Volume 41 - Article 38 | Pages 1091–1130
Smooth constrained mortality forecasting
References
Abel, Guy, Bijak, Jakub, Forster, Jonathan J., Raymer, James, Smith, Peter W. F., and Wong, Jackie S. T. (2013). Integrating uncertainty in time series population forecasts: An illustration using a simple projection model. Demographic Research 29(43): 1187-1226.
Ahmadi, Seyed Saeed and Li, Johnny Siu-Hang (2014). Coherent mortality forecasting with generalized linear models: A modified time-transformation approach. Insurance: Mathematics and Economics 59: 194-221.
Barrieu, Pauline, Bensusan, Harry, El Karoui, Nicole, Hillairet, Caroline, Loisel, Stéphane, Ravanelli, Claudia, and Salhi, Yahia (2012). Understanding, modelling and managing longevity risk: key issues and main challenges. Scandinavian Actuarial Journal 2012(3): 203-231.
Blake, David, Cairns, Andrew J. G., and Dowd, Kevin (2006). Living with mortality: Longevity bonds and other mortality-linked securities. British Actuarial Journal 12(1): 153-197.
Bohk-Ewald, C., Ebeling, M., and Rau, R. (2017). Lifespan disparity as an additional indicator for evaluating mortality forecasts. Demography 54(4): 1559-1577.
Bohk-Ewald, C. and Rau, R. (2017). Probabilistic mortality forecasting with varying age-specific survival improvements. Genus 73(1): 1-37.
Bollaerts, Kaatje, Eilers, Paul H. C., and van Mechelen, Iven (2006). Simple and multiple P-splines regression with shape constraints. British Journal of Mathematical and Statistical Psychology 59: 451-469.
Booth, H. and Tickle, L. (2008). Mortality modelling and forecasting: A review of methods. Annals of Actuarial Science 3(1–2): 3-43.
Booth, Heather, Maindonald, John, and Smith, Len (2002). Applying Lee–Carter under conditions of variable mortality decline. Population Studies 56: 325-336.
Brouhns, N., Denuit, M., and Van Keilegom, I. (2005). Bootstrapping the Poisson log- bilinear model for mortality forecasting. Scandinavian Actuarial Journal 3: 212-224.
Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., and Khalaf-Allah, M. (2011). Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics 48: 355-367.
Cairns, A., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., and Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal 13: 1-35.
Cairns, Andrew J. G., Blake, David, and Dowd, Kevin (2008). Modelling and management of mortality risk: A review. Scandinavian Actuarial Journal 2008(2-3): 79-113.
Cairns, Andrew J. G., Blake, David, and Dowd, Kevin (2006). Pricing death: Frameworks for the valuation and securitization of mortality risk. ASTIN Bulletin: The Journal of the IAA 36(1): 79-120.
Cairns, Andrew J. G., Blake, David, Dowd, Kevin, Coughlan, Guy D., Epstein, David, Ong, Alen, and Balevich, Igor (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal 13(1): 1-35.
Camarda, C. G. (2008). Smoothing Methods for the Analysis of Mortality Development. Madrid: Programa de Doctorado en Ingeniería Matemática. Universidad Carlos III, Departamento de Estadística.
Camarda, Carlo G. (2012). MortalitySmooth: An R Package for Smoothing Poisson Counts with $P$-Splines. Journal of Statistical Software 50: 1-24 (Available at \textcolorbluejstatsoft.org/v50/i01).
Canudas-Romo, Vladimir, Oeppen, Jim, Vaupel, James W., and Bergeron-Boucher, M. P. (2016). Coherent forecasts of mortality with compositional data analysis. Demographic Research 37(17): 527-566.
Carfora, M. F., Cutillo, L., and Orlando, A. (2017). A quantitative comparison of stochastic mortality models on Italian population data. Computational Statistics and Data Analysis 112: 198-214.
Carstensen, B. (2007). Age-Period-Cohort models for the Lexis diagram. Statistics in Medicine 26: 3018-3045.
Chiang, C. L. (1984). The Life Table and its Application. Malabar: Krieger.
Clayton, D. and Schifflers, E. (1987). Models for temporal variation in cancer rates. II. Age-period-cohort models. Statistics in Medicine 6: 469-481.
Colchero, Fernando, Rau, Roland, Jones, Owen R., Barthold, Julia A., Conde, Dalia A., Lenart, Adam, Nemeth, Laszlo, Scheuerlein, Alexander, Schoeley, Jonas, Torres, Catalina, Zarulli, Virginia, Altmann, Jeanne, Brockman, Diane K., Bronikowski, Anne M., Fedigan, Linda M., Pusey, Anne E., Stoinski, Tara S., Strier, Karen B., Baudisch, Annette, Alberts, Susan C., and Vaupel, James W. (2016). The emergence of longevous populations. Proceedings of the National Academy of Sciences 113(48): E7681-E7690.
Currie, I. (ed.) (2019). Invariance and the forecasting of mortality. Guimaraes: International Workshop of Statistical Modelling: 95–100 (Proceedings of the 34th International Workshop of Statistical Modelling).
Currie, I. D. (2011). Modelling and forecasting the mortality of the very old. ASTIN Bulletin: The Journal of the IAA 41: 419-427.
Currie, I. D. (2016). On fitting generalized linear and non-linear models of mortality. Scandinavian Actuarial Journal 2016(4): 356-383.
Currie, I. D. (2013). Smoothing constrained generalized linear models with an application to the Lee–Carter model. Statistical Modelling 13: 69-93.
Currie, Iain D., Durbán, Maria, and Eilers, Paul H. C. (2006). Generalized linear array models with applications to multidimensional smoothing. Journal of the Royal Statistical Society. Series B 68: 259-280.
Currie, Iain D., Durbán, Maria, and Eilers, Paul H. C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling 4: 279-298.
D’Amato, Valeria, Piscopo, Gabriella, and Russolillo, Maria (2011). The mortality of the Italian population: Smoothing techniques on the Lee–Carter model. The Annals of Applied Statistics 5(2A): 705-724.
de Boor, C. (1978). A Practical Guide to Splines. New York: Springer.
Delwarde, Antoine, Denuit, Michel, and Eilers, Paul H. C. (2007). Smoothing the Lee–Carter and Poisson log-bilinear models for mortality forecasting: A penalized log-likelihood approach. Statistical Modelling 7: 29-48.
Djeundje, V. A. B. and Currie, I. D. (2011). Smoothing dispersed counts with applications to mortality data. Annals of Actuarial Science 5: 33-52.
Dowell, Deborah, Noonan, Rita K., and Houry, Debra (2017). Underlying factors in drug overdose deaths. Journal of the American Medical Association 318(23): 2295-2296.
Efron, B. and Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman and Hall.
Eilers, P. H. C. (2005). Unimodal Smoothing. Journal of Chemometrics 19: 317-328.
Eilers, P. H. C., Marx, B. D., and Durbán, M. (2015). Twenty years of $P$-splines. SORT. Statistics and Operations Research Transactions 39(2): 149-186.
Eilers, Paul H. C. and Marx, Brian D. (1996). Flexible moothing with $B$-splines and penalties (with discussion). Statistical Science 11: 89-102.
Erickson, Roy V., Fabian, Vaclav, and Marik, Jan (1995). An optimum design for estimating the first derivative. The Annals of Statistics 23: 1234-1247.
Gerland, P., Raftery, A. E., Ševčíková, H., Li, N., Gu, D., Spoorenberg, T., Alkema, L., Fosdick, B. K., Chunn, J. L., Lalic, N., Bay, G., Buettner, T., Heilig, G. K., and Wilmoth, J. (2014). World population stabilization unlikely this century. Science 346: 234-237.
Girosi, F. and King, G. (2007). Understanding the Lee–Carter mortality forecasting method.
Goicoa, T., Ugarte, M. D., Etxeberria, J., and Militino, A. F. (2012). Comparing CAR and $P$-spline models in spatial disease mapping. Environmental and Ecological Statistics 19(4): 1-27.
Goldstein, Joshua R. (2011). A secular trend toward earlier male sexual maturity: Evidence from shifting ages of male young adult mortality.
Gompertz, Benjamin (1825). On the nature of the function expressive of the law of human mortality. London: Philosophical Transactions Royal Society.
Grotenhuis, Manfred te, Pelzer, Ben, Luo, Liying, and Schmidt-Catran, Alexander W. (2016). The intrinsic estimator, alternative estimates, and predictions of mortality trends: A comment on Masters, Hummer, Powers, Beck, Lin, and Finch. Demography 53: 1245-1252.
Haberman, Steven and Renshaw, Arthur (2009). On age–period–cohort parametric mortality rate projections. Insurance: Mathematics and Economics 45: 255-270.
Heuer, C. (1997). Modeling of time trends and interactions in vital rates using restricted regression splines. Biometrics 53: 161-177.
Hilton, Jason, Dodd, Erengul, Forster, Jonathan J., and Smith, Peter W. F. (2019). Projecting UK mortality by using Bayesian generalized additive models. Journal of the Royal Statistical Society. Series A 68: 29-49.
Hmd (2019). Human Mortality Database [electronic resource]. (Berkeley: University of California, Rostock: Max Planck Institute for Demographic Research. \textcolorbluewww.mortality.org).
Holford, T. R. (2006). Approaches to fitting age–period–cohort models with unequal intervals. Statistics in Medicine 25: 977-993.
Huang, Fei and Browne, Bridget (2017). Mortality forecasting using a modified Continuous Mortality Investigation Mortality Projections Model for China I: Methodology and country-level results. Annals of Actuarial Science 11(1): 20-45.
Hyndman, R. J. and Ullah, M. S. (2007). Robust forecasting of mortality and fertility rates: A functional data approach. Computational Statistics and Data Analysis 51: 4942-4956.
Hyndman, Rob J., Booth, Heather, and Yasmeen, Farah (2013). Coherent mortality forecasting: The product–ratio method with functional time series models. Demography 50: 261-283.
Jacobsen, R., Von Euler, M., Osler, M., Lynge, E., and Keiding, N. (2004). Women’s death in Scandinavia: What makes Denmark different? European Journal of Epidemiology 19(2): 117-121.
Jones, Owen R., Scheuerlein, Alexander, Salguero-Gomez, Roberto, Camarda, Carlo Giovanni, Schaible, Ralf, Casper, Brenda B., Dahlgren, Johan P., Ehrlen, Johan, Garcia, Maria B., Menges, Eric S., Quintana-Ascencio, Pedro F., Caswell, Hal, Baudisch, Annette, and Vaupel, James W. (2014). Diversity of ageing across the tree of life. Nature 505(7482): 169-173.
Keiding, Niels (1990). Statistical inference in the Lexis diagram. Philosophical Transactions: Physical Sciences and Engineering 332: 487-509.
Knorr-Held, L. and Rainer, E. (2001). Projections of lung cancer mortality in West Germany: A case study in Bayesian prediction. Biostatistics 2: 109-129.
Koissi, Marie-Claire, Shapiro, Arnold F., and Högnäs, G. (2006). Evaluating and extending the Lee–Carter model for mortality forecasting:Bootstrap confidence interval. Insurance: Mathematics and Economics 38: 1-20.
Kuang, D., Nielsen, B., and Nielsen, J. P. (2008). Forecasting with the age–period–cohort model and the extended chain-ladder model. Biometrika 95: 987-991.
Lee, R. D. and Carter, Lawrence R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association 87: 659-671.
Lee, Ronald D. and Miller, Timothy (2001). Evaluating the performance of the Lee–Carter method for forecasting mortality. Demography 38: 537-549.
Levitis, D. A. (2011). Before senescence : The evolutionary demography of ontogenesis. Proceedings of the Royal Society B: Biological Sciences 278(1707): 801-809.
Li, Nan and Lee, Roland D. (2005). Coherent mortality forecasts for a group of populations: An extension of the Lee–Carter method. Demography 42: 575-594.
Li, Nan, Lee, Ronald D., and Gerland, Patrick (2013). Extending the Lee–Carter method to model the rotation of age patterns of mortality-decline for long-term projection. Demography 50: 2037-2051.
Lindahl-Jacobsen, Rune, Rau, Roland, Jeune, Bernard, Canudas-Romo, Vladimir, Lenart, Adam, Christensen, Kaare, and Vaupel, James W. (2016). Rise, stagnation, and rise of Danish women’s life expectancy. Proceedings of the National Academy of Sciences 113(15): 4015-4020.
Lopez, A., Shibuya, K., Rao, C., Mathers, C., Hansell, A., Held, L., Schmid, V., and Buist, S. (2006). Chronic obstructive pulmonary disease: Current burden and future projections. European Respiratory Journal 27: 397-412.
Lu, J. L. C., Wong, W., and Bajekal, M. (2014). Mortality improvement by socio-economic circumstances in England (1982 to 2006). British Actuarial Journal 19(1): 1-35.
Mammen, E., Martínez-Miranda, M. D., and Nielsen, J. P. (2015). In-sample forecasting applied to reserving and mesothelioma mortality. Insurance: Mathematics and Economics 61: 76-86.
Martínez-Miranda, M. D., Nielsen, B., and Nielsen, J. P. (2014). Inference and forecasting in the age–period–cohort model with unknown exposure with an application to mesothelioma mortality. Journal of the Royal Statistical Society. Series A 178: 29-55.
Masters, Ryan K., Reither, Eric N., Powers, Daniel A., Yang, Y. Claire, Burger, Andrew E., and Link, Bruce G. (2013). The impact of obesity on US mortality levels: The importance of age and cohort factors in population estimates. American Journal of Public Health 103(10): 1895-1901.
McCullagh, P. and Nelder, J. A. (1989). Generalized linear models. London: Chapman and Hall (Monographs on Statistics Applied Probability).
Minton, Jon, Shaw, Richard, Green, Mark A., Vanderbloemen, Laura, Popham, Frank, and McCartney, Gerry (2017). Visualising and quantifying ‘excess deaths’ in Scotland compared with the rest of the UK and the rest of Western Europe. Journal of Epidemiology and Community Health 71(5): 461-467.
Muennig, Peter A. and Glied, Sherry A. (2010). What changes In survival rates tell us about US health care. Health Affairs 29(11): 2105-2113.
Nielsen, B. and Nielsen, J. P. (2014). Identification and forecasting in mortality models. The Scientific World Journal 2014: 1-24.
Ogata, Y., Katsura, K., Keiding, N., Holst, C., and Green, A. (2000). Empirical Bayes age–period–cohort analysis of retrospective incidence data. Scandinavian Journal of Statistics 27: 415-432.
Ouellette, N. and Bourbeau, R. (2011). Changes in the age-at-death distribution in four low mortality countries: A nonparametric approach. Demographic Research 25(19): 595-628.
Ouellette, N., Bourbeau, R., and Camarda, C. G. (2012). Regional disparities in canadian adult and old-age mortality: A comparative study based on smoothed mortality ratio surfaces and age-at-death distributions. Canadian Studies in Population 39(3-4): 79-106.
Pitacco, Ermanno, Denuit, Michel, and Haberman, Steven (2009). Modelling longevity dynamics for pensions and annuity business. Oxford: Oxford University Press.
Preston, Samuel H. (1976). Mortality patterns in national populations. With special reference to recorded causes of death. Cambridge: Academic Press.
Raftery, A. E., Alkema, L., and Gerland, P. (2014). Bayesian Population Projections for the United Nations. Statistical Science 29: 58-68.
Raftery, A. E., Chunn, J., Gerland, P., and Ševčíková, Hana (2013). Bayesian probabilistic projections of life expectancy for all countries. Demography 50: 777-801.
Remund, A. (2015). Jeunesses vulnérables? Mesures, composantes et causes de la surmortalité des jeunes adultes [PhD Thesis]. (Geneva: Université de Genève).
Renshaw, A. E. and Haberman, S. (2003). Lee–Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics 33: 255-272.
Renshaw, Arthur and Haberman, Steven (2003). Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections. Applied Statistics 52: 119-137.
Ribeiro, Filipe (2015). Statistical analysis and forecasting of cause of death data: Novel approaches and insights [PhD Thesis]. (Évora: Universidade de Évora).
Richards, S. J., Kirkby, J., and Currie, I. D. (2006). The importance of year of birth in two-dimentional mortality data. British Actuarial Journal 12: 5-61.
Richards, Stephen J., Currie, I. D., and Ritchie, G. P. (2014). A value-at-risk framework for longevity trend risk. British Actuarial Journal 19(1): 116-139.
Riebler, A. and Held, L. (2017). Projecting the future burden of cancer: Bayesian age–period–cohort analysis with integrated nested Laplace approximations. Biometrical Journal 59: 531-549.
Schmertmann, Carl, Zagheni, Emilio, Goldstein, Joshua R., and Myrskylä, Mikko (2014). Bayesian forecasting of cohort fertility. Journal of the American Statistical Association 109: 500-513.
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics 6: 461-464.
Ševčíková, H., Li, N., Kantorova, V., Gerland, P., and Raftery, A. E. (2016). Age-specific mortality and fertility rates for probabilistic population projections. In: Schoen, R. (ed.). The Springer series on demographic methods and population analysis: Vol. 39. Dynamic demographic analysis. Berlin: Springer: 285-310.
Shang, H. L. (2016). Mortality and life expectancy forecasting for a group of populations in developed countries: A multilevel functional data method. The Annals of Applied Statistics 10: 1639-1672.
Smith, Theresa R. and Wakefield, Jon (2016). A Review and comparison of age–period–cohort models for cancer incidence. Statistical Science 31: 591-610.
Tabeau, E., Willekens, F., and van Poppel, F. (2002). Parameterisation as a tool in analysing age, period and cohort effects on mortality: A case study of the Netherlands. In: Wunsch, G., Mouchart, M., and Duchene, J. (eds.). The life table: Modelling survival and death. Dordrecht: Kluwer Academic Publishers: 141-169.
Team, R. Development Core (2019). R: A Language and Environment for Statistical Computing [electronic resource]. (Vienna: R Foundation for Statistical Computing. \textcolorblueR-project.org).
Thatcher, Roger, Kannisto, Vaino, and Vaupel, James W. (1998). The force of mortality at ages 80 to 120. Odense: Odense University Press (Monographs on Population Aging).
Thun, Michael J., Carter, Brian D., Feskanich, Diane, Freedman, Neal D., Prentice, Ross, Lopez, Alan D., Hartge, Patricia, and Gapstur, Susan M. (2013). 50-Year Trends in Smoking-Related Mortality in the United States. New England Journal of Medicine 368(4): 351-364.
Trias-Llimós, Sergi, Bijlsma, Maarten J., and Janssen, Fanny (2016). The role of birth cohorts in long-term trends in liver cirrhosis mortality across eight European countries. Addiction 112: 250-258.
Tzeng, I. S. and Lee, W. C. (2015). Forecasting hepatocellular carcinoma mortality in Taiwan using an age–period–cohort model. Asia-Pacific Journal of Public Health 27: NP65-NP73.
Ugarte, M. D., Goicoa, T., Etxeberria, J., and Militino, A. F. (2012). Projections of cancer mortality risks using spatio-temporal $P$-spline models. Statistical Methods in Medical Research 21(5): 545-560.
Ugarte, M. D., Goicoa, T., and Militino, A. F. (2010). Spatio-temporal modeling of mortality risks using penalized splines. Environmetrics 21(3–4): 270-289.
United, Nations (2019). World Population Prospects 2019: Data Booklet. Department of Economic and Social Affairs, Population Division.
Vaupel, J. W. and Canudas-Romo, V. (2003). Decomposing change in life expectancy: A bouquet of formulas in honor of Nathan Keyfitz’s 90th birthday. Demography 40: 201-216.
Wang, Hsin Chung, Yue, Jack C., and Tsai, Yi-Hsuan (2016). Marital status as a risk factor in life insurance: An empirical study in Taiwan. ASTIN Bulletin: The Journal of the IAA 46(2): 487-505.
Wong, Irene O. L., Cowling, Benjamin J., Leung, Gabriel M., and Schooling, C. Mary (2013). Age-period-cohort projections of ischaemic heart disease mortality by socio-economic position in a rapidly transitioning Chinese population. PLOS-One 8: e61495.
Zhang, Z. and Vaupel, J. W. (2009). The age separating early deaths from late deaths. Demographic Research 20(29): 721-730.