Regression modeling of semicompeting risks data

Semicompeting risks data are often encountered in clinical trials with intermediate endpoints subject to dependent censoring from informative dropout. Unlike with competing risks data, dropout may not be dependently censored by the intermediate event. There has recently been increased attention to these data, in particular inferences about the marginal distribution of the intermediate event without covariates. In this article, we incorporate covariates and formulate their effects on the survival function of the intermediate event via a functional regression model. To accommodate informative censoring, a time-dependent copula model is proposed in the observable region of the data which is more flexible than standard parametric copula models for the dependence between the events. The model permits estimation of the marginal distribution under weaker assumptions than in previous work on competing risks data. New nonparametric estimators for the marginal and dependence models are derived from nonlinear estimating equations and are shown to be uniformly consistent and to converge weakly to Gaussian processes. Graphical model checking techniques are presented for the assumed models. Nonparametric tests are developed accordingly, as are inferences for parametric submodels for the time-varying covariate effects and copula parameters. A novel time-varying sensitivity analysis is developed using the estimation procedures. Simulations and an AIDS data analysis demonstrate the practical utility of the methodology.