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

Abstract

Recurrent event data are commonly encountered in longitudinal follow-up studies related to biomedical science, econometrics, reliability, and demography. In many studies, recurrent events serve as important measurements for evaluating disease progression, health deterioration, or insurance risk. When analyzing recurrent event data, an independent censoring condition is typically required for the construction of statistical methods. Nevertheless, in some situations, the terminating time for observing recurrent events could be correlated with the recurrent event process and, as a result, the assumption of independent censoring is violated. In this paper, we consider joint modeling of a recurrent event process and a failure time in which a common subjectspecific latent variable is used to model the association between the intensity of the recurrent event process and the hazard of the failure time. The proposed joint model is flexible in that no parametric assumptions on the distributions of censoring times and latent variables are made and, under the model, informative censoring is allowed for observing both the recurrent events and failure times. We propose a 'borrow-strength estimation procedure' by first estimating the value of the latent variable from recurrent event data, and next using the estimated value in the failure time model. Some interesting implications and trajectories of the proposed model will be presented. Properties of the regression parameter estimates and the estimated baseline cumulative hazard functions are also studied.

Semiparametric Analysis of Correlated Recurrent and Terminal Events

“…This has a variance of 0.10, which is close to independence. It is the same as one of the settings in the simulation study of Huang and Wang (2004). We increased the variance of the Poisson frailty on the suggestion of a reviewer, and obtained similar results with respect to bias (simulation not shown).…”

“…The differences from our suggested model (MR model) and this non-parametric frailty approach (NPF model) proposed by Huang and Wang (2004) can be summarized as follows:…”

“…where R (j) is the total number of events with event time and observed terminating time Huang and Wang (2004) extended the method to incorporate situations where one aspect of informative censoring is associated with a terminal event (e.g. death).…”

“…In Section 3, the proposed approach is compared with the method of Huang and Wang (2004). Section 4 gives results of some simulation studies and the method is applied to the data from a prospective study of peritoneal dialysis patients in Section 5.…”

“…Thus, they assume that the complete intensity of the recurrent events and the terminal event is fully specified by the observed covariates and the unobserved frailty (e.g. Wang, Qin and Chiang, 2001;Huang and Wang, 2004;Liu, Wolfe and Huang, 2004). In all of the frailty models, it is assumed that given the frailty, the recurrent event process is a nonhomogeneous Poisson process and this plays a central role in all aspects of the estimation.…”