumi () and Takeshi Emura ()
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Kosuke Nakazono: The Institute of Statistical Mathematics, Research Center for Medical and Health Data Science
Ryuji Uozumi: Institute of Science Tokyo, Department of Industrial Engineering and Economics
Takeshi Emura: The Institute of Statistical Mathematics, Research Center for Medical and Health Data Science

Statistical Papers, 2025, vol. 66, issue 7, No 13, 48 pages

Abstract: Abstract The Mann–Whitney effect is one of the most important measures for comparing the survival times of two independent groups. Under the independence assumption of two survival times, the Mann-Whitney effect can be estimated by Efron’s classical estimator. However, without the independence assumption, the Mann–Whitney effect cannot be estimated by the classical estimator without further assumptions. In this study, we use parametric copulas to model the joint distribution of two survival times, and propose an inference procedure for the Mann–Whitney effect under dependence models. We also derive the asymptotic variance estimator of the Mann-Whitney effect under various copulas and parametric marginal distributions. We conduct simulation studies to evaluate the accuracy of the proposed estimators under the correct and misspecified models. Finally, the proposed inference procedures are illustrated using a real dataset.

Keywords: Copula; Hand’s paradox; Mann–Whitney effect; Potential outcome; Stress-strength model; Two-sample comparison; 62-04; 62D20; 62F10; 62N01; 62N03; 62N05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01746-2

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