Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-12-01T02:52:34.922Z Has data issue: false hasContentIssue false
  • English
  • Français

Application of Frailty-Based Mortality Models Using Generalized Linear Models

Published online by Cambridge University Press:  17 April 2015

Zoltan Butt  and
Steven Haberman
Steven Haberman
Affiliation:
Faculty of Actuarial Science and Statistics, City University, London
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Two families of frailty models – Makeham/Gompertz-gamma and Gompertz-inverse Gaussian – have been considered to graduate insurance-based mortality data. The aims of this exercise are twofold. The first aim is to make use of generalized linear models and to evaluate these against traditional techniques. The second aim is to measure the scale of individual heterogeneity in insurance-based populations. The results indicate that (subject to issues of identifiability) there is evidence of frailty in these populations.

Keywords

FrailtyMortality rates graduationGeneralized linear modellingGompertz-Makeham functionPerks model
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 34 , Issue 1 , May 2004 , pp. 175 - 197
Copyright
Copyright © ASTIN Bulletin 2004

References

Aalen, O.O. (1988) Heterogeneity in survival analysis, Statistics in Medicine 7, 1121–1137.CrossRefGoogle ScholarPubMed
Ainslie, R. (2000) Annuity and insurance products for impaired lives. Presented to the Staple Inn Actuarial Society, Institute of Actuaries, London.Google Scholar
Benjamin, B. and Pollard, J.H. (1993) The analysis of mortality and other actuarial statistics, The Institute of Actuaries and the Faculty of Actuaries, London.Google Scholar
Blumen, I., Kogan, M. and McCarthy, P.J. (1955) The industrial mobility of labour as a probability process, Cornell Studies of Industrial and Labour Relations, Vol. vi, Cornell University Press, Ithaca, New York.Google Scholar
Butt, Z. and Haberman, S. (2002) Application of frailty-based mortality models to insurance data, Actuarial Research Paper No. 142, Department of Actuarial Science & Statistics, City University, London.Google Scholar
Congdon, P. (1994) Analyzing mortality in London: Life Tables with frailty, Journal of the Royal Statistical Society, Series D, 43, 277–308.Google Scholar
Forfar, D.O. and Smith, D.M. (1988) The changing shape of English Life Tables, Transactions of the Faculty of Actuaries, 40, 98–134.CrossRefGoogle Scholar
Gini, C. (1924) Premières recherches sur la fécondabilité de la femme, Proceedings of the International Mathematical Congress, 2, 889–892.Google Scholar
Haberman, S. and Renshaw, A.E. (1996) Generalised linear models and actuarial science, Journal of the Royal Statistical Society, Series D, 45, 407–436.Google Scholar
Hoem, J.M. (1990) Identifiability in hazard model with unobserved heterogeneity: The compatibility of two apparently contradicting results, Theoretical Population Biology 37, 124–128.CrossRefGoogle Scholar
Horiuchi, S. and Coale, A.J. (1990) Age patterns of mortality for older women: An analysis using the age-specific rate of mortality change with age, Mathematical Population Studies 2, 245–267.CrossRefGoogle ScholarPubMed
Hougaard, P. (1984) Life Table methods for heterogeneous populations: Distributions describing heterogeneity, Biometrika 71, 75–83.CrossRefGoogle Scholar
Keyfitz, N. (1985) Applied mathematical demography, Second Edition, Springer, New York.CrossRefGoogle Scholar
Lancaster, T. (1990) The econometric analysis of transition data, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Le Bras, H. (1976) Lois de mortalité et age limité, Population 31, 655–692.CrossRefGoogle Scholar
Manton, K.G. and Stallard, E. (1984) Recent trends in mortality analysis, Academic press, Inc., 236–299.Google Scholar
Manton, K.G., Stallard, E. and Vaupel, J.W. (1981) Methods for comparing the mortality experience of heterogeneous populations, Demography 18, 389–410.CrossRefGoogle ScholarPubMed
Manton, K.G., Stallard, E. and Vaupel, J.W. (1986) Alternative models for the heterogeneity of mortality risks among the aged, Journal of the American Statistical Association 81, 635–644.CrossRefGoogle ScholarPubMed
McCullagh, P. and Nelder, J.A. (1989) Generalized linear models, Second Edition, Chapman and Hall, London.CrossRefGoogle Scholar
McNown, R. and Rogers, A. (1989) Time-series analysis forecasts of a parameterised mortality schedule, in Congdon, P. and Batey, P., eds, “Advances in regional demography: Information, forcasts, models”, Bellhaven Press, London, pp. 107–123.Google Scholar
Renshaw, A.E. (1991) Actuarial graduation practice and generalised linear and non-linear models, Journal of the Institute of Actuaries 118, 295–312.CrossRefGoogle Scholar
Renshaw, A.E. (1995) Graduation and generalized linear models: An overview, Actuarial Research Paper No. 73, Department of Actuarial Science & Statistics, City University, London.Google Scholar
Thatcher, A.R. (1999) The long-term pattern of adult mortality and the highest attained age, Journal of the Royal Statistical Society, Series A, 162, 5–30.CrossRefGoogle ScholarPubMed
Vaupel, J.W. (1999) Contribution to the discussion of ‘The long-term pattern of adult mortality and highest attained age’, by Thatcher, A.R., Journal of the Royal Statistical Society, Series A, 162, 31–32.Google Scholar
Vaupel, J.W., Manton, K.G. and Stallard, E. (1979) The impact of heterogeneity in individual frailty on the dynamics of mortality, Demography, 16, 439–454.CrossRefGoogle ScholarPubMed
Vaupel, J.W. and Yashin, A.I. (1985) The deviant dynamics of death in heterogeneous populations, Sociological Methodology, 179–211. Edited by Tuma, N.B, Jossey-Bas, San Francisco.Google Scholar
Wang, S.S. and Brown, R.L. (1998) A frailty model for projection of human mortality improvement, Journal of Actuarial Practice 6, 221–241.Google Scholar
Yashin, A.I., Vaupel, J.W. and Iachine, I.A. (1994) A duality in ageing: The equivalance of mortality models based on radically different concept, Mechanisms of Ageing and Development 74, 1–14.CrossRefGoogle Scholar