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Frailty models

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Frailty Models Max-Planck-Institut für demografische Forschung Max Planck Institute for Demographic Research Konrad-Zuse-Strasse 1 · D-18057 Rostock · GERMANY Tel +49 (0) 3 81 20 81 - 0; Fax +49 (0) 3 81 20 81 - 202; This working paper has been approved for release by: Anatoli Yashin ([email protected]), Head of the Laboratory of Advanced Statistical Methods. © Copyright is held by the authors. Working papers of the Max Planck Institute for Demographic Research receive only limited review. Views or opinions expressed in working papers are attributable to the authors and do not necessarily reflect those of the Institute. Frailty Models MPIDR WORKING PAPER WP 2003-032 SEPTEMBER 2003 Andreas Wienke 1 Introduction The notion of frailty provides a convenient way to introduce random effects, association and unobserved heterogeneity into models for survival data. In its simplest form, a frailty is an unobserved random proportionality factor that modifies the hazard function of an individual, or of related individuals. In essence, the frailty concept goes back to work of Greenwood and Yule (1920) on "accident proneness’’. The term frailty itself was introduced by Vaupel et al. (1979) in univariate survival models and the model was substantially promoted by its application to multivariate survival data in a seminal paper by Clayton (1978) (without using the notion "frailty") on chronic disease incidence in families. Frailty models are extensions of the proportional hazards model which is best known as the Cox model (Cox, 1972), the most popular model in survival analysis. Normally, in most clinical applications, survival analysis implicitly assumes a homogenous population to be studied. This means that all individuals sampled into that study are subject in principle under the same risk (e.g., risk of death, risk of disease recurrence). In many applications, the study population can not be assumed to be homogeneous but mu

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