A family of cumulative hazard functions and their frailty connections

Karim Anaya-Izquierdo; Alice Davis; Michael Christopher Jones

doi:10.1016/j.spl.2021.109059

A family of cumulative hazard functions and their frailty connections

Karim Anaya-Izquierdo, Alice Davis, Michael Christopher Jones

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Abstract

We consider a novel family of cumulative hazard functions (CHFs) controlled by a single shape parameter, which corresponds to proportionality on a certain scale, in such a way that the family is closed under inversion of the CHF and under frailty mixing using an appropriate mixing distribution. The latter leads to natural shared frailty models in the bivariate case. We also suggest how best to incorporate a second, complementary, shape parameter in order to obtain especially useful parametric models for survival and reliability analysis.

Original language	English
Article number	109059
Journal	Statistics and Probability Letters
Volume	172
Early online date	18 Feb 2021
DOIs	https://doi.org/10.1016/j.spl.2021.109059
Publication status	Published - 31 May 2021

Keywords

Archimedean survival copula
Parametric survival analysis
Proportionality parameter
Reliability analysis
Shared frailty

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2021.109059

Anaya-Jones-Davis-SPL-revision.PDFAccepted author manuscript, 213 KBLicence: CC BY-NC-ND

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title = "A family of cumulative hazard functions and their frailty connections",

abstract = "We consider a novel family of cumulative hazard functions (CHFs) controlled by a single shape parameter, which corresponds to proportionality on a certain scale, in such a way that the family is closed under inversion of the CHF and under frailty mixing using an appropriate mixing distribution. The latter leads to natural shared frailty models in the bivariate case. We also suggest how best to incorporate a second, complementary, shape parameter in order to obtain especially useful parametric models for survival and reliability analysis.",

keywords = "Archimedean survival copula, Parametric survival analysis, Proportionality parameter, Reliability analysis, Shared frailty",

author = "Karim Anaya-Izquierdo and Alice Davis and Jones, {Michael Christopher}",

note = "Funding Information: Alice Davis was supported by a UK EPSRC DTA doctoral studentship at the University of Bath. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

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AU - Davis, Alice

AU - Jones, Michael Christopher

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N2 - We consider a novel family of cumulative hazard functions (CHFs) controlled by a single shape parameter, which corresponds to proportionality on a certain scale, in such a way that the family is closed under inversion of the CHF and under frailty mixing using an appropriate mixing distribution. The latter leads to natural shared frailty models in the bivariate case. We also suggest how best to incorporate a second, complementary, shape parameter in order to obtain especially useful parametric models for survival and reliability analysis.

AB - We consider a novel family of cumulative hazard functions (CHFs) controlled by a single shape parameter, which corresponds to proportionality on a certain scale, in such a way that the family is closed under inversion of the CHF and under frailty mixing using an appropriate mixing distribution. The latter leads to natural shared frailty models in the bivariate case. We also suggest how best to incorporate a second, complementary, shape parameter in order to obtain especially useful parametric models for survival and reliability analysis.

KW - Archimedean survival copula

KW - Parametric survival analysis

KW - Proportionality parameter

KW - Reliability analysis

KW - Shared frailty

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JF - Statistics & Probability Letters

SN - 0167-7152

M1 - 109059

ER -

A family of cumulative hazard functions and their frailty connections

Abstract

Keywords

ASJC Scopus subject areas

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