Analyzing recurrent event data with informative censoring

Recurrent event data are frequently encountered in longitudinal follow-up studies. In statistical literature, noninformative censoring is typically assumed when statistical methods and theory are developed for analyzing recurrent event data. In many applications, however, the observation of recurrent events could be terminated by informative dropouts or failure events, and it is unrealistic to assume that the censoring mechanism is independent of the recurrent event process. In this article we consider recurrent events of the same type and allow the censoring mechanism to be possibly informative. The occurrence of recurrent events is modeled by a subject-specific nonstationary Poisson process via a latent variable. A multiplicative intensity model is used as the underlying model for nonparametric estimation of the cumulative rate function. The multiplicative intensity model is also extended to a regression model by taking the covariate information into account. Statistical methods and theory are developed for estimation of the cumulative rate function and regression parameters. As a major feature of this article, we treat the distributions of both the censoring and latent variables as nuisance parameters. We avoid modeling and estimating the nuisance parameters by proper procedures. An analysis of the AIDS Link to Intravenous Experiences cohort data is presented to illustrate the proposed methods.