IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v81y2012i4p292-299.html
   My bibliography  Save this article

On ordered subpopulations and population mortality at advanced ages

Author

Listed:
  • Finkelstein, Maxim

Abstract

We consider hazard (mortality) rates in heterogeneous populations consisting of ordered (in the defined stochastic sense) subpopulations. This setting can be interpreted via the fixed frailty models with one or more frailty parameters. The shape of the hazard rate is of main interest in this paper. Specifically, the deceleration and leveling off in the hazard rates (mortality plateaus) are discussed and some examples of lifetime distributions that can result in asymptotically flat hazard rates are considered. These examples are based on vitality models when an organism’s initial vitality (resource) is ‘consumed’ in the course of life in accordance with a simple stochastic process (e.g., the Wiener process with drift or the gamma process).

Suggested Citation

  • Finkelstein, Maxim, 2012. "On ordered subpopulations and population mortality at advanced ages," Theoretical Population Biology, Elsevier, vol. 81(4), pages 292-299.
  • Handle: RePEc:eee:thpobi:v:81:y:2012:i:4:p:292-299
    DOI: 10.1016/j.tpb.2012.01.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S004058091200007X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.tpb.2012.01.005?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Missov, Trifon I. & Finkelstein, Maxim, 2011. "Admissible mixing distributions for a general class of mixture survival models with known asymptotics," Theoretical Population Biology, Elsevier, vol. 80(1), pages 64-70.
    2. repec:cai:popine:popu_p1976_31n3_0692 is not listed on IDEAS
    3. David Steinsaltz & Kenneth Wachter, 2006. "Understanding Mortality Rate Deceleration and Heterogeneity," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(1), pages 19-37.
    4. Maxim Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 643-663, November.
    5. Maxim S. Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," MPIDR Working Papers WP-2009-031, Max Planck Institute for Demographic Research, Rostock, Germany.
    6. Li, Ting & Anderson, James J., 2009. "The vitality model: A way to understand population survival and demographic heterogeneity," Theoretical Population Biology, Elsevier, vol. 76(2), pages 118-131.
    7. Anatoli Yashin & Ivan Iachine & Alexander Begun, 2000. "Mortality modeling: A review," Mathematical Population Studies, Taylor & Francis Journals, vol. 8(4), pages 305-332.
    8. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
    9. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    10. Liao, Haitao & Elsayed, Elsayed A. & Chan, Ling-Yau, 2006. "Maintenance of continuously monitored degrading systems," European Journal of Operational Research, Elsevier, vol. 175(2), pages 821-835, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "Justifying the Gompertz curve of mortality via the generalized Polya process of shocks," Theoretical Population Biology, Elsevier, vol. 109(C), pages 54-62.
    2. Elizabeth Wrigley-Field, 2020. "Multidimensional Mortality Selection: Why Individual Dimensions of Frailty Don’t Act Like Frailty," Demography, Springer;Population Association of America (PAA), vol. 57(2), pages 747-777, April.
    3. Finkelstein, Maxim, 2013. "Lifesaving, delayed deaths and cure in mortality modeling," Theoretical Population Biology, Elsevier, vol. 83(C), pages 15-19.
    4. Cha, Ji Hwan & Finkelstein, Maxim, 2014. "Some notes on unobserved parameters (frailties) in reliability modeling," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 99-103.

    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. Maxim S. Finkelstein, 2011. "On ordered subpopulations and population mortality at advanced ages," MPIDR Working Papers WP-2011-022, Max Planck Institute for Demographic Research, Rostock, Germany.
    2. 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.
    3. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "Justifying the Gompertz curve of mortality via the generalized Polya process of shocks," Theoretical Population Biology, Elsevier, vol. 109(C), pages 54-62.
    4. Maxim Finkelstein, 2012. "Discussing the Strehler-Mildvan model of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 26(9), pages 191-206.
    5. Ting Li & James Anderson, 2013. "Shaping human mortality patterns through intrinsic and extrinsic vitality processes," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(12), pages 341-372.
    6. MARK BEBBINGTON & CHIN-DIEW LAI & RIcARDAS ZITIKIS, 2011. "Modelling Deceleration in Senescent Mortality," Mathematical Population Studies, Taylor & Francis Journals, vol. 18(1), pages 18-37.
    7. Cha, Ji Hwan & Finkelstein, Maxim, 2014. "Some notes on unobserved parameters (frailties) in reliability modeling," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 99-103.
    8. Lai, Chin-Diew & Izadi, Muhyiddin, 2012. "Generalized logistic frailty model," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1969-1977.
    9. Elizabeth Wrigley-Field, 2014. "Mortality Deceleration and Mortality Selection: Three Unexpected Implications of a Simple Model," Demography, Springer;Population Association of America (PAA), vol. 51(1), pages 51-71, February.
    10. Li, Ting & Anderson, James J., 2009. "The vitality model: A way to understand population survival and demographic heterogeneity," Theoretical Population Biology, Elsevier, vol. 76(2), pages 118-131.
    11. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2021. "Optimal warranty policy with inspection for heterogeneous, stochastically degrading items," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1142-1152.
    12. Cha, Ji Hwan & Finkelstein, Maxim, 2013. "The failure rate dynamics in heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 120-128.
    13. Hal Caswell, 2014. "A matrix approach to the statistics of longevity in heterogeneous frailty models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(19), pages 553-592.
    14. Kenneth Manton & Igor Akushevich & Alexander Kulminski, 2008. "Human Mortality at Extreme Ages: Data from the NLTCS and Linked Medicare Records," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(3), pages 137-159.
    15. James W. Vaupel & Trifon Missov, 2014. "Unobserved population heterogeneity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(22), pages 659-686.
    16. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2023. "Improving classical optimal age-replacement policies for degrading items," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    17. Annamaria Olivieri & Ermanno Pitacco, 2016. "Frailty and Risk Classification for Life Annuity Portfolios," Risks, MDPI, vol. 4(4), pages 1-23, October.
    18. Hui Zheng, 2014. "Aging in the Context of Cohort Evolution and Mortality Selection," Demography, Springer;Population Association of America (PAA), vol. 51(4), pages 1295-1317, August.
    19. M S Finkelstein, 2008. "Reliability modelling for biological ageing," Journal of Risk and Reliability, , vol. 222(1), pages 1-6, March.
    20. Ting Li & Yang Yang & James Anderson, 2013. "Mortality Increase in Late-Middle and Early-Old Age: Heterogeneity in Death Processes as a New Explanation," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1563-1591, October.

    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:eee:thpobi:v:81:y:2012:i:4:p:292-299. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/intelligence .

    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.