Health sciences research often involves both right- and interval-censored events because the occurrence of a symptomatic disease can only be observed up to the end of follow-up, while the occurrence of an asymptomatic disease can only be detected through periodic examinations. We formulate the effects of potentially time-dependent covariates on the joint distribution of multiple right- and interval-censored events through semiparametric proportional hazards models with random effects that capture the dependence both within and between the two types of events. We consider nonparametric maximum likelihood estimation and develop a simple and stable EM algorithm for computation. We show that the resulting estimators are consistent and the parametric components are asymptotically normal and efficient with a covariance matrix that can be consistently estimated by profile likelihood or nonparametric bootstrap. In addition, we leverage the joint modelling to provide dynamic prediction of disease incidence based on the evolving event history. Furthermore, we assess the performance of the proposed methods through extensive simulation studies. Finally, we provide an application to a major epidemiological cohort study. Supplementary materials for this article are available online.
Keywords: Dynamic prediction; Joint models; Nonparametric likelihood; Proportional hazards; Random effects; Semiparametric efficiency.