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Longevity à la mode: A discretized derivative tests method for accurate estimation of the adult modal age at death

Author

Listed:
  • Paola Vazquez-Castillo

    (Syddansk Universitet)

  • Marie-Pier Bergeron-Boucher

    (Syddansk Universitet)

  • Trifon Missov

    (Syddansk Universitet)

Abstract

Background: The modal age at death (or mode) is an important indicator of longevity associated with different mortality regularities. Accurate estimates of the mode are essential, but existing methods are not always able to provide them. Objective: Our objective is to develop a method to estimate the modal age at death, which is purely based on its mathematical properties. Methods: The mode maximizes the density of the age-at-death distribution. In addition, at the mode, the rate of aging equals the force of mortality. Using these properties, we develop a novel discrete estimation method for the mode, the discretized derivative tests (DDT) method, and compare its outcomes to those of other existing models. Results: Both the modal age at death and the rate of aging have been increasing since 1960 in low-mortality countries. The DDT method produces close estimates to the ones generated by the P-spline smoothing. Conclusions: The modal age at death plays a central role in estimating longevity advancement, quantifying mortality postponement, and estimating the rate of aging. The novel DDT method proposed here provides a simple and mathematically based estimation of the modal age at death. The method accounts for the mathematical properties of the mode and is not computationally demanding. Contribution: Our research was motivated by James W. Vaupel, who wanted to find a way to accurately estimate the mode based on its mathematical properties. This article also expands on some of his last research papers that link the modal age at death for populations to the one for individuals.

Suggested Citation

  • Paola Vazquez-Castillo & Marie-Pier Bergeron-Boucher & Trifon Missov, 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.
    • Handle: RePEc:dem:demres:v:50:y:2024:i:11
    DOI: 10.4054/DemRes.2024.50.11
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    References listed on IDEAS

    as
    1. Vaupel, James W, 1998. "Demographic Analysis of Aging and Longevity," American Economic Review, American Economic Association, vol. 88(2), pages 242-247, May.
    2. James W. Vaupel & Zhen Zhang, 2010. "Attrition in heterogeneous cohorts," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 23(26), pages 737-748.
    3. repec:cai:popine:popu_p2001_13n1_0171 is not listed on IDEAS
    4. Vladimir Canudas-Romo, 2010. "Three measures of longevity: Time trends and record values," Demography, Springer;Population Association of America (PAA), vol. 47(2), pages 299-312, May.
    5. A. Roger Thatcher & Siu Lan Karen Cheung & Shiro Horiuchi & Jean-Marie Robine, 2010. "The compression of deaths above the mode," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 22(17), pages 505-538.
    6. repec:cai:poeine:pope_303_0303 is not listed on IDEAS
    7. Trifon Missov & Adam Lenart & Laszlo Nemeth & Vladimir Canudas-Romo & James W. Vaupel, 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.
    8. Marie-Pier Bergeron-Boucher & Marcus Ebeling & Vladimir Canudas-Romo, 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.
    9. Nadine Ouellette & Robert Bourbeau, 2011. "Changes in the age-at-death distribution in four low mortality countries: A nonparametric approach," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 25(19), pages 595-628.
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    11. Ugofilippo Basellini & Carlo Giovanni Camarda, 2019. "Modelling and forecasting adult age-at-death distributions," Population Studies, Taylor & Francis Journals, vol. 73(1), pages 119-138, January.
    12. Shiro Horiuchi & Nadine Ouellette & Siu Lan Karen Cheung & Jean-Marie Robine, 2013. "Modal age at death: lifespan indicator in the era of longevity extension," Vienna Yearbook of Population Research, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna, vol. 11(1), pages 37-69.
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    14. Viorela Diaconu & Alyson van Raalte & Pekka Martikainen, 2022. "Why we should monitor disparities in old-age mortality with the modal age at death," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-13, February.
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    More about this item

    Keywords

    longevity; modal age at death; mathematical demography;
    All these keywords.

    JEL classification:

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

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