BIOM&S Seminar: Conditional Copula-Graphic Estimator for Semi-Competing Risks Data

 In semi-competing risks data, the interest lies in the estimation of the survival function of a non-terminal event time, which is subject to dependent censoring by a terminal event. This problem has been extensively studied in the literature, but mostly focusing on unconditional settings. In this work, we propose a conditional copula-graphic estimator that allows for covariate adjustment in the marginal survival functions of the non-terminal and terminal event times as well as in their dependence structure. The proposed estimator is semiparametric in that the conditional copula is specified parametrically using an Archimedean copula, but its dependence parameter function and margins are estimated nonparametrically. The performance of the conditional copula-graphic estimator is assessed using simulated and real data, and is compared to that of the unconditional copula-graphic estimator to investigate the cost of ignoring covariate effects.