Abstract

Interval censoring arises frequently in medical, financial, and sociological studies, where the event or failure of interest is not observed at an exact time point but is rather known to occur within a time interval induced by periodic monitoring. We formulate the effects of potentially time-dependent covariates on the interval-censored failure time through semiparametric regression models, such as the Cox proportional hazards model. We study nonparametric maximum likelihood estimation with an arbitrary number of monitoring times for each study subject. We develop an EM algorithm that involves very simple calculations and converges stably for any dataset, even in the presence of time-dependent covariates. We show that the estimators for the regression parameters are consistent, asymptotically normal, and asymptotically efficient with an easily estimated covariance matrix. In addition, we extend the numerical algorithm and asymptotic theory to competing risks and multivariate failure time data, as well as to big data involving potentially millions of subjects. Finally, we demonstrate the desirable performance of the proposed numerical and inferential procedures through simulation studies and applications to real medical studies.