IDEAS home Printed from https://ideas.repec.org/a/dem/demres/v22y2010i17.html
   My bibliography  Save this article

The compression of deaths above the mode

Author

Listed:
  • A. Roger Thatcher

    (Office for National Statistics)

  • Siu Lan Karen Cheung

    (University of Hong Kong)

  • Shiro Horiuchi

    (City University of New York)

  • Jean-Marie Robine

    (Institut National de la Santé et de la Recherche Médicale (INSERM))

Abstract

Kannisto (2001) has shown that as the frequency distribution of ages at death has shifted to the right, the age distribution of deaths above the modal age has become more compressed. In order to further investigate this old-age mortality compression, we adopt the simple logistic model with two parameters, which is known to fit data on old-age mortality well (Thatcher 1999). Based on the model, we show that three key measures of old-age mortality (the modal age of adult deaths, the life expectancy at the modal age, and the standard deviation of ages at death above the mode) can be estimated fairly accurately from death rates at only two suitably chosen high ages (70 and 90 in this study). The distribution of deaths above the modal age becomes compressed when the logits of death rates fall more at the lower age than at the higher age. Our analysis of mortality time series in six countries, using the logistic model, endorsed Kannisto’s conclusion. Some possible reasons for the compression are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:dem:demres:v:22:y:2010:i:17
    DOI: 10.4054/DemRes.2010.22.17
    as

    Download full text from publisher

    File URL: https://www.demographic-research.org/volumes/vol22/17/22-17.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.4054/DemRes.2010.22.17?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. Siu Lan Karen Cheung & Jean-Marie Robine & Fred Paccaud & Alfio Marazzi, 2009. "Dissecting the compression of mortality in Switzerland, 1876-2005," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 21(19), pages 569-598.
    2. repec:cai:popine:popu_p2001_13n1_0171 is not listed on IDEAS
    3. 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.
    4. Väinö Kannisto, 2000. "Measuring the compression of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(6).
    5. John Wilmoth & Shiro Horiuchi, 1999. "Rectangularization revisited: Variability of age at death within human populations," Demography, Springer;Population Association of America (PAA), vol. 36(4), pages 475-495, November.
    6. A. R. Thatcher, 1999. "The long‐term pattern of adult mortality and the highest attained age," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 5-43.
    7. Siu Cheung & Jean-Marie Robine & Edward Tu & Graziella Caselli, 2005. "Three dimensions of the survival curve: horizontalization, verticalization, and longevity extension," Demography, Springer;Population Association of America (PAA), vol. 42(2), pages 243-258, May.
    8. John Bongaarts, 2005. "Long-range trends in adult mortality: Models and projection methods," Demography, Springer;Population Association of America (PAA), vol. 42(1), pages 23-49, February.
    9. Vladimir Canudas-Romo, 2008. "The modal age at death and the shifting mortality hypothesis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 19(30), pages 1179-1204.
    10. 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.
    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. Ediev, Dalkhat M. & Sanderson, Warren C. & Scherbov, Sergei, 2019. "The inverse relationship between life expectancy-induced changes in the old-age dependency ratio and the prospective old-age dependency ratio," Theoretical Population Biology, Elsevier, vol. 125(C), pages 1-10.
    2. 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.
    3. Jean-Marie Robine & Siu Lan Karen Cheung & Shiro Horiuchi, 2010. "Arthur Roger Thatcher's contributions to longevity research," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 22(18), pages 539-548.
    4. Viorela Diaconu & Nadine Ouellette & Carlo Giovanni Camarda & Robert Bourbeau, 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.
    5. Matthias Börger & Martin Genz & Jochen Ruß, 2018. "Extension, Compression, and Beyond: A Unique Classification System for Mortality Evolution Patterns," Demography, Springer;Population Association of America (PAA), vol. 55(4), pages 1343-1361, August.
    6. Magdalena Muszyńska, 2012. "Zróżnicowanie długości trwania życia w Polsce," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 28, pages 85-96.
    7. Ainhoa-Elena Léger & Stefano Mazzuco, 2021. "What Can We Learn from the Functional Clustering of Mortality Data? An Application to the Human Mortality Database," European Journal of Population, Springer;European Association for Population Studies, vol. 37(4), pages 769-798, November.
    8. Dustin Brown & Mark Hayward & Jennifer Montez & Robert Hummer & Chi-Tsun Chiu & Mira Hidajat, 2012. "The Significance of Education for Mortality Compression in the United States," Demography, Springer;Population Association of America (PAA), vol. 49(3), pages 819-840, August.
    9. 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.
    10. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1615-1640, October.
    11. Alyson A. van Raalte & Pekka Martikainen & Mikko Myrskylä, 2012. "Lifespan variation by occupational class: compression or stagnation over time?," MPIDR Working Papers WP-2012-010, Max Planck Institute for Demographic Research, Rostock, Germany.
    12. 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.
    13. Alberto Palloni & Laeticia Souza, 2013. "The fragility of the future and the tug of the past," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 29(21), pages 543-578.
    14. Mikhail A. Maksimov, 2019. "Dynamics of modal age at death in 1959−2014 in Russia," Population and Economics, ARPHA Platform, vol. 3(4), pages 86-96, December.
    15. Konstantinos N. Zafeiris, 2023. "Greece since the 1960s: the mortality transition revisited: a joinpoint regression analysis," Journal of Population Research, Springer, vol. 40(1), pages 1-31, March.
    16. Isaac Sasson, 2016. "Trends in Life Expectancy and Lifespan Variation by Educational Attainment: United States, 1990–2010," Demography, Springer;Population Association of America (PAA), vol. 53(2), pages 269-293, April.
    17. 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.
    18. Basellini, Ugofilippo & Kjærgaard, Søren & Camarda, Carlo Giovanni, 2020. "An age-at-death distribution approach to forecast cohort mortality," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 129-143.

    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. 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.
    2. 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.
    3. 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.
    4. Gonzaga, Marcos Roberto & Queiroz, Bernardo L & Lima, Everton, 2017. "Compression of mortality: the evolution in the variability in the age of death in Latin America," OSF Preprints pdnfk, Center for Open Science.
    5. 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.
    6. Jean-Marie Robine & Siu Lan Karen Cheung & Shiro Horiuchi, 2010. "Arthur Roger Thatcher's contributions to longevity research," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 22(18), pages 539-548.
    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. Shripad Tuljapurkar & Ryan Edwards, 2011. "Variance in death and its implications for modeling and forecasting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 24(21), pages 497-526.
    9. Matthias Börger & Martin Genz & Jochen Ruß, 2018. "Extension, Compression, and Beyond: A Unique Classification System for Mortality Evolution Patterns," Demography, Springer;Population Association of America (PAA), vol. 55(4), pages 1343-1361, August.
    10. Pinheiro, Pedro Cisalpino & Queiroz, Bernardo L, 2018. "Regional Disparities in Brazilian Adult Mortality: an analysis using Modal Age at Death (M) and Compression of Mortality (IQR)," OSF Preprints t2ey3, Center for Open Science.
    11. Konstantinos N. Zafeiris, 2023. "Greece since the 1960s: the mortality transition revisited: a joinpoint regression analysis," Journal of Population Research, Springer, vol. 40(1), pages 1-31, March.
    12. Christina Bohk-Ewald & Marcus Ebeling & Roland Rau, 2017. "Lifespan Disparity as an Additional Indicator for Evaluating Mortality Forecasts," Demography, Springer;Population Association of America (PAA), vol. 54(4), pages 1559-1577, August.
    13. Siu Lan Karen Cheung & Jean-Marie Robine & Fred Paccaud & Alfio Marazzi, 2009. "Dissecting the compression of mortality in Switzerland, 1876-2005," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 21(19), pages 569-598.
    14. Dustin Brown & Mark Hayward & Jennifer Montez & Robert Hummer & Chi-Tsun Chiu & Mira Hidajat, 2012. "The Significance of Education for Mortality Compression in the United States," Demography, Springer;Population Association of America (PAA), vol. 49(3), pages 819-840, August.
    15. Isaac Sasson, 2016. "Trends in Life Expectancy and Lifespan Variation by Educational Attainment: United States, 1990–2010," Demography, Springer;Population Association of America (PAA), vol. 53(2), pages 269-293, April.
    16. Ediev, Dalkhat M. & Sanderson, Warren C. & Scherbov, Sergei, 2019. "The inverse relationship between life expectancy-induced changes in the old-age dependency ratio and the prospective old-age dependency ratio," Theoretical Population Biology, Elsevier, vol. 125(C), pages 1-10.
    17. Duncan Gillespie & Meredith Trotter & Shripad Tuljapurkar, 2014. "Divergence in Age Patterns of Mortality Change Drives International Divergence in Lifespan Inequality," Demography, Springer;Population Association of America (PAA), vol. 51(3), pages 1003-1017, June.
    18. 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.
    19. Basellini, Ugofilippo & Kjærgaard, Søren & Camarda, Carlo Giovanni, 2020. "An age-at-death distribution approach to forecast cohort mortality," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 129-143.
    20. Michal Engelman & Vladimir Canudas‐Romo & Emily M. Agree, 2010. "The Implications of Increased Survivorship for Mortality Variation in Aging Populations," Population and Development Review, The Population Council, Inc., vol. 36(3), pages 511-539, September.

    More about this item

    Keywords

    compression of mortality; logistic model; modal age of death; standard deviation; oldest old mortality decline; Lexis model;
    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:22:y:2010:i:17. 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.