IDEAS home Printed from https://ideas.repec.org/a/dem/demres/v51y2024i18.html
   My bibliography  Save this article

Makeham mortality models as mixtures: Advancing mortality estimations through competing risks frameworks

Author

Listed:
  • Silvio Cabral Patricio

    (Syddansk Universitet)

  • Trifon Missov

    (Syddansk Universitet)

Abstract

Background: The Makeham term serves as a fundamental component in mortality modeling, offering a constant additive hazard that accounts for background mortality factors usually unrelated to the aging process. This term, widely employed in mortality analysis, provides a crucial mechanism for capturing mortality risks unrelated to age-related deterioration. Objective: The objective of this paper is to explore how Makeham models, which are widely used for studying mortality, can be understood and analyzed within the context of competing risks. The paper seeks to provide insights into the mathematical properties, interpretation, and applicability of Makeham models in modeling age-dependent and age-independent mortality risks. Additionally, the paper aims to demonstrate formally that competing-risk models can be represented as mixture models, thereby facilitating a deeper understanding of risk-specific mortality dynamics. Contribution: Expressing competing-risk models as mixtures aids identifying the overall and agespecific share of deaths according to each of the competing risks. In particular, Makeham mortality models, when represented as mixtures, provide, first, a semantically and computationally convenient platform to disentangle age-dependent from age-independent mortality, and second, a straightforward specification that can easily be extended to account for unobserved heterogeneity. By expressing Makeham models as a convex combination of probability distributions, we are able to estimate the age-profile of age-independent mortality, especially at the oldest ages, at which we intuitively assume that most deaths are age-dependent (senescent). We are also able to estimate the senescent mortality component, which is the one to focus on when studying the aging process and its characteristics.

Suggested Citation

  • Silvio Cabral Patricio & Trifon Missov, 2024. "Makeham mortality models as mixtures: Advancing mortality estimations through competing risks frameworks," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 51(18), pages 595-624.
    • Handle: RePEc:dem:demres:v:51:y:2024:i:18
    DOI: 10.4054/DemRes.2024.51.18
    as

    Download full text from publisher

    File URL: https://www.demographic-research.org/volumes/vol51/18/51-18.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.4054/DemRes.2024.51.18?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Castellares, Fredy & Patrício, Silvio C. & Lemonte, Artur J., 2020. "On gamma-Gompertz life expectancy," Statistics & Probability Letters, Elsevier, vol. 165(C).
    2. Trifon Missov & Vladimir Canudas-Romo & James W. Vaupel & Adam Lenart & Laszlo Nemeth, 2015. "The Gompertz force of mortality in terms of the modal age at death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(36), pages 1031-1048.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chiara Micheletti & Francisco Villavicencio, 2024. "On the relationship between life expectancy, modal age at death, and the threshold age of the life table entropy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 51(24), pages 763-788.
    2. Breen, Casey & Goldstein, Joshua R., 2022. "Berkeley Unified Numident Mortality Database: Public Administrative Records for Individual-Level Mortality Research," SocArXiv pc294, Center for Open Science.
    3. Jonas Šiaulys & Rokas Puišys, 2022. "Survival with Random Effect," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    4. Joel E. Cohen & Roland Rau & Christina Bohk-Ewald, 2018. "Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 38(29), pages 773-842.
    5. Alexander, Monica, 2018. "Deaths without denominators: using a matched dataset to study mortality patterns in the United States," SocArXiv q79ye, Center for Open Science.
    6. María-Dolores Huete-Morales & Esteban Navarrete-Álvarez & María-Jesús Rosales-Moreno & María-José Del-Moral-Ávila & José-Manuel Quesada-Rubio, 2020. "Modelling the survival function of the Spanish population by the Wong–Tsui model with the incorporation of frailty and covariates," Letters in Spatial and Resource Sciences, Springer, vol. 13(2), pages 151-163, August.
    7. Søren Kjærgaard & Vladimir Canudas-Romo, 2017. "Potential support ratios: Cohort versus period perspectives," Population Studies, Taylor & Francis Journals, vol. 71(2), pages 171-186, May.
    8. Paola Vazquez-Castillo & Trifon Missov & Marie-Pier Bergeron-Boucher, 2024. "Longevity à la mode: A discretized derivative tests method for accurate estimation of the adult modal age at death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 50(11), pages 325-346.
    9. Casey Breen & Joshua R. Goldstein, 2022. "Berkeley Unified Numident Mortality Database: Public administrative records for individual-level mortality research," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 47(5), pages 111-142.
    10. Lucia Zanotto & Vladimir Canudas-Romo & Stefano Mazzuco, 2021. "A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 1-27, March.
    11. Viorela Diaconu & Nadine Ouellette & Robert Bourbeau, 2020. "Modal lifespan and disparity at older ages by leading causes of death: a Canada-U.S. comparison," Journal of Population Research, Springer, vol. 37(4), pages 323-344, December.
    12. Jose Valderrama & Javier Olivera, 2023. "The effects of social pensions on mortality among the extreme poor elderly," LISER Working Paper Series 2023-05, Luxembourg Institute of Socio-Economic Research (LISER).
    13. Hartemink, Nienke & Missov, Trifon I. & Caswell, Hal, 2017. "Stochasticity, heterogeneity, and variance in longevity in human populations," Theoretical Population Biology, Elsevier, vol. 114(C), pages 107-116.
    14. Alois Pichler & Dana Uhlig, 2023. "Mortality in Germany during the COVID-19 Pandemic," IJERPH, MDPI, vol. 20(20), pages 1-11, October.
    15. Nico Keilman & Dinh Q. Pham & Astri Syse, 2018. "Mortality shifts and mortality compression. The case of Norway, 1900-2060," Discussion Papers 884, Statistics Norway, Research Department.
    16. Marie-Pier Bergeron-Boucher & Vladimir Canudas-Romo & Marcus Ebeling, 2015. "Decomposing changes in life expectancy: Compression versus shifting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(14), pages 391-424.
    17. Alois Pichler & Dana Uhlig, 2021. "Mortality in Germany during the Covid-19 pandemic," Papers 2107.12899, arXiv.org, revised Apr 2022.
    18. Alfredo Omar Palafox-Roca, 2023. "Consumo óptimo en el retiro con diferentes leyes de mortalidad," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 18(3), pages 1-30, Julio - S.
    19. Ugofilippo Basellini & Vladimir Canudas-Romo & Adam Lenart, 2019. "Location–Scale Models in Demography: A Useful Re-parameterization of Mortality Models," European Journal of Population, Springer;European Association for Population Studies, vol. 35(4), pages 645-673, October.
    20. Viorela Diaconu & Robert Bourbeau & Nadine Ouellette & Carlo Giovanni Camarda, 2016. "Insight on 'typical' longevity: An analysis of the modal lifespan by leading causes of death in Canada," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 35(17), pages 471-504.

    More about this item

    Keywords

    Makeham; mortality models; mixture model; competing risks; background mortality; senescent mortality;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:dem:demres:v:51:y:2024:i:18. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Editorial Office (email available below). General contact details of provider: https://www.demogr.mpg.de/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.