Multivariate frailty models for two types of recurrent events with a dependent terminal event: Application to breast cancer data

Abstract

Individuals may experience more than one type of recurrent event and a terminal event during the life course of a disease. Follow-up may be interrupted for several reasons, including the end of a study, or patients lost to follow-up, which are non informative censoring events. Death could also stop the follow-up, hence, it is considered as a dependent terminal event. We propose a multivariate frailty model that jointly analyzes two types of recurrent events with a dependent terminal event. Two estimation methods are proposed: a semiparametrical approach using penalized likelihood estimation where baseline hazard functions are approximated by M-s plines, and another one with piecewise constant baseline hazard functions. Finally, we derived martingale residuals to check the goodness-of-fit. We illustrate our proposals with a real dataset on breast cancer. The main objective was to model the dependency between the two types of recurrent events (locoregional and metastatic) and the terminal event (death) after a breast cancer.

Bayesian analysis of multi-type recurrent events and dependent termination with nonparametric covariate functions

“…We have chosen a multivariate normal distribution for the random effects vector because it is flexible in modeling the covariance structure within and between various types of recurrent events and it has meaningful interpretation on correlation. Due to these reasons, it has been used in modeling multi-type recurrent event data in several articles 12,19 . In generalized linear mixed models, misspecification of random effects distribution has little impact on the parameters that are not associated with the random effects 53–55 .…”

“…Zhu et al 18 treated both the distributions of the dependent termination and latent variables as nuisance parameters and developed statistical methods for estimating regression parameters of recurrent events. Mazroui et al 19 later developed a multivariate frailty model for multi-type recurrent events with dependent termination and applied a Gauss-Hermite quadrature approximation with the penalized likelihood method for statistical inference.…”

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

“…Some extensions to joint frailty models include incorporation of a nonparametric covariate function (Yu and Liu 2011), inclusion of two frailty terms for the identification of the origin of the dependence between the processes (Mazroui, Mathoulin-Pélissier, Soubeyran, and Rondeau 2012), consideration of the diseasespecific mortality process (Belot, Rondeau, Remontet, Roch, and CENSUR Working Survival Group 2014) and accommodation of time-varying coefficients (Yu, Liu, Bravata, and Williams 2014;Mazroui, Mauguen, Macgrogan, Mathoulin-Pélissier, Brouste, and Rondeau 2016). Finally, Mazroui, Mathoulin-Pélissier, Macgrogan, Brouste, and Rondeau (2013) proposed a model with two types of recurrent events following the approach of Zhao, Liu, Liu, and Xu (2012). A review of joint frailty models in the Bayesian context was given by Sinha, Maiti, Ibrahim, and Ouyang (2008).…”

“…Two types of recurrent events are taken into account in a multivariate frailty model proposed by Mazroui et al (2013). The aim of the model is to analyze dependencies between all types of events.…”

Multivariate frailty models for multi-type recurrent event data and its application to cancer prevention trial

“…Rondeau, Mazroui, and Gonzalez (2012) developed an R package for the analysis of correlated survival data with frailty models. Mazroui et al (2013) considered multivariate frailty models for two types of recurrent events with parametric baseline and spline based baseline functions. Mazroui et al (2015) considered multivariate frailty models for two types of recurrent events with time-varying coefficients.…”