Model Schedules of Mortality

Chapter
Part of the International Handbooks of Population book series (IHOP, volume 2)

Abstract

The observation of empirical regularities in mortality risks across many populations with reliable data (see Chapter 10 by Robine, this volume) led to the development of model schedules of mortality. These models are parsimonious representations of typical age and gender variations in the risk of death. These representations take one or a combination of two forms: mathematical and tabular. Mathematical representations incorporate empirical regularities in a parametric function linking each age to a mortality risk. Tabular representations incorporate these regularities in a set of tables showing mortality rates corresponding to different age groups. Each table is indexed by one or a few parameters. Hybrid representations combine both strategies by applying a parametric function to transform a “standard” table of age-specific mortality rates. Any parameter set thus yields a new table of age-specific mortality rates. In either mathematical, tabular, or hybrid form, a model mortality schedule requires only a few parameters to provide mortality risks over the life span that vary with age in a manner consistent with one of a few typical patterns observed in our massive extant mortality records.

References

  1. Anderson, J.J., M.C. Gildea, D.W. Williams, and T. Li.. 2008. “Linking Growth, Survival, and Heterogeneity Through Vitality.” The American Naturalist 171:E20–E43.CrossRefGoogle Scholar
  2. Bhat, P.N.B.. 1987. Mortality in India: Levels, Trends and Patterns. Ph.D. Dissertation. Philadelphia, PA, University of Pennsylvania.Google Scholar
  3. Bourgeois-Pichat, J. 1946. De la Mesure de la Mortalité Infantile. Population 1(1):53–68.CrossRefGoogle Scholar
  4. Brass, W. 1971. On the Scale of Mortality. In W. Brass (ed.), Biological Aspects of Demography, pp. 69–110. London, Taylor and Francis Ltd; New York, NY, Barnes and Noble Inc.Google Scholar
  5. Carey, J.R. and D. Judge. 2001. “Life Span Extension in Humans Is Self-Reinforcing: A General Theory of Longevity.” Population and Development Review 27(3):411–36.CrossRefGoogle Scholar
  6. Carnes, B.A., S.J. Olshansky, and D. Grahn. 1996. “The Search for a Law of Mortality.” Population and Development Review 22(2):231–64.CrossRefGoogle Scholar
  7. Charlesworth, B.. 2000. “Fisher, Medawar, Hamilton and the Evolution of Aging.” Genetics 156(3):927–31.Google Scholar
  8. Chu, C.Y. and R.D. Lee.. 2006. “The Co-evolution of Intergenerational Transfers and Longevity: An Optimal Life History Approach.” Theoretical Population Biology 69(2):193–201.CrossRefGoogle Scholar
  9. Clark, S.J., M. Jasseh, A.A. Bawah, and O. Sankoh. 2009. INDEPTH Model Life Tables 2.0. Annual Meeting of the Population Association of America. Detroit, MI, Population Association of America.Google Scholar
  10. Coale, A.J. and P. Demeny. 1966. Regional Model Life Tables and Stable Populations. Princeton, Princeton University Press.Google Scholar
  11. Coale, A.J. and P. Demeny, B. Vaughan. 1983. Regional Model Life Tables and Stable Populations. New York, NY, Academic Press.Google Scholar
  12. Coale, A.J. and G. Guo. 1989. “Revised Regional Model Life Tables at Very Low Levels of Mortality.” Population Studies 55(4):613–43.Google Scholar
  13. Coale, A.J. and E.E. Kisker. 1990. “Defects in Data on Old-Age Mortality in the United States: New Procedures for Calculating Schedules and Life Tables at the Highest Ages.” Asian and Pacific Population Forum 4(1):1–31.Google Scholar
  14. Condran, G.A., C. Himes, and S.H. Preston.. 1991. “Old Age Mortality Patterns in Low-Mortality Countries: An Evaluation of Population and Death Data at Advanced Ages, 1950 to the Present.” Population Bulletin of the United Nations 30:23–60.Google Scholar
  15. Congdon, P. 1993. “Statistical Graduation in Local Demographic Analysis and Projection.” Journal of the Royal Statistical Society. Series A (Statistics in Society) 156(2):237–70.CrossRefGoogle Scholar
  16. Dellaportas, P., A.F.M. Smith, and P. Stavropoulos. 2001. “Bayesian Analysis of Mortality Data.” Journal of the Royal Statistical Society. Series A (Statistics in Society) 164(2):275–91.CrossRefGoogle Scholar
  17. de Moivre, A. 1725. Annuities on Lives. London, W. Pearson.Google Scholar
  18. Dyson, T. and C.Ó. Gráda. 2002. Famine Demography: Perspectives from the Past and Present. Oxford; New York, NY, Oxford University Press.Google Scholar
  19. Ewbank, D.C., J.C. Gomex de Leon, and M.A. Stoto. 1983. “A Reducible Four-Parameter System of Model Life Tables.” Population Studies 37(1):105–27.CrossRefGoogle Scholar
  20. Fisher, R.A.. 1930. The Genetical Theory of Natural Selection. Oxford, Clarendon Press.Google Scholar
  21. Forfar, D.O. 2004. “Mortality Laws.” In J.L. Teugels and B. Sundt (eds.), Encyclopedia of Actuarial Science, vol. 2, pp. 1139–44. Hoboken, NJ, Wiley.Google Scholar
  22. Gabriel, K.R. and I. Ronen. 1958. “Estimates of Mortality from Infant Mortality Rates.” Population Studies 12(2):164–69.CrossRefGoogle Scholar
  23. Gompertz, B. 1825. “On the Nature of the Function Expressive of the Law of Mortality, and a New Mode of Determining the Value of Life Contingencies.” Philosophical Transactions of Royal Society of London 115(Series A):513–83.Google Scholar
  24. Graunt, J. 1662. Natural and Political Observations Mentioned in a Following Index, and Made Upon the Bills of Mortality. London, John Martyn.Google Scholar
  25. Halley, E. 1693. “An Estimate of the Degrees of Mortality of the Manking.” Philosophical Transactions 196:596–610, 654–56.Google Scholar
  26. Heligman, L. and J.H. Pollard. 1980. “The Age Pattern of Mortality.” Journal of the Institute of Actuaries 107 Part 1(434):49–80.Google Scholar
  27. Heuveline, P. 1998. “‘Between One and Three Million’: Towards the Demographic Reconstruction of a Decade of Cambodian History (1970–1979).” Population Studies 52(1):49–65.CrossRefGoogle Scholar
  28. Heuveline, P. 2001. “The Demographic Analysis of Mortality Crises: The Case of Cambodia.” In H. Reed and C. Kelley (eds.), Forced Migration and Mortality, pp. 102–29. Washington, DC, National Academy Press.Google Scholar
  29. Himes, C., S.H. Preston, and G.A. Condran. 1994. “A Relational Model of Mortality at Older Ages in Low Mortality Countries.” Population Studies 48(2):269–91.CrossRefGoogle Scholar
  30. Horiuchi, S. and A.J. Coale. 1982. “A Simple Equation for Estimating the Expectation of Life at Old Ages.” Population Studies 36(2):317–26.CrossRefGoogle Scholar
  31. Horiuchi, S. and A.J. Coale. 1990. “Age Patterns of Mortality for Older Women: An Analysis Using the Age-Specific Rate of Mortality Change with Age.” Mathematical Population Studies 2(4):25–67.CrossRefGoogle Scholar
  32. Human Mortality Database. University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Gernmany). Available at http://www.mortality.org
  33. INDEPTH Network (Prepared by S.J. Clark). 2002. “INDEPTH Mortality Patterns for Africa.” In INDEPTH (ed.), Population, Health, and Survival at INDEPTH Sites, vol. 1. Population and Health in Developing Countries. Ottawa, IDRC Press.Google Scholar
  34. INDEPTH Network. 2010. An International Network of Field Sites with Continuous Demographic Evaluation of Populations and Their Health in Developing Countries – INDEPTH. http://www.indepth-network.net; http://www.indepth-network.org
  35. Jaffar, S., A.D. Grant, J. Whitworth, P.G. Smith, and H. Whittle. 2004. “The Natural History of HIV-1 and HIV-2 Infections in Adults in Africa: A Literature Review.” Bulletin of the World Health Organization 82:462–69.Google Scholar
  36. Knodel, J. and H. Kintner. 1977. “The Impact of Breast Feeding Patterns on the Biometric Analysis of Infant Mortality.” Demography 14(4):391–409.CrossRefGoogle Scholar
  37. Kung, H.C., D.L. Hoyert, J. Xu, and S.L. Murphy. 2008. “Deaths: Final Data for 2005.” National Vital Statistics Reports 56:10.Google Scholar
  38. Lantoine, C. and R. Pressat. 1984. “Nouveaux Aspects de la Mortalité Infantile.” Population 39(2):253–64.CrossRefGoogle Scholar
  39. Lederman, S. 1969. Nouvelles Tables-Types de Mortalité, INED Travaux et Documents, Cahiers 53. Paris, Presses Universitaires de France.Google Scholar
  40. Lederman, S. and J. Breas. 1959. “Les Dimensions de la Mortalité.” Population 14(4):637–82.CrossRefGoogle Scholar
  41. Li, T. and J.J. Anderson. 2009. “The Vitality Model: A Way to Understand Population Survival and Demographic Heterogeneity.” Theoretical Population Biology 76:118–31.Google Scholar
  42. Makeham, W.M. 1860. “On the Law of Mortality and the Construction of Annuity Tables.” The Assurance Magazine and Journal of the Institute of Actuaries 8:301–10.Google Scholar
  43. Marston, M., B. Zaba, J.A. Salomon, H. Brahmbhatt, and D. Bagenda. 2005. “Estimating the Net Effect of HIV on Child Mortality in African Populations Affected by Generalized HIV Epidemics.” JAIDS Journal of Acquired Immune Deficiency Syndromes 38(2):219.CrossRefGoogle Scholar
  44. McDaniel, A. 1995. Swing Low, Sweet Chariot: The Mortality Cost of Colonizing Liberia in the Nineteenth Century. Chicago and London, The University of Chicago.Google Scholar
  45. Morgan, D., C. Mahe, B. Mayanja, J.M. Okongo, R. Lubega, and J.A.G. Whitworth. 2002. “HIV-1 Infection in Rural Africa: Is There a Difference in Median Time to AIDS and Survival Compared with that in Industrialized Countries?” Aids 16(4):597.CrossRefGoogle Scholar
  46. OECD. 1980. Mortality in Developing Countries, vol. 3. Paris, France, Organization for Economic Cooperation and Development.Google Scholar
  47. Perks, W. 1932. “On Some Experiments in the Graduation of Mortality Statistics.” Journal of the Institute of Actuaries 63:12–57.Google Scholar
  48. Poole, D. and A.E. Raftery. 2000. “Inference for Deterministic Simulation Models: The Bayesian Melding Approach.” Journal of the American Statistical Association 95:452.CrossRefGoogle Scholar
  49. Preston, S.H. 1976. Mortality Patterns in National Populations. New York, NY, Academic Press.Google Scholar
  50. Preston, S.H.; Heuveline, P., and M. Guillot. 2000. Demography: Measuring and Modeling Population Processes. Oxford, UK; Malder, MA, Blackwell Publishers.Google Scholar
  51. Preston, S.H., A. McDaniel, and C. Grushka. 1993. “New Model Life Tables for High-Mortality Populations.” Historical Methods 26(4):149–59.Google Scholar
  52. Raftery, A.E. and L. Bao. 2010. “Estimating and Projecting Trends in HIV/AIDS Generalized Epidemics Using Incremental Mixture Importance Sampling.” Biometrics 9999:9999.Google Scholar
  53. Rogers, A. 1986. “Parameterized Multistate Population Dynamics and Projections.” Journal of the American Statistical Association 81(393):48–61.CrossRefGoogle Scholar
  54. Sharrow, D.J. and S.J. Clark. 2010. “A Parametric Investigation of Mortality at All Ages in a Rural, South African Population.” In Annual Meeting of the Population Association of America. Dallas, TX, Population Association of America.Google Scholar
  55. Sliwinsky, M. 1995. Le Génocide Khmer Rouge: Une Analyse Démographique. Paris, L’Harmattan.Google Scholar
  56. South Africa National Department of Health. 2009. 2008 National Antenatal Sentinel HIV & Syphilis Prevalence Survey South Africa. Report available at http://www.doh.gov.za/docs/nassps-f.html.
  57. Steinsaltz, D. and S.N. Evans. 2004. “Markov Mortality Models: Implications of Quasistationarity and Varying Initial Distributions.” Theoretical Population Biology 65(4):319–37.CrossRefGoogle Scholar
  58. Steinsaltz, D. and S.N. Evans. 2007. “Quasistationary Distributions for One-Dimensional Diffusions with Killing.” Transactions of the American Mathematical Society 359(3):1285.CrossRefGoogle Scholar
  59. Steinsaltz, D.R. and K.W. Wachter. 2006. “Understanding Mortality Rate Deceleration and Heterogeneity.” Mathematical Population Studies 13(1):19–37.CrossRefGoogle Scholar
  60. Sutherland, I. 1963. “John Graunt: A Tercentenary Tribute.” Journal of the Royal Statistical Society 126(Series A):537–56.Google Scholar
  61. Thiele, T.N. 1872. “On a Mathematical Formula to Express the Rate of Mortality Throughout the Whole Life.” Journal of the Institute of Actuaries and Assurance Magazine 16:313–29.Google Scholar
  62. UNAIDS. 2008. 2008 Report on the Global AIDS Epidemic. Report, UNAIDS, Gevena. http://www.unaids.org/en/KnowledgeCentre/HIVData/GlobalReport/2008/2008_Global_report.asp
  63. United Nations. 1955. Age and Sex Patterns of Mortality: Model Life Tables for Underdeveloped Countries. Population Studies 22. New York, NY, United Nations.Google Scholar
  64. United Nations. 1982. Model Life Tables for Developing Countries. Population Studies 77. New York, NY, United Nations.Google Scholar
  65. United Nations. 2003. Mortpak for Windows, Version 4.0. New York, NY, United Nations.Google Scholar
  66. Vaupel, J.W. 1997. “The Remarkable Improvement of Survival at Old Ages.” Philosophical Transactions of the Royal Society of London 352(1363, Series B):1799–804.CrossRefGoogle Scholar
  67. Vaupel, J.W., K.G. Manton, and E. Stallard. 1979. “The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality.” Demography 16(3):439–54.CrossRefGoogle Scholar
  68. Wilmoth, J.R., V. Canudas-Romo, S. Zureick, and C.C. Sawyer. 2009. A Flexible Two-Dimensional Mortality Model for Use in Indirect Estimation. Annual Meeting of the Population Association of America. Detroit, MI, Population Association of America.Google Scholar
  69. Zaba, B. 1979. “The Four-Parameter Logit Life Table System.” Population Studies 33(1):79–100.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Sociology and California Center for Population Research, University of CaliforniaLos AngelesUSA
  2. 2.Assistant Professor of Sociology, and a Research Affiliate of the Center for Studies in Demography and EcologyUniversity of WashingtonSeattleUSA

Personalised recommendations