Semiparametric copula-based regression modeling of semi-competing risks data

Semi-competing risks data often arise in medical studies where the terminal event (e.g., death) censors the non terminal event (e.g., cancer recurrence), but the non terminal event does not prevent the subsequent occurrence of the terminal event. This article considers regression modeling of semi-competing risks data to assess the covariate effects on the respective non terminal and terminal event times. We propose a copula-based framework for semi-competing risks regression with time-varying coefficients, where the dependence between the non terminal and terminal event times is characterized by a copula and the time-varying covariate effects are imposed on two marginal regression models. We develop a two-stage inferential procedure for estimating the association parameter in the copula model and time-varying regression parameters. We evaluate the finite sample performance of the proposed method through simulation studies and illustrate the method through an application to Surveillance, Epidemiology, and End Results–Medicare data for elderly women diagnosed with early-stage breast cancer and initially treated with breast-conserving surgery.