Joint modeling and estimation for recurrent event processes and failure time data

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. In some situations, however, the terminating time for observing recurrent events could be correlated with the recurrent event process, thus violating the assumption of independent censoring. In this article, we consider joint modeling of a recurrent event process and a failure time in which a common subject-specific 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, then using the estimated value in the failure time model. Some interesting implications and trajectories of the proposed model are presented. Properties of the regression parameter estimates and the estimated baseline cumulative hazard functions are also studied.