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Abstract:
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In medical studies, subjects may experience multiple asymptomatic and symp- tomatic events such that some of the events are interval-censored and some are right-censored. In this paper, we formulate the effects of covariates on multiple events using proportional haz- ards models with random effects. We consider nonparametric maximum likelihood estimation and develop a simple and stable EM algorithm. We show that the resulting estimators of the regression parameters are consistent, asymptotic normal, and asymptotically efficient with a covariance matrix that can be consistently estimated through profile likelihood. In addition, we show how to consistently estimate the probability of occurrence for one event conditional on the developments of other events. Furthermore, we assess the performance of the proposed numerical and inferential procedures through extensive simulation studies. Finally, we pro- vide an application to data on diabetes, hypertension, stroke, MI, and death derived from the Atherosclerosis Risk in Communities Study.
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