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.
Keywords: Copula model; dependent censoring; nonlinear estimating equation; pseudo-likelihood; semi-competing risks.