title: A comparison of different bivariate correlated frailty models and estimation strategies.
abstract: Frailty models are becoming increasingly popular in multivariate survival analysis. Shared frailty models in particular are often used despite their limitations. To overcome their disadvantages numerous correlated frailty models were established during the last decade. In the present study, we examine bivariate correlated frailty models, and especially the behavior of the parameter estimates when using different estimation strategies. We consider three different bivariate frailty models: the gamma model and two versions of the log-normal model. The traditional maximum likelihood procedure of parameter estimation in the gamma case with an explicit available likelihood function is compared with maximum likelihood methods based on numerical integration and a Bayesian approach using MCMC methods with the help of a comprehensive simulation study. We detected a strong dependence between the two parameter estimates (variance and correlation of frailties) in the bivariate correlated frailty model and analyzed this dependence in detail.
authors.affiliation: Institute of Medical Epidemiology, Biostatistics and Informatics, Martin-Luther-University Halle-Wittenberg, Magdeburger Strasse 27, 06097 Halle, Germany. andreas.wienke@medizin.uni-halle.de
authors.forename: Andreas
authors.initials: A
authors.lastname: Wienke
authors.forename: Konstantin G
authors.initials: KG
authors.lastname: Arbeev
authors.forename: Isabella
authors.initials: I
authors.lastname: Locatelli
authors.forename: Anatoli I
authors.initials: AI
authors.lastname: Yashin
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D016013:Likelihood Functions; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D015999:Multivariate Analysis; D009716:Numerical Analysis, Computer-Assisted