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Interval-censored survival data arise naturally in many fields such as medical follow-up studies, in which the event or failure is not observed exactly but only known to occur within a time interval. Most existing approaches for analyzing interval-censored failure time data assume that the examination times and the failure time are independent or conditionally independent given covariates. While this assumption offers considerable simplification, it is not plausible in some situations, e.g., the visiting rate can be positively or negatively correlated with the risk of failure due to unobservable health status even after adjusting for observable covariates. In this article, we consider dependent interval-censored data, where there exists dependence between the failure time and the entire visiting process. A shared frailty is used to characterize the dependence of hazard function of failure time and intensity function of visiting process. Moreover, the joint model could describe the possible none, positive or negative association between failure time and visiting process. We propose the semiparametric maximum likelihood estimators and develop an EM algorithm based on a Poisson data augmentation. The performance of the proposed method is examined through extensive simulation studies and an application to a bladder cancer dataset is presented.

A gamma-frailty model for interval-censored data with dependent examination times: a computationally efficient approach