Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-01T14:19:13.631Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling cause-of-death mortality and the impact of cause-elimination

Published online by Cambridge University Press:  17 November 2014

Daniel H. Alai ,
Séverine Arnold (-Gaille)  and
Michael Sherris
Daniel H. Alai*
Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, UK
Séverine Arnold (-Gaille)
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics (HEC Lausanne), University of Lausanne, 1015 Lausanne, Switzerland
Michael Sherris
Affiliation:
CEPAR, Risk and Actuarial Studies, UNSW Australia Business School, Sydney, NSW 2052, Australia
*
*Correspondence to: Daniel H. Alai, School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, UK. Tel: +44 (0) 1227 824753; Fax: +44 (0) 1227 827932; E-mail: d.h.alai@kent.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

The analysis of causal mortality provides rich insight into changes in mortality trends that are hidden in population-level data. Therefore, we develop and apply a multinomial logistic framework to model causal mortality. We use internationally classified cause-of-death categories and data obtained from the World Health Organization. Inherent dependence amongst the competing causes is accounted for in the framework, which also allows us to investigate the effects of improvements in, or the elimination of, cause-specific mortality. This has applications to scenario-based forecasting often used to assess the impact of changes in mortality. The multinomial model is shown to be more conservative than commonly used approaches based on the force of mortality. We use the model to demonstrate the impact of cause-elimination on aggregate mortality using residual life expectancy and apply the model to a French case study.

Keywords

Cause-of-death mortalityMultinomial logistic regressionCause-eliminationLife expectancyMortality forecasts

JEL classification

G22: Insurance • Insurance Companies • Actuarial Studies G32: Financing Policy • Financial Risk and Risk Management • Capital and Ownership Structure • Value of Firms • Goodwill C18: Methodological Issues: General C51: Model Construction and Estimation
Type
Papers
Information
Annals of Actuarial Science , Volume 9 , Issue 1 , March 2015 , pp. 167 - 186
Copyright
© Institute and Faculty of Actuaries 2014 

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.)

References

Anderson, R.N. (1999). US decennial life tables: 1989-91. United States life tables eliminating certain causes of death. DHHS Publication No (PHS) 99-1150-4, 1(4), 1–7.Google Scholar
Bayo, F. (1968). Life tables: 1959-61. United States life tables by causes of death: 1959-61. Public Health Service Publication No 1252, 1(6), 1–14.Google Scholar
Booth, H., Maindonald, J. & Smith, L. (2001). Age-time interactions in mortality projection: applying Lee-Carter to Australia. Working Papers in Demography, 85, 2–28.Google Scholar
Booth, H. & Tickle, L. (2008). Mortality modelling and forecasting: a review of methods. Annals of Actuarial Science, 3, 3–43.CrossRefGoogle Scholar
Borooah, V.K. (2002). Logit and Probit: Ordered and Multinominal Models. Sage Publications, Thousand Oaks, CA.Google Scholar
Bowers, N., Gerber, H., Hickman, J., Jones, D. & Nesbitt, C. (1986). Actuarial Mathematics. Society of Actuaries, Itasca, Illinois.Google Scholar
Bradshaw, D., Groenewald, P., Laubscher, R., Nannan, N., Nojilana, B., Norman, R., Pieterse, D. & Schneider, M. (2003). Initial burden of disease estimates for South Africa, 2000, technical report, Burden of Disease Research Unit, Cape Town: South African Medical Research Council.Google Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D. & Khalaf-Allah, M. (2011). Mortality density forecasts: an analysis of six stochastic mortality models. Insurance: Mathematics and Economics, 48(3), 335–367.Google Scholar
Carriere, J.F. (1994). Dependent decrement theory. Society of Actuaries Transactions, 46, 45–65.Google Scholar
Caselli, G. (1996). Future longevity among the elderly. In G. Caselli & A.D. Lopez (Eds.), Health and Mortality Among Elderly Populations (pp. 235–265). Clarendon Press, Oxford.Google Scholar
Caselli, G., Vallin, J. & Marsili, M. (2006). How useful are the causes of death when extrapolating mortality trends. An update. In Tommy Bengtsson & Kaare Christensen (Eds.), Perspectives on Mortality Forecasting: IV. The Causes of Death (pp. 9-36). Stockholm: Swedish Social Insurance Agency.Google Scholar
Chiang, C.L. (1968). Introduction to Stochastic Process in Biostatistics. John Wiley and Sons, New York, NY.Google Scholar
Chiang, C.L. (1984). The Life Table and its Applications. Robert E Krieger Publishing Company, Malabar.Google Scholar
Curtin, L.R. & Armstrong, R.J. (1988). US decennial life tables: 1979-81. United States life tables eliminating certain causes of death. DHHS Publication No (PHS) 88-1150-2, 1(2), 1–13.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
Eberstein, I.W., Nam, C.B. & Hummer, R.A. (1990). Infant mortality by cause of death: main and interaction effects. Demography, 27(3), 413–430.CrossRefGoogle ScholarPubMed
Elandt-Johnson, R.C. (1976). Conditional failure time distributions under competing risk theory with dependent failure times and proportional hazard rates. Scandinavian Actuarial Journal, 1976(1), 37–51.Google Scholar
Foreman, K.J., Lozano, R., Lopez, A.D. & Murray, C.J. (2012). Modeling causes of death: an integrated approach using CODEm. Population Health Metrics, 10(1), 1–23.Google Scholar
Gaille, S. & Sherris, M. (2011). Modeling mortality with common stochastic long-run trends. The Geneva Papers on Risk and Insurance – Issues and Practice, 36(4), 595–621.Google Scholar
Greville, T.N.E., Bayo, F. & Foster, R.S. (1975). Life tables: 1969-71. United States life tables by causes of death: 1969-71. DHEW Publication No (HRA) 75-1150, 1(5), 5–15.Google Scholar
Gutterman, S. & Vanderhoof, I.T. (1998). Forecasting changes in mortality: a search for a law of causes and effects. North American Actuarial Journal, 2(4), 135–138.Google Scholar
Haberman, S. & Renshaw, A.E. (2011). A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics, 48(1), 35–55.Google Scholar
Heligman, L. & Pollard, J.H. (1980). The age pattern of mortality. Journal of the Institute of Actuaries, 107, 49–80.Google Scholar
Hougaard, P. (1984). Life table methods for heterogeneous populations: distributions describing the heterogeneity. Biometrika, 71(1), 75–83.CrossRefGoogle Scholar
Human Mortality Database (2012). Methods protocol for the human mortality database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Accessed on April 2012 from www. mortality.org or www.humanmortality.de.Google Scholar
Johnson, H.L., Liu, L., Fischer-Walker, C. & Black, R.E. (2010). Estimating the distribution of causes of death among children age 1-59 months in high-mortality countries with incomplete death certification. International Journal of Epidemiology, 39, 1103–1114.CrossRefGoogle ScholarPubMed
Kaishev, V.K., Dimitrova, D.S. & Haberman, S. (2007). Modelling the joint distribution of competing risks survival times using copula functions. Insurance: Mathematics and Economics, 41(3), 339–361.Google Scholar
Keyfitz, N. (1977). What difference would it make if cancer were eradicated? An examination of the Taeuber Paradox. Demography, 14(4), 411–418.CrossRefGoogle ScholarPubMed
Lawn, J.E., Wilczynska-Ketende, K. & Cousens, S.N. (2006). Estimating the causes of 4 million neonatal deaths in the year 2000. International Journal of Epidemiology, 35, 706–718.CrossRefGoogle ScholarPubMed
Lee, R.D. & Carter, L.R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659–671.Google Scholar
Liu, L., Johnson, H.L., Cousens, S., Perin, J., Scott, S., Lawn, J.E., Rudan, I., Campbell, H., Cibulskis, R., Li, M., Mathers, C. & Black, R.E. (2012). Global, regional, and national causes of child mortality: an updated systematic analysis for 2010 with time trends since 2000. The Lancet, 379, 2151–2161.Google Scholar
LIWMPC Longevity Research Group (2010). LIWMPC Longevity Research Group Update 2010. The Institute of Actuaries Australia, Sydney.Google Scholar
Lo, 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.Google Scholar
Manton, K.G. (1986). Past and future life expectancy increases at later ages: their implications for the linkage of morbidity, disability, and mortality. Journal of Gerontology, 41(5), 672–681.Google Scholar
Manton, K.G. (1991). The dynamics of population aging: demography and policy analysis. The Milbank Quarterly, 69(2), 309–338.CrossRefGoogle ScholarPubMed
Manton, K.G. & Myers, G. C. (1987). Recent trends in multiple-caused mortality 1968 to 1982: age and cohort components. Population Research and Policy Review, 6, 161–176.Google Scholar
Manton, K.G., Patrick, C.H. & Stallard, E. (1980a). Mortality model based on delays in progression of chronic diseases: alternative to cause elimination model. Public Health Report, 95(6), 580–588.Google ScholarPubMed
Manton, K.G. & Poss, S.S. (1979). Effects of dependency among causes of death for cause elimination life table strategies. Demography, 16(2), 313–327.CrossRefGoogle ScholarPubMed
Manton, K.G., Stallard, E. & Poss, S.S. (1980b). Estimates of U.S. multiple cause life tables. Demography, 17(1), 85–102.Google Scholar
Manton, K.G., Stallard, E. & Vaupel, J.W. (1986). Alternative models for the heterogeneity of mortality risks among the aged. Journal of the American Statistical Association, 81(395), 635–644.CrossRefGoogle ScholarPubMed
Manton, K.G., Tolley, H.D. & Poss, S.S. (1976). Life table techniques for multiple-cause mortality. Demography, 13(4), 541–564.Google Scholar
McNown, R. & Rogers, A. (1992). Forecasting cause-specific mortality using time series methods. International Journal of Forecasting, 8, 413–432.Google Scholar
Menard, S. (2002). Applied Logistic Regression Analysis. Sage Publications, Thousand Oaks, CA.Google Scholar
Murray, C. J., Kulkarni, S.C. & Ezzati, M. (2006). Understanding the coronary heart disease versus total cardiovascular mortality paradox: a method to enhance the comparability of cardiovascular death statistics in the United States. Circulation, 113, 2071–2081.Google Scholar
Olshansky, S.J. (1987). Simultaneous/multiple cause-delay (SIMCAD): an epidemiological approach to projecting mortality. Journal of Gerontology, 42(4), 358–365.Google Scholar
Olshansky, S.J. (1988). On forecasting mortality. The Milbank Quarterly, 66(3), 482–530.Google Scholar
Park, Y., Choi, J.W. & Lee, D.-H. (2006). A parametric approach for measuring the effect of the 10th revision of the international classification of diseases. Journal of the Royal Statistical Society. Series C (Applied Statistics), 55(5), 677–697.Google Scholar
Pitacco, E., Denuit, M., Haberman, S. & Olivieri, A. (2009). Modelling Longevity Dynamics for Pensions and Annuity Business. Oxford University Press, New York.Google Scholar
Prentice, R.L., Kalbfleisch, J.D., Peterson, A.V., Flournoy, N., Farewell, V.T. & Breslow, N.E. (1978). The analysis of failure times in the presence of competing risks. Biometrics, 34, 541–554.Google Scholar
Richards, S.J. (2009). Selected issues in modelling mortality by cause and in small populations. British Actuarial Journal, 15, 267–283.Google Scholar
Rogers, A. & Gard, K. (1991). Applications of the Heligman/Pollard model mortality schedule. Population Bulletin of the United Nations, 30, 79–105.Google Scholar
Rosen, M. (2006). Forecasting Life Expectancy and Mortality in Sweden - Some Comments on Methodological Problems and Potential Approaches. In Tommy Bengtsson & Kaare Christensen (Eds.), Perspectives on Mortality Forecasting: IV. The Causes of Death (pp. 37–48). Stockholm: Swedish Social Insurance Agency.Google Scholar
Shahraz, S., Bhalla, K., Lozano, R., Bartels, D. & Murray, C.J.L. (2013). Improving the quality of road injury statistics by using regression models to redistribute ill-defined events. Injury Prevention, 19(1), 1–5.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, 15, 153–183.CrossRefGoogle Scholar
Tabeau, E., Van Den Bergh Jeths, A. & Heathcote, C. (2001). Forecasting Mortality in Developed Countries. Insights from a Statistical, Demographic and Epidemiological Perspective. Kluwer Academic Publishers, Dordrecht.Google Scholar
Tsai, S.P., Lee, E.S. & Hardy, R.J. (1978). The effect of a reduction in leading causes of death: potential gains in life expectancy. American Journal of Public Health, 68(10), 966–971.Google Scholar
Tuljapurkar, S. (1998). Forecasting mortality change: questions and assumptions. North American Actuarial Journal, 2(4), 127–134.Google Scholar
Vaupel, J.W. & Yashin, A.I. (1983). The deviant dynamics of death in heterogeneous populations, Technical Report No. RR-83-001, International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria.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.Google Scholar
Wilmoth, J.R. (1996). Mortality projections for Japan: a comparison of four methods. In G. Caselli & A.D. Lopez (Eds.), Health and Mortality Among Elderly Populations (pp. 266–287). Clarendon Press, Oxford.Google Scholar
Wong-Fupuy, C. & Haberman, S. (2004). Projecting mortality trends: recent developments in the United Kingdom and the United States. North American Actuarial Journal, 8(2), 56–83.Google Scholar
World Health Organization (2012). WHO Mortality Database. Accessed on April 2012 from http://www.who.int/whosis/mort/download/en/index.html.Google Scholar