Analyzing Recurrent Event Data With Informative Censoring

Abstract

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.

Joint Modeling and Estimation for Recurrent Event Processes and Failure Time Data

“…It is clearly seen that the estimation focus of Wang et al(2001) was placed on the recurrent event process where the occurrence of the failure event is treated as a nuisance. In section 4.2 we shall consider inferential results for the failure event as well as the joint model.…”

“…The observation of recurrent events could be terminated (i.e., censored) by loss to follow-up, end of the study, or a failure event such as death. Conventional analysis usually focuses on either failure time data (Cox 1972;Cox and Oakes 1984) or recurrent event data (Prentice, Williams, and Peterson 1981;Andersen and Gill 1982;Pepe and Cai 1993;Lin et al 2000;Wang, Qin, and Chiang 2001). In this paper, the event process and the failure time are both of interest, and we consider the joint modeling of a recurrent event process and a failure time.…”

“…In their work, a latent variable is used to characterize the association between the recurrent event process and the failure time, and a common baseline function is shared by the intensity of the recurrent event process and the hazard of the failure time. In nonparametric and semiparametric settings, Wang, Qin, and Chiang (2001) proposed estimation procedures for estimating the cumulative rate function and regression parameters under multiplicative intensity models with dependent censoring. In the WQC model, the focus was placed on the distributional pattern of the recurrent event process where the censoring time was treated as a nuisance, and the joint modeling of recurrent event process and failure time was not considered.…”

“…Under Assumption (M3), D, C and N (·) are allowed to be correlated via their connection with (x, z). This model relaxes the requirement that a common baseline function be shared by the intensity of N (·) and the hazard of D assumed by Lancaster and Intrator (1998), and still keeps the semiparametric model features of Wang et al (2001).…”

“…Under these regularity conditions, the large sample properties ofΛ 0 andα were established in Wang et al (2001). We denote the following asymptotic representations:…”