### Resumé

Today, we know that demographic rates can be greatly influenced by differences among individuals in their capacity to survive and reproduce. These intrinsic differences, commonly known as individual heterogeneity, can rarely be measured and are thus treated as latent variables when modeling mortality. Finite mixture models and mixed effects models have been proposed as alternative approaches for inference on individual heterogeneity in mortality. However, in general models assume that individual heterogeneity influences mortality proportionally, which limits the possibility to test hypotheses on the effect of individual heterogeneity on other aspects of mortality such as ageing rates. Here, we propose a Bayesian model that builds upon the mixture models previously developed, but that facilitates making inferences on the effect of individual heterogeneity on mortality parameters other than the baseline mortality. As an illustration, we apply this framework to the Gompertz-Makeham mortality model, commonly used in human and wildlife studies, by assuming that the Gompertz rate parameter is affected by individual heterogeneity. We provide results of a simulation study where we show that the model appropriately retrieves the parameters used for simulation, even for low variances in the heterogeneous parameter. We then apply the model to a dataset on captive chimpanzees and on a cohort life table of 1751 Swedish men, and show how model selection against a null model (i.e., without heterogeneity) can be carried out.

Originalsprog | Engelsk |
---|---|

Tidsskrift | Biometrical Journal |

Vol/bind | 62 |

Udgave nummer | 1 |

Sider (fra-til) | 124-135 |

ISSN | 0323-3847 |

DOI | |

Status | Udgivet - jan. 2020 |

### Fingeraftryk

### Bibliografisk note

© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.### Citer dette

*Biometrical Journal*,

*62*(1), 124-135. https://doi.org/10.1002/bimj.201800280

}

*Biometrical Journal*, bind 62, nr. 1, s. 124-135. https://doi.org/10.1002/bimj.201800280

**Beyond the proportional frailty model : Bayesian estimation of individual heterogeneity on mortality parameters.** / Colchero, Fernando; Kiyakoglu, Burhan Y.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - Beyond the proportional frailty model

T2 - Bayesian estimation of individual heterogeneity on mortality parameters

AU - Colchero, Fernando

AU - Kiyakoglu, Burhan Y

N1 - © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

PY - 2020/1

Y1 - 2020/1

N2 - Today, we know that demographic rates can be greatly influenced by differences among individuals in their capacity to survive and reproduce. These intrinsic differences, commonly known as individual heterogeneity, can rarely be measured and are thus treated as latent variables when modeling mortality. Finite mixture models and mixed effects models have been proposed as alternative approaches for inference on individual heterogeneity in mortality. However, in general models assume that individual heterogeneity influences mortality proportionally, which limits the possibility to test hypotheses on the effect of individual heterogeneity on other aspects of mortality such as ageing rates. Here, we propose a Bayesian model that builds upon the mixture models previously developed, but that facilitates making inferences on the effect of individual heterogeneity on mortality parameters other than the baseline mortality. As an illustration, we apply this framework to the Gompertz-Makeham mortality model, commonly used in human and wildlife studies, by assuming that the Gompertz rate parameter is affected by individual heterogeneity. We provide results of a simulation study where we show that the model appropriately retrieves the parameters used for simulation, even for low variances in the heterogeneous parameter. We then apply the model to a dataset on captive chimpanzees and on a cohort life table of 1751 Swedish men, and show how model selection against a null model (i.e., without heterogeneity) can be carried out.

AB - Today, we know that demographic rates can be greatly influenced by differences among individuals in their capacity to survive and reproduce. These intrinsic differences, commonly known as individual heterogeneity, can rarely be measured and are thus treated as latent variables when modeling mortality. Finite mixture models and mixed effects models have been proposed as alternative approaches for inference on individual heterogeneity in mortality. However, in general models assume that individual heterogeneity influences mortality proportionally, which limits the possibility to test hypotheses on the effect of individual heterogeneity on other aspects of mortality such as ageing rates. Here, we propose a Bayesian model that builds upon the mixture models previously developed, but that facilitates making inferences on the effect of individual heterogeneity on mortality parameters other than the baseline mortality. As an illustration, we apply this framework to the Gompertz-Makeham mortality model, commonly used in human and wildlife studies, by assuming that the Gompertz rate parameter is affected by individual heterogeneity. We provide results of a simulation study where we show that the model appropriately retrieves the parameters used for simulation, even for low variances in the heterogeneous parameter. We then apply the model to a dataset on captive chimpanzees and on a cohort life table of 1751 Swedish men, and show how model selection against a null model (i.e., without heterogeneity) can be carried out.

KW - Bayesian inference

KW - frailty

KW - individual heterogeneity

KW - mortality

KW - survival analysis

U2 - 10.1002/bimj.201800280

DO - 10.1002/bimj.201800280

M3 - Journal article

C2 - 31574180

VL - 62

SP - 124

EP - 135

JO - Biometrical Journal

JF - Biometrical Journal

SN - 0323-3847

IS - 1

ER -