title: Incorporation of nested frailties into semiparametric multi-state models.
abstract: Proportional hazards models are among the most popular regression models in survival analysis. Multi-state models generalize them by jointly considering different types of events and their interrelations, whereas frailty models incorporate random effects to account for unobserved risk factors, possibly shared by clusters of subjects. The integration of multi-state and frailty methodology is an interesting way to control for unobserved heterogeneity in the presence of complex event history structures and is particularly appealing for multicenter clinical trials. We propose the incorporation of correlated frailties in the transition-specific hazard function, thanks to a nested hierarchy. We studied a semiparametric estimation approach based on maximum integrated partial likelihood. We show in a simulation study that the nested frailty multi-state model improves the estimation of the effect of covariates, as well as the coverage probability of their confidence intervals. We present a case study concerning a prostate cancer multicenter clinical trial. The multi-state nature of the model allows us to evidence the effect of treatment on death taking into account intermediate events.
authors.affiliation: Gustave Roussy, Service de Biostatistique et d'Epidémiologie, Villejuif, F-94805, France.|CESP Centre for Research in Epidemiology and Population Health, INSERM U1018 (Team 2, Methodology and clinical epidemiology in molecular oncology), Université Paris-Sud, Villejuif, F-94805, France.|Dipartimento di Scienze Statistiche, Universitá degli Studi di Padova, Padova, I-35121, Italy.|Institut de Statistique Biostatistique et Sciences Actuarielles, Université catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium.
authors.forename: Federico
authors.identifier: http://orcid.org/0000-0003-4837-6501
authors.initials: F
authors.lastname: Rotolo
authors.affiliation: INSERM, U897 (Biostatistics), Bordeaux, F-33076, France.|Université Victor Segalen Bordeaux 2, Bordeaux, F-33076, France.
authors.forename: Virginie
authors.initials: V
authors.lastname: Rondeau
authors.affiliation: Institut de Statistique Biostatistique et Sciences Actuarielles, Université catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium.
authors.forename: Catherine
authors.initials: C
authors.lastname: Legrand
mesh_terms: D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D003198:Computer Simulation; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D008390:Markov Chains; D015233:Models, Statistical; D015337:Multicenter Studies as Topic / Q000706:statistics & numerical data*; D011471:Prostatic Neoplasms / Q000401:mortality*; D016019:Survival Analysis
keywords: cancer; frailty; multi-state; multicenter; semiparametric