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Multivariate frailty models for two types of recurrent events with a dependent terminal event: Application to breast cancer data
Author(s) -
Mazroui Yassin,
MathoulinPélissier Simone,
MacGrogan Gaetan,
Brouste Véronique,
Rondeau Virginie
Publication year - 2013
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201200196
Subject(s) - censoring (clinical trials) , multivariate statistics , statistics , martingale (probability theory) , event (particle physics) , breast cancer , piecewise , covariate , proportional hazards model , multivariate analysis , mathematics , medicine , cancer , mathematical analysis , physics , quantum mechanics
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 noninformative 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‐splines, 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.