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Phase-type aging modeling for health dependent costs

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  • Govorun, Maria
  • Latouche, Guy
  • Loisel, Stéphane

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 parametrization, 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. Based on Canadian government data on health expenditures, we study the impact on the NPV of the health cost structure by age.

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  • Govorun, Maria & Latouche, Guy & Loisel, Stéphane, 2015. "Phase-type aging modeling for health dependent costs," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 173-183.
    • Handle: RePEc:eee:insuma:v:62:y:2015:i:c:p:173-183
    DOI: 10.1016/j.insmatheco.2015.03.005
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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.
    2. 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.
    3. 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.
    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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    1. 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.
    2. 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.
    3. 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.
    4. 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.

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