<p>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.</p>