Mazroui, Yassin; Mathoulin-Pélissier, Simone; MacGrogan, Gaetan; Brouste, Véronique; Rondeau, Virginie Multivariate frailty models for two types of recurrent events with a dependent terminal event: application to breast cancer data. (English) Zbl 1441.62435 Biom. J. 55, No. 6, 866-884 (2013). Summary: 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. Cited in 7 Documents MSC: 62P10 Applications of statistics to biology and medical sciences; meta analysis Keywords:breast cancer; frailty models; penalized likelihood; recurrent events Software:frailtypack PDFBibTeX XMLCite \textit{Y. Mazroui} et al., Biom. 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