Semiparametric regression analysis of interval‐censored data with informative dropout

Interval‐censored data arise when the event time of interest can only be ascertained through periodic examinations. In medical studies, subjects may not complete the examination schedule for reasons related to the event of interest. In this article, we develop a semiparametric approach to adjust for such informative dropout in regression analysis of interval‐censored data. Specifically, we propose a broad class of joint models, under which the event time of interest follows a transformation model with a random effect and the dropout time follows a different transformation model but with the same random effect. We consider nonparametric maximum likelihood estimation and develop an EM algorithm that involves simple and stable calculations. We prove that the resulting estimators of the regression parameters are consistent, asymptotically 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 survival function when dropout represents voluntary withdrawal and the cumulative incidence function when dropout is an unavoidable terminal event. Furthermore, we assess the performance of the proposed numerical and inferential procedures through extensive simulation studies. Finally, we provide an application to data on the incidence of diabetes from a major epidemiological cohort study.