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Healthy longevity from incidence-based models: More kinds of health than stars in the sky

Author

Listed:
  • Hal Caswell

    (Woods Hole Oceanographic Institute)

  • Silke van Daalen

    (Universiteit van Amsterdam)

Abstract

Background: Healthy longevity (HL) is an important measure of the prospects for quality of life in ageing societies. Incidence-based (cf. prevalence-based) models describe transitions among age classes and health stages. Despite the probabilistic nature of those transitions, analyses of healthy longevity have focused persistently on means (``health expectancy''), neglecting variances and higher moments. Objective: Our goal is a comprehensive methodology to analyze HL in terms of any combination of health stages and age classes, or of transitions among health stages, or of values (e.g., quality of life) associated with health stages or transitions. Methods: We construct multistate Markov chains for individuals classified by age and health stage and use Markov chains with rewards to compute all moments of HL. Results: We present a new and straightforward algorithm to create the multistate reward matrices for occupancy, transitions, or values associated with occupancy or transitions. As an example, we analyze a published model for colorectal cancer. The possible definitions of HL in this simple model outnumber the stars in the visible universe. Our method can analyze any of them; we show four examples: longevity without abnormal cells, cancer-free longevity, and longevity with cancer before or after a critical age. Contribution: Our methods make it possible to analyze any incidence-based model,with any number of health stages, any pattern of transitions, and any kind of values assigned to stages. It is easily computable, requires no simulations, provides all the moments of healthy longevity, and solves the inhomogeneity problem.

Suggested Citation

  • Hal Caswell & Silke van Daalen, 2021. "Healthy longevity from incidence-based models: More kinds of health than stars in the sky," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 45(13), pages 397-452.
    • Handle: RePEc:dem:demres:v:45:y:2021:i:13
    DOI: 10.4054/DemRes.2021.45.13
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    References listed on IDEAS

    as
    1. James Vaupel & Vladimir Romo, 2003. "Decomposing change in life expectancy: A bouquet of formulas in honor of Nathan Keyfitz’s 90th birthday," Demography, Springer;Population Association of America (PAA), vol. 40(2), pages 201-216, May.
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    10. Hal Caswell, 2020. "The formal demography of kinship II: Multistate models, parity, and sibship," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 42(38), pages 1097-1146.
    11. Hal Caswell, 2014. "A matrix approach to the statistics of longevity in heterogeneous frailty models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(19), pages 553-592.
    12. Marty Parker & Milica Bucknall & Carol Jagger & Ross Wilkie, 2020. "Extending Working Lives: A Systematic Review of Healthy Working Life Expectancy at Age 50," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 150(1), pages 337-350, July.
    13. Agnes Lievre & Nicolas Brouard & Christopher Heathcote, 2003. "The Estimation Of Health Expectancies From Cross-Longitudinal Surveys," Mathematical Population Studies, Taylor & Francis Journals, vol. 10(4), pages 211-248.
    14. Hal Caswell, 2011. "Beyond R0: Demographic Models for Variability of Lifetime Reproductive Output," PLOS ONE, Public Library of Science, vol. 6(6), pages 1-21, June.
    15. Hal Caswell & Fanny Annemarie Kluge, 2015. "Demography and the statistics of lifetime economic transfers under individual stochasticity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(19), pages 563-588.
    16. Govert Ewout Bijwaard, 2014. "Multistate event history analysis with frailty," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(58), pages 1591-1620.
    17. Nicole L. Van Der Gaag & Luc Bonneux & Govert Ewout Bijwaard & Joop de Beer, 2015. "A multistate model to project elderly disability in case of limited data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(3), pages 75-106.
    18. Roth, Gregory & Caswell, Hal, 2018. "Occupancy time in sets of states for demographic models," Theoretical Population Biology, Elsevier, vol. 120(C), pages 62-77.
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    Cited by:

    1. Daniel C. Schneider, 2025. "Recent developments in discrete-time multistate estimation in Stata," German Stata Conference 2025 08, Stata Users Group.
    2. Hal Caswell & Lotte de Vries, 2025. "The formal demography of kinship VII: Lifetime kin overlap within and across generations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 53(5), pages 123-174.
    3. Hal Caswell, 2023. "The contributions of stochastic demography and social inequality to lifespan variability," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 49(13), pages 309-354.
    4. Magdalena Muszyńska-Spielauer & Marc Luy, 2022. "Well-Being Adjusted Health Expectancy: A New Summary Measure of Population Health," European Journal of Population, Springer;European Association for Population Studies, vol. 38(5), pages 1009-1031, December.

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    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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