IDEAS home Printed from https://ideas.repec.org/p/osf/socarx/2fkw3.html
   My bibliography  Save this paper

How do populations aggregate?

Author

Listed:
  • Feehan, Dennis
  • Wrigley-Field, Elizabeth

Abstract

BACKGROUND Understanding the relationship between populations at different scales plays an important role in many demographic analyses. OBJECTIVE We show that when a population can be partitioned into subgroups, the death rate for the entire population can be written as the weighted harmonic mean of the death rates in each subgroup, where the weights are given by the numbers of deaths in each subgroup. This decomposition can be generalized to other types of occurrence-exposure rate. Using different weights, the death rate for the entire population can also be expressed as an arithmetic mean of the death rates in each subgroup. CONTRIBUTION We use these relationships as a starting point for investigating how demographers can correctly aggregate rates across non-overlapping subgroups. Our analysis reveals conceptual links between classic demographic models and length-biased sampling. To illustrate how the harmonic mean can suggest new interpretations of demographic relationships, we present as an application a new expression for the frailty of the dying, given a standard demographic frailty model.

Suggested Citation

  • Feehan, Dennis & Wrigley-Field, Elizabeth, 2020. "How do populations aggregate?," SocArXiv 2fkw3, Center for Open Science.
    • Handle: RePEc:osf:socarx:2fkw3
    DOI: 10.31219/osf.io/2fkw3
    as

    Download full text from publisher

    File URL: https://osf.io/download/5fc7db456ebcc6012b46b099/
    Download Restriction: no
    File URL: https://libkey.io/10.31219/osf.io/2fkw3?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. Samuel Preston, 1976. "Family sizes of children and family sizes of women," Demography, Springer;Population Association of America (PAA), vol. 13(1), pages 105-114, February.
    2. Miguel de Carvalho, 2016. "Mean, What do You Mean?," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 270-274, July.
    3. 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.
    4. 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.
    5. Sen, Pranab Kumar, 1987. "What do the arithmetic, geometric and harmonic means tell us in length-biased sampling?," Statistics & Probability Letters, Elsevier, vol. 5(2), pages 95-98, March.
    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. Dennis Feehan & Elizabeth Wrigley-Field, 2021. "How do populations aggregate?," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 44(15), pages 363-378.
    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. Giambattista Salinari & Gustavo De Santis, 2020. "One or more rates of ageing? The extended gamma-Gompertz model (EGG)," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 211-236, June.
    4. Hui Zheng, 2020. "Unobserved population heterogeneity and dynamics of health disparities," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 43(34), pages 1009-1048.
    5. Lindholm, Mathias, 2017. "A note on the connection between some classical mortality laws and proportional frailty," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 76-82.
    6. Anders Ledberg, 2020. "Exponential increase in mortality with age is a generic property of a simple model system of damage accumulation and death," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-17, June.
    7. Alberto Palloni & Hiram Beltrán-Sánchez, 2017. "Discrete Barker Frailty and Warped Mortality Dynamics at Older Ages," Demography, Springer;Population Association of America (PAA), vol. 54(2), pages 655-671, April.
    8. Bagdonavicius, Vilijandas & Nikulin, Mikhail, 2000. "On goodness-of-fit for the linear transformation and frailty models," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 177-188, April.
    9. Filipe Costa Souza & Wilton Bernardino & Silvio C. Patricio, 2024. "How life-table right-censoring affected the Brazilian social security factor: an application of the gamma-Gompertz-Makeham model," Journal of Population Research, Springer, vol. 41(3), pages 1-38, September.
    10. David Lam, 2011. "How the World Survived the Population Bomb: Lessons From 50 Years of Extraordinary Demographic History," Demography, Springer;Population Association of America (PAA), vol. 48(4), pages 1231-1262, November.
    11. K. Motarjem & M. Mohammadzadeh & A. Abyar, 2020. "Geostatistical survival model with Gaussian random effect," Statistical Papers, Springer, vol. 61(1), pages 85-107, February.
    12. Xu, Linzhi & Zhang, Jiajia, 2010. "An EM-like algorithm for the semiparametric accelerated failure time gamma frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1467-1474, June.
    13. Annamaria Olivieri & Ermanno Pitacco, 2016. "Frailty and Risk Classification for Life Annuity Portfolios," Risks, MDPI, vol. 4(4), pages 1-23, October.
    14. James W. Vaupel, 2002. "Post-Darwinian longevity," MPIDR Working Papers WP-2002-043, Max Planck Institute for Demographic Research, Rostock, Germany.
    15. Maxim S. Finkelstein, 2005. "Shocks in homogeneous and heterogeneous populations," MPIDR Working Papers WP-2005-024, Max Planck Institute for Demographic Research, Rostock, Germany.
    16. Luping Zhao & Timothy E. Hanson, 2011. "Spatially Dependent Polya Tree Modeling for Survival Data," Biometrics, The International Biometric Society, vol. 67(2), pages 391-403, June.
    17. Yeo, Keng Leong & Valdez, Emiliano A., 2006. "Claim dependence with common effects in credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 609-629, June.
    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. Graziella Caselli & Franco Peracchi & Elisabetta Barbi & Rosa Maria Lipsi, 2003. "Differential Mortality and the Design of the Italian System of Public Pensions," LABOUR, CEIS, vol. 17(s1), pages 45-78, August.
    20. Enrique Acosta & Alain Gagnon & Nadine Ouellette & Robert R. Bourbeau & Marilia R. Nepomuceno & Alyson A. van Raalte, 2020. "The boomer penalty: excess mortality among baby boomers in Canada and the United States," MPIDR Working Papers WP-2020-003, Max Planck Institute for Demographic Research, Rostock, Germany.

    More about this item

    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:osf:socarx:2fkw3. 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: OSF (email available below). General contact details of provider: https://arabixiv.org .

    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.