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A relaxation of the gamma frailty (Burr) model

Perperoglou, A and van Houwelingen, HC and Henderson, R (2006) 'A relaxation of the gamma frailty (Burr) model.' Statistics in Medicine, 25 (24). 4253 - 4266. ISSN 0277-6715

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Abstract

Frailty models are used in univariate data to account for individual heterogeneity. In the popular gamma frailty model the marginal hazard has the form of a Burr model. Although the Burr model is very useful and can offer insight on the data, it is far from perfect. The estimation of the covariate effects is linked to the baseline hazard and this makes the model coefficients hard to interpret. At the same time, the frailties are assumed constant over time, while biological reasoning in some cases may indicate that frailties may be time dependent. In this paper we present a relaxation of the Burr model which is based on loosening the link between the estimation of the covariate effects and the baseline hazard. This can be achieved by replacing the cumulative baseline hazard in the Burr model by a set of time functions, and the frailty variance by a vector of coefficients directly estimated from the data using a partial likelihood. We illustrate the similarities of the model with the Burr model and a further extension of the latter, a model with an autoregressive stochastic process for the frailty. We compare the models on simulated data sets with constant and time-dependent frailties and show how the relaxed Burr models performs on two different real data sets. We show that the relaxed Burr model serves as a good approximation to the Burr model when the frailty is constant, and furthermore it gives better results when the frailty is time dependent. Copyright © 2006 John Wiley & Sons, Ltd.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Aris Perperoglou
Date Deposited: 06 Nov 2012 11:57
Last Modified: 23 Jan 2019 05:15
URI: http://repository.essex.ac.uk/id/eprint/3824

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