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

Research output: Contribution to journal › Article › peer-review

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 multivariate case. We also suggest how best to incorporate a sec- ond, 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
Proportional- ity parameter
Reliability analysis
Shared frailty

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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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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 multivariate case. We also suggest how best to incorporate a sec- ond, complementary, shape parameter in order to obtain especially useful parametric models for survival and reliability analysis.",

keywords = "Archimedean survival copula, Parametric survival analysis, Proportional- ity parameter, Reliability analysis, Shared frailty",

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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 multivariate case. We also suggest how best to incorporate a sec- ond, 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 multivariate case. We also suggest how best to incorporate a sec- ond, 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 - Proportional- ity parameter

KW - Reliability analysis

KW - Shared frailty

U2 - 10.1016/j.spl.2021.109059

DO - 10.1016/j.spl.2021.109059

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JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

SN - 0167-7152

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ER -

A family of cumulative hazard functions and their frailty connections

Abstract

Keywords

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