IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v126y2026ics0167668725001404.html

An age–period–cohort model in a Dirichlet framework: A coherent causes of death estimation

Author

Listed:
  • Graziani, Rebecca
  • Nigri, Andrea

Abstract

Though pivotal in longevity studies, multi-outcome modelling is largely neglected in the associated statistical literature. Here, we focus on the case of compositional data, especially relevant in longevity analysis, where overall mortality can be described as the composition of several causes of death. We propose an age–period–cohort model within the Dirichlet framework with a specific interest in its use for modelling longevity with multiple causes of death. We introduce a flexible approach to incorporating the Dirichlet distribution into the age–period–cohort framework. Then, using US cause-specific mortality data, we provide a comprehensive discussion and comparison of alternative modelling approaches.

Suggested Citation

  • Graziani, Rebecca & Nigri, Andrea, 2026. "An age–period–cohort model in a Dirichlet framework: A coherent causes of death estimation," Insurance: Mathematics and Economics, Elsevier, vol. 126(C).
    • Handle: RePEc:eee:insuma:v:126:y:2026:i:c:s0167668725001404
    DOI: 10.1016/j.insmatheco.2025.103194
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668725001404
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2025.103194?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

    for a different version of it.

    References listed on IDEAS

    as
    1. R. Thompson & R. J. Baker, 1981. "Composite Link Functions in Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(2), pages 125-131, June.
    2. Andrew Hunt & David Blake, 2014. "A General Procedure for Constructing Mortality Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 116-138.
    3. 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.
    4. Søren Kjærgaard & Yunus Emre Ergemen & Malene Kallestrup‐Lamb & Jim Oeppen & Rune Lindahl‐Jacobsen, 2019. "Forecasting causes of death by using compositional data analysis: the case of cancer deaths," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(5), pages 1351-1370, November.
    5. Gueorguieva, Ralitza & Rosenheck, Robert & Zelterman, Daniel, 2008. "Dirichlet component regression and its applications to psychiatric data," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5344-5355, August.
    6. 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.
    7. John Hobcraft & Jane Menken & Samuel Preston, 1985. "Age, Period, and Cohort Effects in Demography: A Review," Springer Books, in: William M. Mason & Stephen E. Fienberg (ed.), Cohort Analysis in Social Research, chapter 4, pages 89-135, Springer.
    8. Søren Kjærgaard & Yunus Emre Ergemen & Malene Kallestrup-Lamb & Jim Oeppen & Rune Lindahl-Jacobsen, 2019. "Forecasting Causes of Death using Compositional Data Analysis: the Case of Cancer Deaths," CREATES Research Papers 2019-07, Department of Economics and Business Economics, Aarhus University.
    9. Francesco Billari & Rebecca Graziani, 2024. "Age-period-cohort analysis of U.S. fertility: a realistic approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(4), pages 3021-3040, August.
    10. Colin D Mathers & Dejan Loncar, 2006. "Projections of Global Mortality and Burden of Disease from 2002 to 2030," PLOS Medicine, Public Library of Science, vol. 3(11), pages 1-20, November.
    11. Dimitrova, Dimitrina S. & Haberman, Steven & Kaishev, Vladimir K., 2013. "Dependent competing risks: Cause elimination and its impact on survival," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 464-477.
    12. Jason Hilton & Erengul Dodd & Jonathan J. Forster & Peter W. F. Smith, 2019. "Projecting UK mortality by using Bayesian generalized additive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(1), pages 29-49, January.
    13. Andrew Cairns & David Blake & Kevin Dowd & Guy Coughlan & David Epstein & Alen Ong & Igor Balevich, 2009. "A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 1-35.
    14. Séverine Arnold (-Gaille) & Michael Sherris, 2013. "Forecasting Mortality Trends Allowing for Cause-of-Death Mortality Dependence," North American Actuarial Journal, Taylor & Francis Journals, vol. 17(4), pages 273-282.
    15. Kaishev, Vladimir K. & Dimitrova, Dimitrina S. & Haberman, Steven, 2007. "Modelling the joint distribution of competing risks survival times using copula functions," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 339-361, November.
    16. Alai, Daniel H. & Arnold (-Gaille), Séverine & Sherris, Michael, 2015. "Modelling cause-of-death mortality and the impact of cause-elimination," Annals of Actuarial Science, Cambridge University Press, vol. 9(1), pages 167-186, March.
    17. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    18. Marco Stefanucci & Stefano Mazzuco, 2022. "Analysing cause‐specific mortality trends using compositional functional data analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 61-83, January.
    19. Kenneth Manton & Sharon Poss, 1979. "Effects of dependency among causes of death for cause elimination life table strategies," Demography, Springer;Population Association of America (PAA), vol. 16(2), pages 313-327, May.
    20. Cesare, Mariachiara Di & Murphy, Mike, 2009. "Forecasting Mortality, Different Approaches for Different Cause of Deaths? The Cases of Lung Cancer; Influenza, Pneumonia, and Bronchitis; and Motor Vehicle Accidents," British Actuarial Journal, Cambridge University Press, vol. 15(S1), pages 185-211, January.
    21. repec:cup:bracjl:v:24:y:2019:i::p:-_13 is not listed on IDEAS
    22. Terence Mills, 2010. "Forecasting compositional time series," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(4), pages 673-690, June.
    23. Richards, S. J., 2009. "Selected Issues in Modelling Mortality by Cause and in Small Populations," British Actuarial Journal, Cambridge University Press, vol. 15(S1), pages 267-283, January.
    24. Kyle J. Foreman & Guangquan Li & Nicky Best & Majid Ezzati, 2017. "Small area forecasts of cause-specific mortality: application of a Bayesian hierarchical model to US vital registration data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 121-139, January.
    25. Giovanni Cardillo & Paolo Giordani & Susanna Levantesi & Andrea Nigri & Alessandro Spelta, 2023. "Mortality forecasting using the four-way CANDECOMP/PARAFAC decomposition," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2023(9), pages 916-932, October.
    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. repec:osf:socarx:856yw_v1 is not listed on IDEAS
    2. Graziani, Rebecca & NIGRI, ANDREA, 2023. "An Age–Period–Cohort Model in a Dirichlet Framework: A Coherent Causes of Death Estimation," SocArXiv 856yw, Center for Open Science.
    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. repec:osf:socarx:8u34d_v1 is not listed on IDEAS
    5. 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.
    6. 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.
    7. Søren Kjærgaard & Yunus Emre Ergemen & Marie-Pier Bergeron Boucher & Jim Oeppen & Malene Kallestrup-Lamb, 2019. "Longevity forecasting by socio-economic groups using compositional data analysis," CREATES Research Papers 2019-08, Department of Economics and Business Economics, Aarhus University.
    8. S⊘ren Kjærgaard & Yunus Emre Ergemen & Marie‐Pier Bergeron‐Boucher & Jim Oeppen & Malene Kallestrup‐Lamb, 2020. "Longevity forecasting by socio‐economic groups using compositional data analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1167-1187, June.
    9. Li, Han & Li, Hong & Lu, Yang & Panagiotelis, Anastasios, 2019. "A forecast reconciliation approach to cause-of-death mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 122-133.
    10. 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.
    11. Søren Kjærgaard & Yunus Emre Ergemen & Malene Kallestrup-Lamb & Jim Oeppen & Rune Lindahl-Jacobsen, 2019. "Forecasting Causes of Death using Compositional Data Analysis: the Case of Cancer Deaths," CREATES Research Papers 2019-07, Department of Economics and Business Economics, Aarhus University.
    12. repec:osf:socarx:d7hbp_v1 is not listed on IDEAS
    13. Bergeron-Boucher, Marie-Pier & Kjærgaard, Søren, 2022. "Mortality forecasts by age and cause of death: How to forecast both dimensions?," SocArXiv d7hbp, Center for Open Science.
    14. 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.
    15. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2021. "Addressing the life expectancy gap in pension policy," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 200-221.
    16. Tickle Leonie & Booth Heather, 2014. "The Longevity Prospects of Australian Seniors: An Evaluation of Forecast Method and Outcome," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 8(2), pages 259-292, July.
    17. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    18. Nicholas Bett & Juma Kasozi & Daniel Ruturwa, 2022. "Temporal Clustering of the Causes of Death for Mortality Modelling," Risks, MDPI, vol. 10(5), pages 1-34, May.
    19. 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.
    20. Li, Li & Li, Han & Panagiotelis, Anastasios, 2025. "Boosting domain-specific models with shrinkage: An application in mortality forecasting," International Journal of Forecasting, Elsevier, vol. 41(1), pages 191-207.
    21. Jonas Hirz & Uwe Schmock & Pavel V. Shevchenko, 2017. "Actuarial Applications and Estimation of Extended CreditRisk+," Risks, MDPI, vol. 5(2), pages 1-29, March.
    22. Zuo, Wenyun & Damle, Anil & Tuljapurkar, Shripad, 2025. "Sensitivity and uncertainty in the Lee–Carter mortality model," International Journal of Forecasting, Elsevier, vol. 41(2), pages 781-797.
    23. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • I14 - Health, Education, and Welfare - - Health - - - Health and Inequality

    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:eee:insuma:v:126:y:2026:i:c:s0167668725001404. 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: http://www.elsevier.com/locate/inca/505554 .

    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.