Skip to main content

Mortality Models Incorporating Theoretical Concepts of Ageing

  • Chapter
Forecasting Mortality in Developed Countries

Part of the book series: European Studies of Population ((ESPO,volume 9))

  • 338 Accesses

Abstract

Among the basic attributes of ageing, heterogeneity, homeostasis and stochasticity were studied extensively in the second half of the 20th century. A selection of mortality models developed on the basis of these attributes are reviewed in this chapter, including older as well as more recent concepts. The older models of vitality, fixed heterogeneity and debilitation, being unsuitable for practical use, proved to be appropriate for testing simple hypotheses about the importance of certain factors for survival. In contrast, the more recent models of changing frailty, and in particular the stochastic process models of mortality, allow an explicit description of the physiological mechanisms of ageing. These models also appeared to be successful in complex applications. Irrespective of when they were devised, the models of evolutionary theories of ageing are less certain in their conclusions than any other models mentioned above. However, all models discussed here have contributed to improvements in our understanding of age patterns of mortality. Some of them (i.e. changing frailty and stochastic process models) can be safely recommended as a tool for both the justification and the prediction of mortality changes in the future.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Abrams, P.A. and D. Ludwig (1995), Optimality theory, Gompertz law, and the disposable soma theory of senescence. Evolution 49, pp. 1055–1066.

    Article  Google Scholar 

  • Andersen, P.K., O. Borgan, R.D. Gill and N. Keyding (1992), Statistical methods based on counting processes. London, New York: Springer Verlag.

    Google Scholar 

  • Atlan, H. (1968), Strehler’s theory of mortality and the second principle of thermodynamics. Journal of Gerontology 23(1–4), pp. 196–200.

    PubMed  CAS  Google Scholar 

  • Beard, R.E. (1959), Note on some mathematical mortality models. In: C.E.W. Wolstenholme and M.O. Connor (eds.). The Lifespan of Animals. Boston: Little, Brown. pp. 302–311.

    Google Scholar 

  • Bafitis, H. and F. Sargent (1977), Human physiological adaptability through the life sequence. Journal of Gerontology 32, pp. 402–410.

    PubMed  CAS  Google Scholar 

  • Bohr, V.A. and R.A. Anson (1995), DNA damage, mutation and fine structure of DNA repair in aging. Mutation Research 338, pp. 25–34.

    Article  PubMed  CAS  Google Scholar 

  • Brooks, A., G.J. Lithgow and T.E. Johnson (1994), Mortality rates in a genetically heterogeneous population of caenorhabditis elegans. Science 263, pp. 668–671.

    Article  PubMed  ADS  CAS  Google Scholar 

  • Carey, J.R., P. Liedo, D. Orzoco and J.W. Vaupel (1992), Slowing of mortality rates at older ages in large medfly cohorts. Science 258, pp. 457–461.

    Article  PubMed  ADS  CAS  Google Scholar 

  • Charlesworth, B. (1990), Optimization models, quantitative genetics, and mutation. Evolution 44, pp. 520–38.

    Article  Google Scholar 

  • Charlesworth, B. (1994), Evolution in age-structured Populations. Cambridge University Press.

    Google Scholar 

  • Charlesworth, B. and L. Partridge (1997), Ageing: levelling off of the grim Reaper. Current Biology 7, pp. 440–442.

    Article  Google Scholar 

  • Curtsinger, J.W., H.H. Fukui, D.R. Townsend and J.W. Vaupel (1992), Demography of genotypes: failure of the limited life span paradigm in Drosophila Melanogaster. Science 258, pp. 461–463.

    Article  PubMed  ADS  CAS  Google Scholar 

  • Cutler, R.G. (1975), Evolution of human longevity and the genetic complexity governing aging rate. Proceedings of the National Academy of Sciences USA 72(11), pp. 4664–4668.

    Article  ADS  CAS  Google Scholar 

  • Economos, A.C. (1981), Beyond rate of living. Gerontology 27, pp. 258–265.

    Article  PubMed  CAS  Google Scholar 

  • Economos, A.C. (1982), Rate of aging, rate of dying and the mechanism of mortality. Archieves of Gerontology and Geriatry, 1, pp. 3–27.

    Article  CAS  Google Scholar 

  • Failla, G. (1958), The aging process and carcinogenis. Annals of the New York Academy of Sciences. 7, 6, pp. 1124–1140.

    Article  Google Scholar 

  • Fisher, R.A. (1930), The genetic Theory of natural Selection. Oxford: Clarendon.

    Google Scholar 

  • Frank, S.A. (1998), Foundations of Social Evolution. Princeton University Press.

    Google Scholar 

  • Gavrilov, L.A. and N.S. Gavrilova (1991), The Biology of Life Span: A quantitative Approach. London, New York: Harwood Academic Publishers.

    Google Scholar 

  • Gompertz, B. (1825), On the nature of the function expressive of the law of human mortality. Phylosophical Transactions 27, pp. 513–519.

    Article  ADS  Google Scholar 

  • Hamilton, W.D. (1966), The moulding of senescence by natural selection. Journal of Theoretical Biology, 12, pp. 12–45.

    Article  PubMed  CAS  Google Scholar 

  • Higham, J.A. (1851), On the value of selection as exercised by the policy-holder against the company. Journal of the Institute of Actuaries 1, pp. 179–202.

    Google Scholar 

  • Johnson, T.E. (1997), Genetic Influence on Aging. Experimental Gerontology 32, pp. 11–22.

    Article  PubMed  CAS  Google Scholar 

  • Kannisto, V. (1996), Development of oldest old Mortality, 1950–1990: Evidence from 28 developed countries. Odense Monographs on Population Aging No. 1, Odense University Press.

    Google Scholar 

  • Kaufman, S.A. (1993), Origins of Order: Self-Organization and Selection in Evolution. Oxford: Oxford University Press.

    Google Scholar 

  • Kirkwood, T.B.L. (1990), The disposable soma theory of aging. In: Genetic Effects of Aging, II: 9–19. Caldwell: Telford Press.

    Google Scholar 

  • Manton, K.G., E. Stallard and J.W. Vaupel (1986), Alternative models for heterogeneity in mortality risks among the aged. The Journal of American Statistical Association 81(395), pp. 635–644.

    Article  CAS  Google Scholar 

  • Medawar, P.B. (1952), An Unsolved Problem in Biology. London: H.K. Lewis.

    Google Scholar 

  • Mueller, L.D. and M.R. Rose (1996), Evolutionary theory predicts late-life mortality plateaus. Proceedings of the National Academy of Sciences, 93, pp. 15249–15253. USA.

    Article  ADS  CAS  Google Scholar 

  • Øksendal, B. (1991), Stochastic Differential Equations: An Introduction with Applications. Berlin, Heidelberg: Springer Verlag.

    Google Scholar 

  • Pletcher, S.D. and J.W. Curtsinger (1998), Mortality plateaus and the evolution of senescence: why are old-age mortality rates so low? Evolution 52(2), pp. 454–464.

    Article  Google Scholar 

  • Sacher, G.A. and E. Trucco (1962), The stochastic theory of mortality. Annals of New York Academy of Sciences 96, pp. 985–1007.

    Article  CAS  Google Scholar 

  • Sacher, G.A. (1982), Evolutionary theory in gerontology. Perspectives in Biological Medicine, 25, pp. 339–353.

    CAS  Google Scholar 

  • Sheps, M.C. and J. Menken (1973), Mathematical Models of Conception and Births. Chicago: University of Chicago Press.

    Google Scholar 

  • Shock, N.W. (1960), Some of the facts of aging. In: N.W. Shock (ed.), Aging: Some Social and Biological Aspects. Washington DC: American Association for the Advancement of Science, pp. 241–260.

    Google Scholar 

  • Shock, N.W. (1974), Physiological theories of aging. In: M. Rockstein (ed.), Theoretical Aspects of Aging. Academic Press, New York, pp. 119–136.

    Google Scholar 

  • Simms, H.S. (1942), The Use of a measurable cause of death (hemorhage) for the evaluation of aging. Journal of General Physiology, 26, pp. 169–178.

    Article  Google Scholar 

  • Simms, H.S. (1948), Logarithmic increase in mortality as a manifestation of aging. Journal of Gerontology 1, pp. 13–26.

    Google Scholar 

  • Strehler, B.L. and A.S. Mildvan (1960), General theory of mortality and aging. Science 132, pp. 14–21.

    Article  PubMed  ADS  CAS  Google Scholar 

  • Szilard, L. (1959), On the nature of the aging process. Proceedings of the National Academy of Sciences, pp. 30–45. USA.

    Google Scholar 

  • Tuma, N.B. and M.T. Hannan (1984), Social dynamics: models and methods. Orlando, Florida: Academic Press.

    Google Scholar 

  • Vaupel, J.W., K.G. Manton and E. Stallard (1979), The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16, pp. 439–454.

    Article  PubMed  CAS  Google Scholar 

  • Vaupel, J.W. and A.I. Yashin (1985), Heterogeneity’s ruses: some surprising effects of selection on population dynamics. American Statistician 39, pp. 176–185.

    Article  PubMed  MathSciNet  CAS  Google Scholar 

  • Vaupel, J.W. and A.I. Yashin (1987), Repeated resuscitation: how life saving alters life tables. Demography 4, pp. 123–135.

    Article  Google Scholar 

  • Vaupel, J.W., J.R. Carey, K. Christensen, T.E. Johnson, A.I. Yashin, N.V. Holm, I.A. Iachine, V. Kannisto, A.A. Khazaeli, P. Liedo, V.D. Longo, Y. Zeng, K.G. Manton and J.W. Curtsinger (1998), Biodemographic trajectories of longevity. Science 280, pp. 855–860.

    Article  PubMed  CAS  Google Scholar 

  • Wachter, K.W. (1999), Evolutionary demographic models for mortality plateaus. Proceedings of the National Academy of Sciences, USA 96, pp. 10544–10547.

    Article  ADS  CAS  Google Scholar 

  • Witteman, J.C., D.E. Grobbee, H.A. Valkenburg, A.M. van Hemert, T. Stijnen, H. Burger and A. Hofman (1994), J-shaped relation between change in diastolic blood pressure and progression of aortic atherosclerosis. Lancet 343, pp. 504–507.

    Article  PubMed  CAS  Google Scholar 

  • Woodbury, M.A. and K.G. Manton (1977), A random work model of human mortality and aging. Theoretical Population Biology 11, pp. 37–48.

    Article  PubMed  MathSciNet  CAS  Google Scholar 

  • Yashin, A.I. (1970), Filtering of jump processes. Automation and Remote Control 31, pp. 725–730.

    MathSciNet  Google Scholar 

  • Yashin, A.I. (1980), Conditional Gaussian estimation of dynamic systems under jumping observations. Automation and Remote Control 5, pp. 618–626 (Translated from Russian).

    MATH  Google Scholar 

  • Yashin, A.I. (1985), Dynamics in Survival analysis: Conditional Gaussian property U.S. Cameron-Martin formula. In: N.V. Krylov, R.Sh. Liptser and A.A. Novikov (eds.), Statistics and Control of stochastic processes. New York: Springer, pp. 466–475.

    Google Scholar 

  • Yashin, A.I., K.G. Manton and J.W. Vaupel (1985), Mortality and aging in heterogeneous populations: a stochastic process model with observed and unobserved variables. Theoretical Population Biology 27, pp. 159–175.

    Article  MathSciNet  Google Scholar 

  • Yashin, A.I., J.W. Vaupel and I.A. Iachine (1994), A duality of aging: the equivalence of mortality models based on radically different concepts. Mechanisms of Aging and Development 74, pp. 1–14.

    Article  CAS  Google Scholar 

  • Yashin, A.I., K.G. Manton, M.A. Woodbury and E. Stallard (1995), The effects of health histories on stochastic process model of aging and mortality. Journal of Mathematical Biology 34, pp. 1–16.

    Article  PubMed  CAS  Google Scholar 

  • Yashin, A.I. and K.G. Manton (1997), Effects of unobserved and partially observed covariate processes on system failure: a review of models and estimation strategies. Statistical Science 12(1), pp. 20–34.

    Article  MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Kluwer Academic Publishers

About this chapter

Cite this chapter

Yashin, A. (2001). Mortality Models Incorporating Theoretical Concepts of Ageing. In: Tabeau, E., van den Berg Jeths, A., Heathcote, C. (eds) Forecasting Mortality in Developed Countries. European Studies of Population, vol 9. Springer, Dordrecht. https://doi.org/10.1007/0-306-47562-6_11

Download citation

  • DOI: https://doi.org/10.1007/0-306-47562-6_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6833-5

  • Online ISBN: 978-0-306-47562-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics