A forecast reconciliation approach to cause-of-death mortality modeling. (English) Zbl 1411.91298

Summary: Life expectancy has been increasing sharply around the globe since the second half of the 20th century. Mortality modeling and forecasting have therefore attracted increasing attention from various areas, such as the public pension systems, commercial insurance sectors, as well as actuarial, demographic and epidemiological research. Compared to the aggregate mortality experience, cause-specific mortality rates contain more detailed information, and can help us better understand the ongoing mortality improvements. However, when conducting cause-of-death mortality modeling, it is important to ensure coherence in the forecasts. That is, the forecasts of cause-specific mortality rates should add up to the forecasts of the aggregate mortality rates. In this paper, we propose a novel forecast reconciliation approach to achieve this goal. We use the age-specific mortality experience in the U.S. during 1970–2015 as a case study. Seven major causes of death are considered in this paper. By incorporating both the disaggregate cause-specific data and the aggregate total-level data, we achieve better forecasting results at both levels and coherence across forecasts. Moreover, we perform a cluster analysis on the cause-specific mortality data. It is shown that combining mortality experience from causes with similar mortality patterns can provide additional useful information, and thus further improve forecast accuracy. Finally, based on the proposed reconciliation approach, we conduct a scenario-based analysis to project future mortality rates under the assumption of certain causes being eliminated.


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M20 Inference from stochastic processes and prediction


Full Text: DOI


[1] Alai, D. H.; Arnold, S.; Bajekal, M.; Villegas, A. M., Mind the gap: a study of cause-specific mortality by socioeconomic circumstances, N. Am. Actuar. J., 22, 2, 161-181, (2018) · Zbl 1393.91096
[2] Alai, D. H.; Arnold, S.; Sherris, M., Modelling cause-of-death mortality and the impact of cause-elimination, Ann. Actuar. Sci., 9, 1, 167-186, (2015)
[3] Arias, E.; Heron, M.; Tejada-Vera, B., National Vital Statistics Reports, (2013), National Center for Health Statistics
[4] Arnold, S.; Sherris, M., Forecasting mortality trends allowing for cause-of-death mortality dependence, N. Am. Actuar. J., 17, 4, 273-282, (2013)
[5] Arnold, S.; Sherris, M., Causes-of-death mortality: what do we know on their dependence?, N. Am. Actuar. J., 19, 2, 116-128, (2015)
[6] Arnold, S.; Sherris, M., International cause-specific mortality rates: new insights from a cointegration analysis, Astin Bull., 46, 1, 9-38, (2016) · Zbl 1390.62332
[7] Athanasopoulos, G.; Ahmed, R. A.; Hyndman, R. J., Hierarchical forecasts for Australian domestic tourism, Int. J. Forecast., 25, 1, 146-166, (2009)
[8] Booth, H.; Tickle, L., Mortality modelling and forecasting: a review of methods, Ann. Actuar. Sci., 3, 1-2, 3-43, (2008)
[9] Borges, C. E.; Penya, Y. K.; Fernandez, I., Evaluating combined load forecasting in large power systems and smart grids, IEEE Trans. Ind. Inf., 9, 3, 1570-1577, (2013)
[10] Capistrán, C.; Constandse, C.; Ramos-Francia, M., Multi-horizon inflation forecasts using disaggregated data, Econ. Model., 27, 3, 666-677, (2010)
[11] Case, A.; Deaton, A., Mortality and morbidity in the 21st century, (Brookings Papers on Economic Activity, Vol. 2017, (2017), NIH Public Access), 397
[12] Caselli, G.; Vallin, J.; Marsili, M., How useful are the causes of death when extrapolating mortality trends. an update, (Social Insurance Studies from the Swedish Social Insurance, Vol. 4, (2006)), 9-36
[13] Centers for Disease Control and Prevention (2010) Mortality among teenagers aged 12-19 years: United states, 1999-2006. Retrieved April, 28:2011.
[14] Dangerfield, B. J.; Morris, J. S., Top-down or bottom-up: aggregate versus disaggregate extrapolations, Int. J. Forecast., 8, 2, 233-241, (1992)
[15] Diebold, F. X.; Mariano, R. S., Comparing predictive accuracy, J. Bus. Econom. Statist., 20, 1, 134-144, (2002)
[16] Dimitrova, D.; Haberman, S.; Kaishev, V., Dependent competing risks: cause elimination and its impact on survival, Insurance Math. Econom., 53, 2, 464-477, (2013) · Zbl 1304.91099
[17] Escarela, G.; Carriere, J. F., Fitting competing risks with an assumed copula, Stat. Methods Med. Res., 12, 4, 333-349, (2003) · Zbl 1121.62601
[18] Frees, E. W.; Valdez, E. A., Understanding relationships using copulas, N. Am. Actuar. J., 2, 1, 1-25, (1998) · Zbl 1081.62564
[19] Gamakumara, P.; Panagiotelis, A.; Athanasopoulos, G.; Hyndman, R. J., Probabilistic forecasts in hierarchical time series, Technical Report, (2018), Monash University, Department of Econometrics and Business Statistics
[20] Giordano, G.; Haberman, S.; Russolillo, M., Three-way data analysis applied to cause specific mortality trends, (Demography and Health Issues, (2018), Springer), 121-130
[21] Graybill, F.A., 1983. Matrices with applications in statistics. · Zbl 0496.15002
[22] Gross, C. W.; Sohl, J. E., Disaggregation methods to expedite product line forecasting, J. Forecast., 9, 3, 233-254, (1990)
[23] Hyndman, R. J.; Ahmed, R. A.; Athanasopoulos, G.; Shang, H. L., Optimal combination forecasts for hierarchical time series, Comput. Statist. Data Anal., 55, 9, 2579-2589, (2011) · Zbl 1464.62095
[24] Hyndman, R. J.; Athanasopoulos, G., Forecasting: Principles and Practice, (2018), OTexts
[25] Hyndman, R. J.; Athanasopoulos, G., Optimally reconciling forecasts in a hierarchy, Foresight: Int. J. Appl. Forecast., 35, 42-48, (2014)
[26] Hyndman, R. J.; Ullah, M. S., Robust forecasting of mortality and fertility rates: a functional data approach, Comput. Statist. Data Anal., 51, 10, 4942-4956, (2007) · Zbl 1162.62434
[27] Jeon, J., Panagiotelis, A., Petropoulos, F., 2018. Reconciliation of probabilistic forecasts with an application to wind power, https://arxiv.org/abs/1808.02635.
[28] Kahn, K. B., Revisiting top-down versus bottom-up forecasting, J. Bus. Forecast., 17, 2, 14, (1998)
[29] Kaishev, V.; Dimitrova, D.; Haberman, S., Modelling the joint distribution of competing risks survival times using copula functions, Insurance Math. Econom., 41, 3, 339-361, (2007) · Zbl 1141.91518
[30] Keyfitz, N., What difference would it make if cancer were eradicated? an examination of the taeuber paradox, Demography, 14, 4, 411-418, (1977)
[31] Kochanek, K. D.; Arias, E.; Bastian, B. A.; for Health Statistics, N. C., The effect of changes in selected age-specific causes of death on non-hispanic white life expectancy between 2000 and 2014, (Heart Disease, Vol. 1, (2017)), 0-581
[32] Lee, R. D.; Carter, L. R., Modeling and forecasting US mortality, J. Amer. Statist. Assoc., 87, 419, 659-671, (1992) · Zbl 1351.62186
[33] Li, H.; Lu, Y., Modeling cause-of-death mortality using hierarchical archimedean copula, Scand. Actuar. J., 1-26, (2018)
[34] Manton, K. G.; Stallard, E.; Vaupel, J. W., Alternative models for the heterogeneity of mortality risks among the aged, J. Amer. Statist. Assoc., 81, 395, 635-644, (1986)
[35] Manton, K. G.; Tolley, H. D.; Poss, S. S., Life table techniques for multiple-cause mortality, Demography, 13, 4, 541-564, (1976)
[36] McNown, R.; Rogers, A., Forecasting cause-specific mortality using time series methods, Int. J. Forecast., 8, 3, 413-432, (1992)
[37] Michael, J.; Krause, J. S.; Lammertse, D. P., Recent trends in mortality and causes of death among persons with spinal cord injury, Arch. Phys. Med. Rehabil., 80, 11, 1411-1419, (1999)
[38] Murtagh, F.; Legendre, P., Wards hierarchical agglomerative clustering method: which algorithms implement wards criterion?, J. Classification, 31, 3, 274-295, (2014) · Zbl 1360.62344
[39] Schwarzkopf, A. B.; Tersine, R. J.; Morris, J. S., Top-down versus bottom-up forecasting strategies, Int. J. Prod. Res., 26, 11, 1833-1843, (1988)
[40] Shang, H. L., Reconciling forecasts of infant mortality rates at national and sub-national levels: grouped time-series methods, Popul. Res. Policy Rev., 36, 1, 55-84, (2017)
[41] Shang, H. L.; Haberman, S., Grouped multivariate and functional time series forecasting: an application to annuity pricing, Insurance Math. Econom., 75, 166-179, (2017) · Zbl 1394.62146
[42] Shang, H. L.; Hyndman, R. J., Grouped functional time series forecasting: an application to age-specific mortality rates, J. Comput. Graph. Statist., 26, 2, 330-343, (2017)
[43] Shlifer, E.; Wolff, R., Aggregation and proration in forecasting, Manage. Sci., 25, 6, 594-603, (1979) · Zbl 0428.62062
[44] Syntetos, A. A.; Babai, Z.; Boylan, J. E.; Kolassa, S.; Nikolopoulos, K., Supply chain forecasting: theory, practice, their gap and the future, European J. Oper. Res., 252, 1, 1-26, (2016) · Zbl 1346.90181
[45] Tabeau, E.; Ekamper, P.; Huisman, C.; Bosch, A., Improving overall mortality forecasts by analysing cause-of-death, period and cohort effects in trends, Eur. J. Population/Revue eur. Démogr., 15, 2, 153-183, (1999)
[46] Ward, J. H., Hierarchical grouping to optimize an objective function, J. Amer. Statist. Assoc., 58, 301, 236-244, (1963)
[47] Weale, M., The reconciliation of values, volumes and prices in the national accounts, J. Roy. Statist. Soc. Ser. A, 151, 1, 211-221, (1988)
[48] Wickramasuriya, S. L.; Athanasopoulos, G.; Hyndman, R. J., Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization, J. Am. Stat. Assoc., 1-16, (2018)
[49] Wilmoth, J. R., Are mortality projections always more pessimistic when disaggregated by cause of death?, Math. Popul. Stud., 5, 4, 293-319, (1995) · Zbl 0876.92032
[50] Xu, J.; Murphy, S. L.; Kochanek, K. D.; Arias, E., Mortality in the United States, 2016, (NCHS Data Brief, Vol. 293, (2016)), 1-8
[51] Zellner, A.; Tobias, J., A note on aggregation, disaggregation and forecasting performance, J. Forecast., 19, 5, 457-465, (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.