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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 ofdisease states and the transition between any two states is only known to occurover a broad time interval. We formulate the effects of potentiallytime-dependent covariates on multi-state processes through semiparametricproportional intensity models with random effects. We adopt nonparametricmaximum likelihood estimation (NPMLE) under general interval censoring anddevelop a stable expectation-maximization (EM) algorithm. We show that theresulting parameter estimators are consistent and that the finite-dimensionalcomponents are asymptotically normal with a covariance matrix that attains thesemiparametric efficiency bound and can be consistently estimated throughprofile likelihood. In addition, we demonstrate through extensive simulationstudies that the proposed numerical and inferential procedures perform well inrealistic settings. Finally, we provide an application to a major epidemiologiccohort study.

Maximum Likelihood Estimation for Semiparametric Regression Models with Interval-Censored Multi-State Data