  Interval-censored multi-state data arise in many studies of chronic diseases,
where the health status of a subject can be characterized by a finite number of
disease states and the transition between any two states is only known to occur
over a broad time interval. We formulate the effects of potentially
time-dependent covariates on multi-state processes through semiparametric
proportional intensity models with random effects. We adopt nonparametric
maximum likelihood estimation (NPMLE) under general interval censoring and
develop a stable expectation-maximization (EM) algorithm. We show that the
resulting parameter estimators are consistent and that the finite-dimensional
components are asymptotically normal with a covariance matrix that attains the
semiparametric efficiency bound and can be consistently estimated through
profile likelihood. In addition, we demonstrate through extensive simulation
studies that the proposed numerical and inferential procedures perform well in
realistic settings. Finally, we provide an application to a major epidemiologic
cohort study.
