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Phase-type aging modeling for health dependent costs

Author

Listed:
  • Maria Govorun

    (UWO - University of Western Ontario)

  • Guy Latouche

    (ULB - Université libre de Bruxelles)

  • Stéphane Loisel

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

In the present paper we develop recursive algorithms to evaluate the distribution of the net present value (abbreviated as "NPV") of a health care contract. The duration of the program is a random variable representing the lifetime of an individual. We suggest a discrete time phase-type approach to model individual health care costs. In this approach, annual health care costs depend naturally on the health state of the individual. We also derive the distribution of the NPV assuming that annual health care costs are iid random variables. We demonstrate analytically that, under special parametrisation, the model with iid costs gives a similar expectation of the NPV to the one of the model with health dependent costs. We propose techniques to evaluate the impact of health related events and demonstrate it on numerical examples.

Suggested Citation

  • Maria Govorun & Guy Latouche & Stéphane Loisel, 2015. "Phase-type aging modeling for health dependent costs," Post-Print hal-01084274, HAL.
    • Handle: RePEc:hal:journl:hal-01084274
    Note: View the original document on HAL open archive server: https://hal.science/hal-01084274v1
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    References listed on IDEAS

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    1. Drummond, Michael F. & Sculpher, Mark J. & Torrance, George W. & O'Brien, Bernie J. & Stoddart, Greg L., 2005. "Methods for the Economic Evaluation of Health Care Programmes," OUP Catalogue, Oxford University Press, edition 3, number 9780198529453, Decembrie.
    2. Zhao, Xiaobing & Zhou, Xian, 2012. "Estimation of medical costs by copula models with dynamic change of health status," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 480-491.
    3. Su, Shu & Sherris, Michael, 2012. "Heterogeneity of Australian population mortality and implications for a viable life annuity market," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 322-332.
    4. Eisele, Karl-Theodor, 2006. "Recursions for compound phase distributions," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 149-156, February.
    5. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
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    Cited by:

    1. Fuino, Michel & Wagner, Joël, 2018. "Long-term care models and dependence probability tables by acuity level: New empirical evidence from Switzerland," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 51-70.
    2. Khouzeima Moutanabbir & Hassan Abdelrahman, 2022. "Bivariate Sarmanov Phase-Type Distributions for Joint Lifetimes Modeling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1093-1118, June.
    3. Boquan Cheng & Rogemar Mamon, 2024. "Examining the identifiability and estimability of the phase-type ageing model," Computational Statistics, Springer, vol. 39(2), pages 963-1004, April.
    4. Shemendyuk, Aleksandr & Wagner, Joël, 2025. "Evolution of institutional long-term care costs based on health factors," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 107-130.

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