Faculty Publications

Stochastic Comparisons In Frailty Models

Document Type

Article

Keywords

Classes of distributions, Frailty among survivors, Hazard rate, Heterogeneity, Stochastic orderings

Journal/Book/Conference Title

Journal of Statistical Planning and Inference

Volume

136

Issue

10

First Page

3647

Last Page

3658

Abstract

The frailty model in survival analysis accounts for unobserved heterogeneity between individuals by assuming that the hazard rate of an individual is the product of an individual specific quantity, called "frailty" and a baseline hazard rate. It is well known that the choice of the frailty distribution strongly affects the nonparametric estimate of the baseline hazard as well as that of the conditional probabilities. This paper reviews the basic concepts of a frailty model, presents various probability inequalities and other monotonicity results which may prove useful in choosing among alternative specifications. More specifically, our main result lies in seeing how well known stochastic orderings between distributions of two frailities translate into orderings between the corresponding survival functions. Some probabilistic aspects and implications of the models resulting from competing choices of the distributions of frailty or the baseline are compared. © 2005 Elsevier B.V. All rights reserved.

Department

Department of Mathematics

Original Publication Date

10-1-2006

DOI of published version

10.1016/j.jspi.2005.02.020

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