Estimating the survival functions in a censored semi-competing risks model

International audienceRivest & Wells (2001) proposed estimators of the marginal survival functions in a right-censored model that assumes an Archimedean copula which joins the survival time and the censoring time. We study the extension of these estimators to the context of right-censored semi-competing risks data with an independent second level censoring time. We intensively use martingale techniques to derive their large sample properties under mild assumptions on the true distribution of the data. As compared to the simpler context of right-censored data, a primary difference is the need to enlarge the filtrations with respect to which we use the Doob-Meyer decompositions of counting processes. Problems and directions for possible future research are discussed at the end of the paper