title: Time-varying coefficients in a multivariate frailty model: Application to breast cancer recurrences of several types and death.
abstract: During their follow-up, patients with cancer can experience several types of recurrent events and can also die. Over the last decades, several joint models have been proposed to deal with recurrent events with dependent terminal event. Most of them require the proportional hazard assumption. In the case of long follow-up, this assumption could be violated. We propose a joint frailty model for two types of recurrent events and a dependent terminal event to account for potential dependencies between events with potentially time-varying coefficients. For that, regression splines are used to model the time-varying coefficients. Baseline hazard functions (BHF) are estimated with piecewise constant functions or with cubic M-Splines functions. The maximum likelihood estimation method provides parameter estimates. Likelihood ratio tests are performed to test the time dependency and the statistical association of the covariates. This model was driven by breast cancer data where the maximum follow-up was close to 20 years.
authors.affiliation: Laboratoire de Statistique Théorique et Appliquée, Sorbonne Universités, UPMC Univ Paris 06, 75013, Paris, France. Yassin.Mazroui@upmc.fr.|Institut Pierre Louis d'Epidémiologie et de Santé Publique, INSERM, UMR_S 1136, 75013, Paris, France. Yassin.Mazroui@upmc.fr.|Institut Pierre Louis d'Epidémiologie et de Santé Publique, Sorbonne Universités, UPMC Univ Paris 06, UMR_S 1136, 75013, Paris, France. Yassin.Mazroui@upmc.fr.
authors.forename: Yassin
authors.initials: Y
authors.lastname: Mazroui
authors.affiliation: INSERM, ISPED, Centre INSERM U-897-Epidemiologie-Biostatistique, Université Bordeaux Segalen, 146 rue Léo Saignat, 33076, Bordeaux, France.
authors.forename: Audrey
authors.initials: A
authors.lastname: Mauguen
authors.affiliation: Institut Bergonié, Unité de recherche et d'épidemiologie cliniques, INSERM CIC-EC7, ISPED, Centre INSERM U-897, 229 Cours de l'Argonne, 33000, Bordeaux, France.
authors.forename: Simone
authors.initials: S
authors.lastname: Mathoulin-Pélissier
authors.affiliation: Unité de recherche et d'épidemiologie cliniques, Institut Bergonié, 229 Cours de l'Argonne, 33000, Bordeaux, France.
authors.forename: Gaetan
authors.initials: G
authors.lastname: MacGrogan
authors.affiliation: Unité de recherche et d'épidemiologie cliniques, Institut Bergonié, 229 Cours de l'Argonne, 33000, Bordeaux, France.
authors.forename: Véronique
authors.initials: V
authors.lastname: Brouste
authors.affiliation: INSERM, ISPED, Centre INSERM U-897-Epidemiologie-Biostatistique, Université Bordeaux Segalen, 146 rue Léo Saignat, 33076, Bordeaux, France.
authors.forename: Virginie
authors.initials: V
authors.lastname: Rondeau
mesh_terms: D001943:Breast Neoplasms / Q000401:mortality*; D003198:Computer Simulation; D005260:Female; D006801:Humans; D053208:Kaplan-Meier Estimate; D016013:Likelihood Functions; D015233:Models, Statistical; D015999:Multivariate Analysis; D009364:Neoplasm Recurrence, Local / Q000401:mortality*; D016016:Proportional Hazards Models
keywords: Breast cancer; Frailty model; Penalized likelihood; Recurrent events