A Copula-Based Extension of the Kaplan-Meier Estimator under Dependent Censoring with Unknown Association

This paper proposes a novel estimator of the survival function under dependent random right censoring, a situation frequently encountered in survival analysis. We model the relation between the survival time T and the censoring C by using a parametric copula, whose association parameter is not supposed to be known. Moreover, the survival time distribution is left unspecified, while the censoring time distribution is modeled parametrically. We develop su!cient conditions under which our model for (T, C) is identifiable, and propose an estimation
procedure for the distribution of the survival time T of interest. Our model and estimation procedure build further on the work on the copula-graphic estimator proposed by Zheng and Klein (1995) and Rivest and Wells (2001), which has the drawback of requiring the association parameter of the copula to be known, and on the recent work by Czado and Van Keilegom (2023), who suppose that both marginal distributions are parametric whereas we allow one margin to be unspecified. Our estimator is based on a pseudo-likelihood approach, and maintains low computational complexity. The asymptotic properties of the proposed estimator are shown. Additionally, we discuss an extension to include a cure fraction, addressing both identifiability and estimation issues. The practical performance of our method is validated through extensive simulation studies and an application to a breast cancer data set.