Abstract
In studies of chronic diseases, the health status of a subject can often be characterized by a finite number of transient disease states and an absorbing state, such as death. The times of transitions among the transient states are ascertained through periodic examinations and thus interval-censored. The time of reaching the absorbing state is known or right-censored, with the transient state at the previous instant being unobserved. In this paper, we provide a general framework for analyzing such multi-state data. We formulate the effects of potentially time-dependent covariates on the multi-state disease process through semiparametric proportional intensity models with random effects. We combine nonparametric maximum likelihood estimation with sieve estimation and develop a stable expectation-maximization algorithm. We establish the asymptotic properties of the proposed estimators through novel use of modern empirical process theory, sieve estimation theory, and semiparametric efficiency theory. In addition, we dynamically predict future states and survival time using the evolving disease history. Finally, we assess the performance of the proposed methods through extensive simulation studies and provide an illustration with a cardiac allograft vasculopathy study.