IDEAS home Printed from https://ideas.repec.org/a/spr/eurpop/v37y2021i1d10.1007_s10680-019-09552-x.html
   My bibliography  Save this article

A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality

Author

Listed:
  • Lucia Zanotto

    (Ca’ Foscari University of Venice)

  • Vladimir Canudas-Romo

    (Australian National University)

  • Stefano Mazzuco

    (University of Padua)

Abstract

Premature mortality is often a neglected component of overall deaths, and the most difficult to identify. However, it is important to estimate its prevalence. Following Pearson’s theory about mortality components, a definition of premature deaths and a parametric model to study its transformations are introduced. The model is a mixture of three distributions: a Half Normal for the first part of the death curve and two Skew Normals to fit the remaining pieces. One advantage of the model is the possibility of obtaining an explicit equation to compute life expectancy at birth and to break it down into mortality components. We estimated the mixture model for Sweden, France, East Germany and Czech Republic. In addition, to the well-known reduction in infant deaths, and compression and shifting trend of adult mortality, we were able to study the trend of the central part of the distribution of deaths in detail. In general, a right shift of the modal age at death for young adults is observed; in some cases, it is also accompanied by an increase in the number of deaths at these ages: in particular for France, in the last twenty years, premature mortality increases.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:eurpop:v:37:y:2021:i:1:d:10.1007_s10680-019-09552-x
    DOI: 10.1007/s10680-019-09552-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10680-019-09552-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10680-019-09552-x?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. Scott Lynch & J. Brown, 2001. "Reconsidering mortality compression and deceleration: an alternative model of mortality rates," Demography, Springer;Population Association of America (PAA), vol. 38(1), pages 79-95, February.
    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. Peter Congdon, 1993. "Statistical Graduation in Local Demographic Analysis and Projection," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 156(2), pages 237-270, March.
    4. Marcus Ebeling, 2018. "How Has the Lower Boundary of Human Mortality Evolved, and Has It Already Stopped Decreasing?," Demography, Springer;Population Association of America (PAA), vol. 55(5), pages 1887-1903, October.
    5. Mullen, Katharine M. & Ardia, David & Gil, David L. & Windover, Donald & Cline, James, 2011. "DEoptim: An R Package for Global Optimization by Differential Evolution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i06).
    6. 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.
    7. Adrien Remund & Carlo G. Camarda & Tim Riffe, 2018. "A Cause-of-Death Decomposition of Young Adult Excess Mortality," Demography, Springer;Population Association of America (PAA), vol. 55(3), pages 957-978, June.
    8. repec:cai:popine:popu_p2001_13n1_0171 is not listed on IDEAS
    9. 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.
    10. Steve Bennett, 1983. "Log‐Logistic Regression Models for Survival Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(2), pages 165-171, June.
    11. Trifon Missov, 2013. "Gamma-Gompertz life expectancy at birth," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(9), pages 259-270.
    12. Stefano Mazzuco & Bruno Scarpa & Lucia Zanotto, 2018. "A mortality model based on a mixture distribution function," Population Studies, Taylor & Francis Journals, vol. 72(2), pages 191-200, May.
    13. 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.
    14. Väinö Kannisto, 2000. "Measuring the compression of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(6).
    15. 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.
    16. Willets, R. C., 2004. "The Cohort Effect: Insights and Explanations," British Actuarial Journal, Cambridge University Press, vol. 10(4), pages 833-877, October.
    17. Michal Engelman & Hal Caswell & Emily Agree, 2014. "Why do lifespan variability trends for the young and old diverge? A perturbation analysis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(48), pages 1367-1396.
    18. 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.
    19. 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.
    20. James Vaupel & Vladimir Romo, 2003. "Decomposing change in life expectancy: A bouquet of formulas in honor of Nathan Keyfitz’s 90th birthday," Demography, Springer;Population Association of America (PAA), vol. 40(2), pages 201-216, May.
    21. 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.
    22. 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.
    23. Ryan D. Edwards & Shripad Tuljapurkar, 2005. "Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries," Population and Development Review, The Population Council, Inc., vol. 31(4), pages 645-674, December.
    24. Virginia Zarulli & Domantas Jasilionis & Dmitri Jdanov, 2012. "Changes in educational differentials in old-age mortality in Finland and Sweden between 1971-1975 and 1996-2000," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 26(19), pages 489-510.
    25. 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.
    26. Missov, Trifon I. & Lenart, Adam, 2013. "Gompertz–Makeham life expectancies: Expressions and applications," Theoretical Population Biology, Elsevier, vol. 90(C), pages 29-35.
    27. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2008. "The centred parametrization for the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1362-1382, August.
    28. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    29. Shiro Horiuchi & John Wilmoth, 1998. "Deceleration in the age pattern of mortality at olderages," Demography, Springer;Population Association of America (PAA), vol. 35(4), pages 391-412, November.
    30. repec:cai:popine:popu_p2001_13n1_0193 is not listed on IDEAS
    31. Dalstra, J.A.A. & Kunst, A.E. & Mackenbach, J.P., 2006. "A comparative appraisal of the relationship of education, income and housing tenure with less than good health among the elderly in Europe," Social Science & Medicine, Elsevier, vol. 62(8), pages 2046-2060, April.
    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. Lanfiuti Baldi, Giacomo & NIGRI, ANDREA, 2023. "An Age-Period-Cohort model for gender gap in youth mortality," OSF Preprints z3qmw, Center for Open Science.

    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. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Jorge M. Uribe & Helena Chuliá & Montserrat Guillen, 2018. "Trends in the Quantiles of the Life Table Survivorship Function," European Journal of Population, Springer;European Association for Population Studies, vol. 34(5), pages 793-817, December.
    9. 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.
    10. 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.
    11. 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.
    12. Joel E. Cohen & Christina Bohk & Roland Rau, 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.
    13. Alexander, Monica, 2018. "Deaths without denominators: using a matched dataset to study mortality patterns in the United States," SocArXiv q79ye, Center for Open Science.
    14. 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.
    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. 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.
    17. 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.
    18. Bonetti, Marco & Basellini, Ugofilippo & NIGRI, ANDREA, 2023. "The Average Uneven Mortality index: Building on the "e-dagger" measure of lifespan inequality," SocArXiv xb6vq, Center for Open Science.
    19. Bergeron-Boucher, Marie-Pier & Vázquez-Castillo, Paola & Missov, Trifon, 2022. "A modal age at death approach to forecasting mortality," SocArXiv 5zr2k, Center for Open Science.
    20. Suryakant Yadav, 2021. "Progress of Inequality in Age at Death in India: Role of Adult Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 37(3), pages 523-550, July.

    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:spr:eurpop:v:37:y:2021:i:1:d:10.1007_s10680-019-09552-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.