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Coherent modeling and forecasting of mortality patterns for subpopulations using multiway analysis of compositions: an application to Canadian provinces and territories. (English) Zbl 1393.62043

Summary: Mortality levels for subpopulations, such as countries in a region or provinces within a country, generally change in a similar fashion over time, as a result of common historical experiences in terms of health, culture, and economics. Forecasting mortality for such populations should consider the correlation between their mortality levels. In this perspective, we suggest using multilinear component techniques to identify a common time trend and then use it to forecast coherently the mortality of subpopulations. Moreover, this multiway approach is performed on life table deaths by referring to Compositional Data Analysis (CoDa) methodology. Compositional data are strictly positive values summing to a constant and represent part of a whole. Life table deaths are compositional by definition because they provide the age composition of deaths per year and sum to the life table radix. In bilinear models the use of life table deaths treated as compositions generally leads to less biased forecasts than other commonly used models by not assuming a constant rate of mortality improvement. As a consequence, an extension of this approach to multiway data is here presented. Specifically, a CoDa adaptation of the Tucker3 model is implemented for life table deaths arranged in three-dimensional arrays indexed by time, age, and population. The proposed procedure is used to forecast the mortality of Canadian provinces in a comparative study. The results show that the proposed model leads to coherent forecasts.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
91D20 Mathematical geography and demography

Software:

MortalitySmooth
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References:

[1] Aitchison, J., The Statistical Analysis of Compositional Data, (1986), Chapman & Hall, London · Zbl 0688.62004
[2] Bergeron-Boucher, M.-P.; Canudas-Romo, V.; Oeppen, J.; Vaupel, J. W., Coherent forecasts of mortality with compositional data analysis, Demographic Research, 37, 527-568, (2017)
[3] Billheimer, D.; Guttorp, P.; Fagan, W. F., Statistical interpretation of species composition, Journal of the American Statistical Association, 96, 456, 1205-1214, (2001) · Zbl 1073.62573
[4] Bohk-Ewald, C.; Rau, R., Probabilistic mortality forecasting with varying age-specific survival improvements, Genus, 73, 1, 1-37, (2017)
[5] Booth, H.; Maindonald, J.; Smith, L., Applying Lee-Carter under conditions of variable mortality decline, Population Studies, 56, 3, 325-336, (2002)
[6] Booth, H.; Tickle, L., Mortality modelling and forecasting: A review of methods, Annals of Actuarial Science, 3, 3-43, (2008)
[7] Brouhns, N.; Denuit, M.; Vermunt, J. K., A Poisson log-bilinear regression approach to the construction of projected lifetables, Insurance: Mathematics and Economics, 31, 373-393, (2002) · Zbl 1074.62524
[8] Camarda, C. G., Mortalitysmooth: an R package for smoothing Poisson counts with P-splines, Journal of Statistical Software, 50, 1, 1-24, (2012)
[9] Department of demography, université de montréal
[10] Carter, L. R.; Lee, R., Modeling and forecasting U.S. mortality differentials in life expectancy by sex, International Journal of Forecasting, 8, 3, 393-412, (1992)
[11] Currie, I. D.; Durban, M.; Eilers, P. H. C., Smoothing and forecasting mortality rates, Statistical Modelling, 4, 4, 279-298, (2004) · Zbl 1061.62171
[12] Debon, A.; Montes, F.; Martinez-Ruiz, F., Statistical methods to compare mortality for a group with non-divergent populations: an application to Spanish regions, European Actuarial Journal, 1, 2, 291-308, (2011)
[13] Debon, A.; Montes, F.; Puig, F., Modelling and forecasting mortality in Spain, European Journal of Operational Research, 189, 3, 624-637, (2008) · Zbl 1142.62419
[14] de Jong, P.; Tickle, L.; Xu, J., Coherent modeling of male and female using Lee-Carter in a complex number framework, Insurance: Mathematics and Economics, 71, 130-137, (2016) · Zbl 1371.91114
[15] Egozcue, J. J.; Pawlowsky-Glahn, V.; Pawlowsky-Glahn, V.; Buccianti, A., Basic concepts and procedures, Compositional Data Analysis: Theory and Applications, 12-28, (2011), John Wiley & Sons, New York
[16] Egozcue, J. J.; Pawlowsky-Glahn, V.; Mateu-Figueras, G.; Barcelo-Vidal, C., Isometric logratio transformations for compositional data analysis, Mathematical Geology, 35, 3, 279-300, (2003) · Zbl 1302.86024
[17] Gallo, M., Tucker3 model for compositional data, Communications in Statistics—Theory and Methods, 44, 21, 4441-4453, (2015) · Zbl 1333.62159
[18] Haberman, S.; Renshaw, A. E., Parametric mortality improvement rate modelling and projecting, Insurance: Mathematics and Economics, 50, 3, 309-333, (2012) · Zbl 1237.91129
[19] Hyndman, R.; Booth, H.; Yasmeen, F., Coherent mortality forecasting: the product-ratio method with functional time series models, Demography, 50, 261-283, (2013)
[20] Hyndman, R.; Ullah, S., Robust forecasting of mortality and fertility rates: A functional data approach, Computational Statistics & Data Analysis, 51, 4942-4956, (2007) · Zbl 1162.62434
[21] Kannisto, V.; Lauritsen, J.; Thatcher, A. R.; Vaupel, J. W., Reductions in mortality at advanced ages: several decades of evidence from 27 countries, Population and Development Review, 20, 4, 793-810, (1994)
[22] Kiers, H. A. L., Bootstrap confidence intervals for the three-way methods, Journal of Chemometrics, 18, 22-36, (2004)
[23] Kroonenberg, P. M., Applied Multi-way Data Analysis, (2008), Wiley-Interscience, Hoboken, NJ
[24] Lee, R. D.; Nault, F., Modeling and forecasting provincial mortality in Canada, Paper presented at the World Congress of the International Union for the Scientific Study of Population, (1993), Montréal.
[25] Lee, R. D.; Carter, L. R., Modeling and forecasting US mortality, Journal of the American Statistical Association, 87, 419, 659-671, (1992) · Zbl 1351.62186
[26] Lee, R. D.; Miller, T., Evaluating the performance of the Lee-Carter method for forecasting mortality, Demography, 38, 537-549, (2001)
[27] Li, N.; Lee, R., Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method, Demography, 42, 3, 575-594, (2005)
[28] Lloyd, C. D.; Pawlowsky-Glahn, V.; Egozcue, J. J., Compositional data analysis in population studies, Annals of the Association of American Geographers, 102, 6, 1251-1266, (2012)
[29] Mert, M. C.; Filzmoser, P.; Endel, G.; Wilbacher, I., Compositional data analysis in epidemiology, Statistical Methods in Medical Research, 1-14, (2016)
[30] Oeppen, J., Coherent forecasting of multiple-decrement life tables: A test using Japanese cause of death data, Paper presented in July at the European Population Conference 2008, (2008), European Association for Population Studies, Barcelona
[31] Pawlowsky-Glahn, V, Statistical Modelling on Coordinates. Universitat de Girona, (2003) · Zbl 1109.86300
[32] Pawlowsky-Glahn, V.; Egozcue, J. J., Geometric approach to statistical analysis on the simplex, Stochastic Environmental Research and Risk Assessment, 15, 5, 384-398, (2001) · Zbl 0987.62001
[33] Preston, S.; Heuveline, P.; Guillot, M., Demography: Measuring and Modeling Population Processes, (2001), Blackwell, Oxford
[34] Raftery, A. E.; Chunn, J. L.; Gerland, P.; Ševčíková, H., Bayesian probabilistic projections of life expectancy for all countries, Demography, 50, 3, 777-801, (2013)
[35] Renshaw, A.; Haberman, S., Lee-Carter mortality forecasting: A parallel generalized linear modelling approach for england and wales mortality projections, Journal of the Royal Statistical Society. Series C, 52, 1, 119-137, (2003) · Zbl 1111.62359
[36] Renshaw, A.; Haberman, S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38, 3, 556-570, (2006) · Zbl 1168.91418
[37] Russolillo, M.; Giordano, G.; Haberman, S., Extending the Lee-Carter model: A three-way decomposition, Scandinavian Actuarial Journal, 2, 96-117, (2011) · Zbl 1277.62260
[38] Schinzinger, E.; Denuit, M. M.; Christiansen, M. C., A multivariate evolutionary credibility model for mortality improvement rates, Insurance: Mathematics and Economics, 69, 70-81, (2016) · Zbl 1369.91097
[39] Smilde, A.; Bro, R.; Geladi, P., Multi-way Analysis: Applications in the Chemical Sciences, (2004), John Wiley & Sons, Chichester
[40] Table 051-0001: estimates of population, by age group and sex for July 1, Canada, provinces and territories, annual (persons unless otherwise noted), (2017)
[41] Timmerman, M. E.; Kiers, H. A., Three‐mode principal components analysis: choosing the numbers of components and sensitivity to local optima, British Journal of Mathematical and Statistical Psychology, 53, 1, 1-16, (2000)
[42] Torri, T.; Vaupel, J., Forecasting life expectancy in an international context, International Journal of Forecasting, 28, 519-531, (2012)
[43] Tucker, L. R., Some mathematical notes on three-mode factor analysis, Psychometrika, 31, 3, 279-311, (1966)
[44] Vaupel, J. W., The remarkable improvements in survival at older ages, Philosophical Transactions of the Royal Society B, 352, 1363, 1799-1804, (1997)
[45] Vaupel, J.; Yashin, A., Repeated resuscitation: how lifesaving alters life tables, Demography, 24, 1, 123-135, (1987)
[46] Villegas, A. M.; Haberman, S., On the modeling and forecasting of socioeconomic mortality differentials: an application to deprivation and mortality in england, North American Actuarial Journal, 18, 1, 168-193, (2014)
[47] Wilson, C., On the scale of global demographic convergence 1950–2000, Population and Development Review, 27, 1, 155-171, (2001)
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