IDEAS home Printed from https://ideas.repec.org/a/spr/eurpop/v37y2021i4d10.1007_s10680-021-09588-y.html
   My bibliography  Save this article

What Can We Learn from the Functional Clustering of Mortality Data? An Application to the Human Mortality Database

Author

Listed:
  • Ainhoa-Elena Léger

    (University of Padua)

  • Stefano Mazzuco

    (University of Padua)

Abstract

This study analyzed whether there are different patterns of mortality decline among low-mortality countries by identifying the role played by all the mortality components. We implemented a cluster analysis using a functional data analysis (FDA) approach, which allowed us to consider age-specific mortality rather than summary measures, as it analyses curves rather than scalar data. Combined with a functional principal component analysis, it can identify what part of the curves is responsible for assigning one country to a specific cluster. FDA clustering was applied to the data from 32 countries in the Human Mortality Database from 1960 to 2018 to provide a comprehensive understanding of their patterns of mortality. The results show that the evolution of developed countries followed the same pattern of stages (with different timings): (1) a reduction of infant mortality, (2) an increase of premature mortality and (3) a shift and compression of deaths. Some countries were following this scheme and recovering the gap with precursors; others did not show signs of recovery. Eastern European countries were still at Stage (2), and it was not clear if and when they will enter Stage 3. All the country differences related to the different timings with which countries underwent the stages, as identified by the clusters.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurpop:v:37:y:2021:i:4:d:10.1007_s10680-021-09588-y
    DOI: 10.1007/s10680-021-09588-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10680-021-09588-y
    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/s10680-021-09588-y?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. C. Abraham & P. A. Cornillon & E. Matzner‐Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B‐Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 581-595, September.
    2. Nan Li & Ronald Lee, 2005. "Coherent mortality forecasts for a group of populations: An extension of the lee-carter method," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 575-594, August.
    3. Anthony Medford & Kaare Christensen & Axel Skytthe & James W. Vaupel, 2019. "A Cohort Comparison of Lifespan After Age 100 in Denmark and Sweden: Are Only the Oldest Getting Older?," Demography, Springer;Population Association of America (PAA), vol. 56(2), pages 665-677, April.
    4. Marie-Pier Bergeron-Boucher & Vladimir Canudas-Romo & James E. Oeppen & James W. Vaupel, 2017. "Coherent forecasts of mortality with compositional data analysis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 37(17), pages 527-566.
    5. Debón, A. & Chaves, L. & Haberman, S. & Villa, F., 2017. "Characterization of between-group inequality of longevity in European Union countries," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 151-165.
    6. 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.
    7. Booth, H. & Tickle, L., 2008. "Mortality Modelling and Forecasting: a Review of Methods," Annals of Actuarial Science, Cambridge University Press, vol. 3(1-2), pages 3-43, September.
    8. Marcus Ebeling & Roland Rau & Annette Baudisch, 2018. "Rectangularization of the survival curve reconsidered: The maximum inner rectangle approach," Population Studies, Taylor & Francis Journals, vol. 72(3), pages 369-379, September.
    9. repec:cai:popine:popu_p2001_13n1_0171 is not listed on IDEAS
    10. 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.
    11. Shripad Tuljapurkar & Nan Li & Carl Boe, 2000. "A universal pattern of mortality decline in the G7 countries," Nature, Nature, vol. 405(6788), pages 789-792, June.
    12. 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.
    13. 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.
    14. Vladimir Shkolnikov & Evgeny Andreev & Zhen Zhang & James Oeppen & James Vaupel, 2011. "Losses of Expected Lifetime in the United States and Other Developed Countries: Methods and Empirical Analyses," Demography, Springer;Population Association of America (PAA), vol. 48(1), pages 211-239, February.
    15. Rob Hyndman & Heather Booth & Farah Yasmeen, 2013. "Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models," Demography, Springer;Population Association of America (PAA), vol. 50(1), pages 261-283, February.
    16. Charles Bouveyron & Julien Jacques, 2011. "Model-based clustering of time series in group-specific functional subspaces," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 281-300, December.
    17. Shang, Han Lin & Haberman, Steven, 2020. "Forecasting age distribution of death counts: an application to annuity pricing," Annals of Actuarial Science, Cambridge University Press, vol. 14(1), pages 150-169, March.
    18. repec:cai:poeine:pope_201_0157 is not listed on IDEAS
    19. 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.
    20. Hatzopoulos, P. & Haberman, S., 2013. "Common mortality modeling and coherent forecasts. An empirical analysis of worldwide mortality data," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 320-337.
    21. James G.M. & Sugar C.A., 2003. "Clustering for Sparsely Sampled Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 397-408, January.
    22. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    23. 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.
    24. Renshaw, A.E. & Haberman, S., 2006. "A cohort-based extension to the Lee-Carter model for mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 556-570, June.
    25. Camarda, Carlo G., 2012. "MortalitySmooth: An R Package for Smoothing Poisson Counts with P-Splines," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i01).
    26. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    27. Julien Jacques & Cristian Preda, 2014. "Functional data clustering: a survey," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 231-255, September.
    28. Nan Li & Ronald Lee & Patrick Gerland, 2013. "Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections," Demography, Springer;Population Association of America (PAA), vol. 50(6), pages 2037-2051, December.
    29. Haberman, Steven & Renshaw, Arthur, 2012. "Parametric mortality improvement rate modelling and projecting," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 309-333.
    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. Alaimo, Leonardo Salvatore & Nigri, Andrea, 2024. "The gender gap in life expectancy and lifespan disparity as social risk indicators for international countries: A fuzzy clustering approach," Socio-Economic Planning Sciences, Elsevier, vol. 91(C).

    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. Marie-Pier Bergeron-Boucher & Søren Kjærgaard & James E. Oeppen & James W. Vaupel, 2019. "The impact of the choice of life table statistics when forecasting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(43), pages 1235-1268.
    2. Carlo G. Camarda & Ugofilippo Basellini, 2021. "Smoothing, Decomposing and Forecasting Mortality Rates," European Journal of Population, Springer;European Association for Population Studies, vol. 37(3), pages 569-602, July.
    3. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2023. "Thirty years on: A review of the Lee–Carter method for forecasting mortality," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1033-1049.
    4. 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.
    5. Ahbab Mohammad Fazle Rabbi & Stefano Mazzuco, 2021. "Mortality Forecasting with the Lee–Carter Method: Adjusting for Smoothing and Lifespan Disparity," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 97-120, March.
    6. de Jong, Piet & Tickle, Leonie & Xu, Jianhui, 2016. "Coherent modeling of male and female mortality using Lee–Carter in a complex number framework," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 130-137.
    7. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2022. "Thirty years on: A review of the Lee-Carter method for forecasting mortality," SocArXiv 8u34d, Center for Open Science.
    8. Ricarda Duerst & Jonas Schöley & Christina Bohk-Ewald, 2023. "A validation workflow for mortality forecasting," MPIDR Working Papers WP-2023-020, Max Planck Institute for Demographic Research, Rostock, Germany.
    9. Hong Li & Johnny Siu-Hang Li, 2017. "Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements," Demography, Springer;Population Association of America (PAA), vol. 54(3), pages 1073-1095, June.
    10. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    11. Marie-Pier Bergeron-Boucher & Vladimir Canudas-Romo & James E. Oeppen & James W. Vaupel, 2017. "Coherent forecasts of mortality with compositional data analysis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 37(17), pages 527-566.
    12. 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.
    13. Carlo Giovanni Camarda, 2019. "Smooth constrained mortality forecasting," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(38), pages 1091-1130.
    14. Guibert, Quentin & Lopez, Olivier & Piette, Pierrick, 2019. "Forecasting mortality rate improvements with a high-dimensional VAR," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 255-272.
    15. 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.
    16. Shang, Han Lin & Haberman, Steven & Xu, Ruofan, 2022. "Multi-population modelling and forecasting life-table death counts," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 239-253.
    17. Rizzi, Silvia & Kjærgaard, Søren & Bergeron Boucher, Marie-Pier & Camarda, Carlo Giovanni & Lindahl-Jacobsen, Rune & Vaupel, James W., 2021. "Killing off cohorts: Forecasting mortality of non-extinct cohorts with the penalized composite link model," International Journal of Forecasting, Elsevier, vol. 37(1), pages 95-104.
    18. Katrien Antonio & Anastasios Bardoutsos & Wilbert Ouburg, 2015. "Bayesian Poisson log-bilinear models for mortality projections with multiple populations," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 485564, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    19. Ugofilippo Basellini & Søren Kjærgaard & Carlo Giovanni Camarda, 2020. "An age-at-death distribution approach to forecast cohort mortality," Working Papers axafx5_3agsuwaphvlfk, French Institute for Demographic Studies.
    20. Emanuele Aliverti & Stefano Mazzuco & Bruno Scarpa, 2022. "Dynamic modelling of mortality via mixtures of skewed distribution functions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1030-1048, 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:4:d:10.1007_s10680-021-09588-y. 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.