Shared Frailty Models for Recurrent Events and a Terminal Event

Abstract

There has been an increasing interest in the analysis of recurrent event data (Cook and Lawless, 2002, Statistical Methods in Medical Research 11, 141-166). In many situations, a terminating event such as death can happen during the follow-up period to preclude further occurrence of the recurrent events. Furthermore, the death time may be dependent on the recurrent event history. In this article we consider frailty proportional hazards models for the recurrent and terminal event processes. The dependence is modeled by conditioning on a shared frailty that is included in both hazard functions. Covariate effects can be taken into account in the model as well. Maximum likelihood estimation and inference are carried out through a Monte Carlo EM algorithm with Metropolis-Hastings sampler in the E-step. An analysis of hospitalization and death data for waitlisted dialysis patients is presented to illustrate the proposed methods. Methods to check the validity of the proposed model are also demonstrated. This model avoids the difficulties encountered in alternative approaches which attempt to specify a dependent joint distribution with marginal proportional hazards and yields an estimate of the degree of dependence.

Tutorial in Joint Modeling and Prediction: A Statistical Software for Correlated Longitudinal Outcomes, Recurrent Events and a Terminal Event

“…Another option for the analysis of correlated data are joint models for recurrent events and a terminal event (Liu, Wolfe, and Huang 2004;Rondeau, Mathoulin-Pélissier, Jacqmin-Gadda, Brouste, and Soubeyran 2007). These models are usually called joint frailty models as the processes are linked via a random effect that represents the frailty of a subject (patient) to experience an event.…”

“…Finally, a frailty u i is a random effect that links the two risk functions and follows a given distribution D and α is a parameter allowing more flexibility. The hazard functions are defined by (Liu et al 2004;Rondeau et al 2007):…”

A dynamic Mover–Stayer model for recurrent event processes subject to resolution

“…There has been considerable recent work on the development of statistical methods for the analysis of recurrent events in the presence of a terminal event. This phenomenon is naturally handled with intensity-based models (Andersen et al, 1993), but robust marginal methods have been developed (Cook and Lawless, 1997;Lin, 2000, 2002) as have models and methods incorporating random effects (Liu, Wolfe and Huang, 2004;Ye, Kalbfleisch and Schaubel, 2007).…”

Joint Survival Analysis of Time to Drug Change and a Terminal Event with Application to Drug Failure Analysis using Transplant Registry Data

“…These models allow for a recurrent and a terminal event that are not independent. An important early paper in this proposed a Cox proportional hazards model with shared frailty for recurrent events and a terminal event in an MCMC approach [4]. The unobserved frailty in the model measures the latent health status of the patient and it is related to both the recurrent event and the terminal event.…”

“…Other important work in the area of multiple time-to-event processes includes [6] where the authors propose a joint frailty model using a nonparametric likelihood method. Both [4] and [6] offer a thorough review of the history of research in this area from the 1990s to the mid 2000s. Another important paper uses two additive shared frailties to model trial and treatment heterogeneity in a meta-analysis [7].…”