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Stochastic modelling of the hybrid survival curve

Author

Listed:
  • Chong It Tan

    (Australian National University)

  • Jackie Li

    (Macquarie University)

  • Johnny Siu-Hang Li

    (University of Waterloo)

  • Uditha Balasooriya

    (Nanyang Technological University)

Abstract

In this paper, building upon the idea of cross-sectional survival probabilities developed by Brouard (Espaces Popul Soc 2(14–15):157–168, 1986), we propose using stochastic models to study the evolution of a new type of survival curves called hybrid survival curve. We find that the three-factor survival model provides a better model fitting than the two-factor survival model. Furthermore, the three time-varying parameters are highly interpretable and their respective trends can be used as an indicator for the rectangularisation of survival curve. On top of that, we demonstrate how the time-varying parameters can be extrapolated into the future to obtain projected hybrid survival curves.

Suggested Citation

  • Chong It Tan & Jackie Li & Johnny Siu-Hang Li & Uditha Balasooriya, 2016. "Stochastic modelling of the hybrid survival curve," Journal of Population Research, Springer, vol. 33(4), pages 307-331, December.
  • Handle: RePEc:spr:joprea:v:33:y:2016:i:4:d:10.1007_s12546-016-9168-x
    DOI: 10.1007/s12546-016-9168-x
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    References listed on IDEAS

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    1. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2011. "Mortality density forecasts: An analysis of six stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 355-367, May.
    2. Jong, Piet De & Marshall, Claymore, 2007. "Mortality Projection Based on the Wang Transform," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 149-161, May.
    3. Andrew Cairns & David Blake & Kevin Dowd & Guy Coughlan & David Epstein & Alen Ong & Igor Balevich, 2009. "A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 1-35.
    4. Väinö Kannisto, 2000. "Measuring the compression of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(6).
    5. Jack Yue, 2012. "Mortality Compression and Longevity Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 16(4), pages 434-448.
    6. Haberman, Steven & Renshaw, Arthur, 2012. "Parametric mortality improvement rate modelling and projecting," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 309-333.
    7. Jackie Li, 2013. "A Poisson common factor model for projecting mortality and life expectancy jointly for females and males," Population Studies, Taylor & Francis Journals, vol. 67(1), pages 111-126, March.
    8. John Wilmoth & Shiro Horiuchi, 1999. "Rectangularization revisited: Variability of age at death within human populations," Demography, Springer;Population Association of America (PAA), vol. 36(4), pages 475-495, November.
    9. Renshaw, A.E. & Haberman, S., 2006. "A cohort-based extension to the Lee-Carter model for mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 556-570, June.
    10. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
    11. Andrew Hunt & David Blake, 2014. "A General Procedure for Constructing Mortality Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 116-138.
    12. Wai-Sum Chan & Johnny Li & Jackie Li, 2014. "The CBD Mortality Indexes: Modeling and Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 38-58.
    13. Kenneth W. Wachter, 2005. "Tempo and its Tribulations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 13(9), pages 201-222.
    14. John R. Wilmoth, 2005. "On the relationship between period and cohort mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 13(11), pages 231-280.
    15. Nan Li & Ronald Lee, 2005. "Coherent mortality forecasts for a group of populations: An extension of the lee-carter method," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 575-594, August.
    16. Siu Cheung & Jean-Marie Robine & Edward Tu & Graziella Caselli, 2005. "Three dimensions of the survival curve: horizontalization, verticalization, and longevity extension," Demography, Springer;Population Association of America (PAA), vol. 42(2), pages 243-258, May.
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    Cited by:

    1. Jacie Jia Liu, 2021. "A Study on Link Functions for Modelling and Forecasting Old-Age Survival Probabilities of Australia and New Zealand," Risks, MDPI, vol. 9(1), pages 1-18, January.

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