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Updated: May 9, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
Multivariate frailty models for two types of recurrent events with a dependent terminal event: application to breast
Yassin Mazroui1, Simone Mathoulin-Pélissier, Gaetan Macgrogan
1INSERM, ISPED, Centre INSERM U-897-Epidemiologie-Biostatistique, 146 rue Léo Saignat, 33076, Bordeaux Cedex, France; Université Bordeaux Segalen, ISPED, Centre INSERM U-897-Epidemiologie-Biostatistique, Bordeaux, F-33000, France.
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.
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