Regression modeling of semi-competing risks data

Semi-competing risks data are encountered in studies with intermediate endpoints subject to dependent censoring. There has recently been increased attention to this data as distinct from classical competing risks data, in particular, inferences without covariates. In this paper, we incorporate covariates. Instead of modelling hazard functions, we formulate the covariate effects on the marginal and joint survival functions of the events via functional regression models. This includes a novel time-dependent copula model which generalizes parametric copula models. New nonparametric estimators are constructed from nonlinear estimating equations, and are shown to be uniformly consistent and to converge weakly. Inferences for the time-varying covariate effects and copula parameters are developed accordingly. Simulations and an AIDS data analysis illustrate the methodology's practical utility.

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