ABSTRACT
Competing risks data arise when study subjects are subject to multiple types of failure events. The competing risks events are terminating, in that the onset of one event precludes the observation of other events. Semi-competing risks data involve a nonterminating event and a terminating event. A commonly encountered scenario of semi-competing risks data involves time to a landmark event of disease T1 $ T_1 $ and time to death T2 $ T_2 $. Instead, the problem can be formulated as a semi-competing risks problem, with T1 $ T_1 $ corresponding to time to the nonterminating event of interest and T2 $ T_2 $ corresponding to time to dropout. In many observational studies, the semi-competing risks data are subject to an additional complication due to left truncation to the terminating event. In the case, posing the copula model assumption is a sensible and convenient solution.
