Likelihood based inference for semi-competing risks

Consider semi-competing risks data (two times to concurrent events are studied but only one of them is right-censored by the other one) where the link between the times Y and C to non-terminal and terminal events respectively, is modeled by a family of Archimedean copulas. Moreover, both Y and C are submitted to an independent right censoring variable D. A new methodology based on a maximum likelihood approach is developed to estimate the parameter of the copula and the resulting survival function of Y. The main advantage of this procedure is that it extends to multidimensional parameters copulas. We perform simulations to study the behavior of our proposed estimation procedure and its impact on other related estimators and we apply our method to real data coming from a study on the Hodgkin disease.