Frailty modeling of semi-competing risks data

Abstract

In biomedical research involving time-to-event data, individuals may be susceptible to several possible outcomes. When an individual experiences more than one event in the follow-up process, this gives rise to multiple failure time data. In the modeling of such data, a random effect or `frailty? term is often introduced to accommodate the dependence between event times. In this paper, we consider a semi-competing risks framework, where a subject may experience two distinct types of events - terminal or non-terminal. In particular, the terminal event censors the non-terminal event but not vice versa. We propose frailty modeling for such data, where the frailty corresponds to an unknown subject-specific quantity which affects both events, leading to a dependence in their times of occurrence. Given frailty, a three-path compartment model is used to describe such data. We investigated the dependence structure between the events, as well as the covariate effects on each event. Extensive simulation studies were conducted to assess the performance of the proposed method. We also applied our methodology to data from a randomized clinical trial of nasopharyngeal cancer, where a positive dependence between recurrence and death was observed, indicating that relapse quickens the occurrence of death. This indicates that the association between non-terminal and terminal events needs to be taken into account, so as to achieve more realistic estimates of morbidity and mortality.