Hostname: page-component-5db58dd55d-h5th4 Total loading time: 0 Render date: 2026-07-09T18:08:59.318Z Has data issue: false hasContentIssue false
  • English
  • Français

Joint models for cause-of-death mortality in multiple populations

Published online by Cambridge University Press:  18 May 2023

Nhan Huynh  and
Mike Ludkovski Open the ORCID record for Mike Ludkovski [Opens in a new window]
Nhan Huynh
Affiliation:
Department of Statistics and Applied Probability, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
Mike Ludkovski*
Affiliation:
Department of Statistics and Applied Probability, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
*
Corresponding author: Mike Ludkovski; Email: ludkovski@pstat.ucsb.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate jointly modelling age–year-specific rates of various causes of death in a multinational setting. We apply multi-output Gaussian processes (MOGPs), a spatial machine learning method, to smooth and extrapolate multiple cause-of-death mortality rates across several countries and both genders. To maintain flexibility and scalability, we investigate MOGPs with Kronecker-structured kernels and latent factors. In particular, we develop a custom multi-level MOGP that leverages the gridded structure of mortality tables to efficiently capture heterogeneity and dependence across different factor inputs. Results are illustrated with datasets from the Human Cause-of-Death Database (HCD). We discuss a case study involving cancer variations in three European nations and a US-based study that considers eight top-level causes and includes comparison to all-cause analysis. Our models provide insights into the commonality of cause-specific mortality trends and demonstrate the opportunities for respective data fusion.

Keywords

Cause-of-death modellingGaussian process modelsMultiple populationsMultiple causes of death

Information

Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 18 , Issue 1 , March 2024 , pp. 51 - 77
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Alai, D.H., (-Gaille), S. A., Bajekal, M. & Villegas, A. M. (2018). Mind the gap: a study of cause-specific mortality by socioeconomic circumstances. North American Actuarial Journal, 22(2), 161–181.CrossRefGoogle Scholar
Alvarez, M.A., Rosasco, L. & Lawrence, N.D. (2012). Kernels for vector-valued functions: a review. Foundations and Trends in Machine Learning, 4(3), 195–266.CrossRefGoogle Scholar
Anderson, R.N., Miniño, A.M., Hoyert, D.L. & Rosenberg, H. M. (2001). Comparability of cause of death between ICD-9 and ICD-10: preliminary estimates. National Vital Statistics Report, 49(2), 1–32.Google ScholarPubMed
Arash, E., Ramin, S., Saeid, S. & Sepanlou, S.G. (2020). The global, regional, and national burden of stomach cancer in 195 countries, 1990–2017: a systematic analysis for the global burden of disease study 2017. The Lancet Gastroenterology and Hepatology, 5(1), 42–54.Google Scholar
Arnold (-Gaille), S. & Sherris, M. (2013). Forecasting mortality trends allowing for cause-of-death mortality dependence. North American Actuarial Journal, 17(4), 273–282.CrossRefGoogle Scholar
Bergeron-Boucher, M.-P., Canudas-Romo, V., Oeppen, J.E. & Vaupel, J. (2017). Coherent forecasts of mortality with compositional data analysis. Demographic Research, 37(17), 527–566.CrossRefGoogle Scholar
Bonilla, E.V., Chai, K.M. & Williams, C. (2008). Multi-task Gaussian Process prediction. In Advances in Neural Information Processing Systems 20 (pp. 153–160). Curran Associates, Inc.Google Scholar
Boumezoued, A., Coulomb, J.-B., Klein, A., Louvet, D. & Titon, E. (2019). Modeling and forecasting cause-of-death mortality, technical report, Society of Actuaries.Google Scholar
Carpenter, B., Gelman, A., D.Hoffman, M., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P. & Riddell, A. (2017). Stan: a probabilistic programming language. Journal of Statistical Software, 76(1), 1–32.CrossRefGoogle Scholar
Caruana, R. (1997). Multi-task learning. Machine Learning, 28(1), 41–75.CrossRefGoogle Scholar
Caselli, G. (1996) Future longevity among elderly populations. In Health and Mortality among Elderly Populations (pp. 235–265). Oxford University Press.CrossRefGoogle Scholar
Caselli, G., Vallin, J. & Marsili, M. (2019). How useful are the causes of death when extrapolating mortality trends. an update. In Bengtsson, T. & Keilman, N. (Eds.), Old and New Perspectives on Mortality Forecasting (pp. 237–259). Springer International Publishing.CrossRefGoogle Scholar
Deville, Y., Ginsbourger, D., Roustant, O. & Durrande, N. (2019). kergp: Gaussian Process Laboratory. R package version 0.5.0.Google Scholar
Dimitrova, D.S., Haberman, S. & Kaishev, V. K. (2013). Dependent competing risks: cause elimination and its impact on survival. Insurance: Mathematics and Economics, 53(2), 464–477.Google Scholar
Dong, Y., Huang, F., Yu, H. & Haberman, S. (2020). Multi-population mortality forecasting using tensor decomposition. Scandinavian Actuarial Journal, 2020(8), 754–775.CrossRefGoogle Scholar
Enchev, V., Kleinow, T. & Cairns, A.J.G. (2017). Multi-population mortality models: fitting, forecasting and comparisons. Scandinavian Actuarial Journal, 2017(4), 319–342.CrossRefGoogle Scholar
Flaxman, S., Wilson, A., Neill, D., Nickisch, H. & Smola, A. (2015). Fast Kronecker inference in Gaussian processes with Non-Gaussian likelihoods. In Bach, F. & Blei, D. (Eds.), Proceedings of the 32nd International Conference on Machine Learning, Proceedings of Machine Learning Research, vol. 37 (pp. 607–616), Lille, France. PMLR.Google Scholar
Foreman, K., Marquez, N., Dolgert, A., Fukutaki, K., Fullman, N., McGaughey, M., Pletcher, M.A., Smith, A., Tang, K., Yuan, C.-W., Brown, J., Friedman, J., He, J., Heuton, K., Holmberg, M., Patel, D.J., Reidy, P., Carter, A., Cercy, K.M., Chapin, A., Douwes-Schultz, D., Frank, T.D., Goettsch, F., Liu, P., Nandakumar, V., Reitsma, M., Reuter, V., Sadat, N., Sorensen, R.J.D., Srinivasan, V., Updike, R., York, H., Lopez, A.D., Lozano, R., Lim, S.S., Mokdad, A., Vollset, S. & Murray, C. (2018). Forecasting life expectancy, years of life lost, and all-cause and cause-specific mortality for 250 causes of death: reference and alternative scenarios for 2016–40 for 195 countries and territories. Lancet (London, England), 392, 2052–2090.CrossRefGoogle ScholarPubMed
Gilboa, E., Saatçi, Y. & Cunningham, J.P. (2015). Scaling multidimensional inference for structured Gaussian processes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 37(2), 424–436.CrossRefGoogle ScholarPubMed
Guibert, Q., Lopez, O. & Piette, P. (2019). Forecasting mortality rate improvements with a high-dimensional VAR. Insurance: Mathematics and Economics, 88, 255–272.Google Scholar
HCD (2021). The Human Cause-of-Death Database. French Institute for Demographic Studies (France) and Max Planck Institute for Demographic Research (Germany).Google Scholar
Huynh, N. & Ludkovski, M. (2021). Multi-output Gaussian processes for multi-population longevity modelling. Annals of Actuarial Science, 15(2), 318–345.CrossRefGoogle Scholar
Huynh, N., Ludkovski, M. & Zail, H. (2020). Multi-population longevity models: a spatial random field approach. In Proceedings of the Society of Actuaries 2020 Living to 100 Symposium.Google Scholar
Hyndman, R.J., Booth, H. & Yasmeen, F. (2013). Coherent mortality forecasting: the product-ratio method with functional time series models. Demography, 50(1), 261–283.CrossRefGoogle ScholarPubMed
Kjaergaard, S., Ergemen, Y.E., Kallestrup-Lamb, M., Oeppen, J. & Lindahl-Jacobsen, R. (2019). Forecasting causes of death by using compositional data analysis: the case of cancer deaths. Journal of the Royal Statistical Society: Series C (Applied Statistics), 68(5), 1351–1370.Google Scholar
Kleinow, T. (2015). A common age effect model for the mortality of multiple populations. Insurance: Mathematics and Economics, 63, 147–152.Google Scholar
Knudsen, C. & McNown, R. (1993). Changing causes of death and the sex differential in the USA: recent trends and projections. Population Research and Policy Review, 12(1), 27–41.CrossRefGoogle Scholar
Letham, B. & Bakshy, E. (2019). Bayesian optimization for policy search via online-offline experimentation. Journal of Machine Learning Research, 20(145), 1–30.Google Scholar
Li, H. & Lu, Y. (2017). Coherent forecasting of mortality rates: a sparse vector-autoregression approach. ASTIN Bulletin: The Journal of the IAA, 47(2), 563–600.CrossRefGoogle Scholar
Li, H. & Lu, Y. (2019). Modeling cause-of-death mortality using hierarchical Archimedean copula. Scandinavian Actuarial Journal, 2019(3), 247–272.CrossRefGoogle Scholar
Li, N. & Lee, R. (2005). Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method. Demography, 42(3), 575–594.CrossRefGoogle ScholarPubMed
Liu, H., Ong, Y.-S., Shen, X. & Cai, J. (2020). When Gaussian process meets big data: a review of scalable GPs. IEEE Transactions on Neural Networks and Learning Systems, 31(11), 4405–4423.CrossRefGoogle ScholarPubMed
Lo, S.M.S. & Wilke, R.A. (2010). A copula model for dependent competing risks. Journal of the Royal Statistical Society. Series C (Applied Statistics), 59(2), 359–376.CrossRefGoogle Scholar
Ludkovski, M., Risk, J. & Zail, H. (2018). Gaussian process models for mortality rates and improvement factors. ASTIN Bulletin: The Journal of the IAA, 48(3), 1307–1347.CrossRefGoogle Scholar
Lyu, P., Waegenaere, A.D. & Melenberg, B. (2021). A multi-population approach to forecasting all-cause mortality using cause-of-death mortality data. North American Actuarial Journal, 25(1), S421–S456.CrossRefGoogle Scholar
McNown, R. & Rogers, A. (1992). Forecasting cause-specific mortality using time series methods. International Journal of Forecasting, 8(3), 413–432.CrossRefGoogle Scholar
Rasmussen, C.E. & Williams, C.K.I. (2005). Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). The MIT Press, Cambridge, MA.CrossRefGoogle Scholar
Saatçi, Y. (2011). Sca Inference for Structured Gaussian Process Models. PhD thesis, University of Cambridge.Google Scholar
Tabeau, E., Ekamper, P., Huisman, C. & Bosch, A. (1999). Improving overall mortality forecasts by analysing cause-of-death, period and cohort effects in trends. European Journal of Population/Revue Européenne de Démographie, 15(2), 153–183.CrossRefGoogle Scholar
Teh, Y., Seeger, M. & Jordan, M. I. (2005). Semiparametric latent factor models. In International Workshop on Artificial Intelligence and Statistics (AISTATS) (pp. 333–340). PMLR.Google Scholar
Tsai, C.C.-L. & Zhang, Y. (2019). A multi-dimensional Bühlmann credibility approach to modeling multi-population mortality rates. Scandinavian Actuarial Journal, 2019(5), 406–431.CrossRefGoogle Scholar
WHO (2021). Cancer.Google Scholar
Williams, C., Klanke, S., Vijayakumar, S. & Chai, K. (2009). Multi-task Gaussian process learning of robot inverse dynamics. In Koller, D., Schuurmans, D., Bengio, Y. & Bottou, L. (Eds.), Advances in Neural Information Processing Systems, vol. 21. Curran Associates, Inc.Google Scholar
Wilmoth, J.R. (1995). Are mortality projections always more pessimistic when disaggregated by cause of death? Mathematical Population Studies, 5(4), 293–319.CrossRefGoogle ScholarPubMed
Wojtys, P., Antczak, A. & Godlewski, D. (2014). Predictions of cancer mortality in Poland in 2020. Central European Journal of Medicine, 9, 667–675.Google Scholar
Zhe, S., Xing, W. & Kirby, R.M. (2019). Scalable high-order Gaussian process regression. In Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research, vol. 89 (pp. 2611–2620). PMLR.Google Scholar