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Asymptotic failure rates for a general class of frailty models

Part of: Survival analysis and censored data Distribution theory

Published online by Cambridge University Press:  17 November 2017

Ramesh C. Gupta  and
David M. Bradley
Ramesh C. Gupta*
Affiliation:
University of Maine
David M. Bradley*
Affiliation:
University of Maine
*
* Postal address: Department of Mathematics & Statistics, University of Maine, 5752 Neville Hall, Orono, ME 04469-5752, USA.
* Postal address: Department of Mathematics & Statistics, University of Maine, 5752 Neville Hall, Orono, ME 04469-5752, USA.
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Abstract

We elucidate the long-term behavior of failure rates for a broad class of frailty models in survival analysis. The class properly includes the proportional hazard frailty model, the additive frailty model, and the accelerated failure time frailty model. A complete asymptotic expansion is derived and compared with the corresponding result for the limiting behavior obtained by Finkelstein and Esaulova (2006a). Several examples are provided to facilitate the comparison and to illustrate both the applicability and the limitations of our approach.

Keywords

Mixtureproportional hazard modeladditive hazard modelaccelerated failure time modelfrailty modelmonotonicitymixing distributionsasymptotic expansion

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 62E20: Asymptotic distribution theory
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 4 , December 2017 , pp. 1230 - 1259
Copyright
Copyright © Applied Probability Trust 2017 

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