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Estimating optimal willingness to pay thresholds for cost‐effectiveness analysis: A generalized method


  • Charles E Phelps
  • Chris Cinatl


Operationalizing cost‐effectiveness analysis (CEA) requires that decisionmakers select maximum willingness to pay thresholds (K). We generalize previous methods used to estimate K using highly flexible hyperbolic absolute risk aversion (HARA) utility functions that encompass a wide range of risk behavior. For HARA utility, we calculate formulas for relative risk aversion (r*) and relative prudence (π∗), using literature‐based estimates to calibrate our HARA model. We then assess optimal WTP thresholds (K) in absolute value and relative to income (K/M). Across the most‐plausible range of risk preference parameters (r* and π∗), optimal K/M ratios sit (approximately) in the range of 1 to 3, although we cannot readily rule out larger K/M values. The optimal K always increases with income, while K/M falls with income if utility has increasing relative risk aversion. Results of this more‐general model of economic utility are broadly consistent with previous work using more‐restrictive Weibull functions. More precision in measuring the key parameters—particularly relative prudence (π∗) will narrow down the range of K/M estimates. The highly general HARA structure illuminates why and how optimal CEA thresholds change with income. An appendix illuminates how relative risk aversion and relative prudence relate to each other.

Suggested Citation

  • Charles E Phelps & Chris Cinatl, 2021. "Estimating optimal willingness to pay thresholds for cost‐effectiveness analysis: A generalized method," Health Economics, John Wiley & Sons, Ltd., vol. 30(7), pages 1697-1702, July.
  • Handle: RePEc:wly:hlthec:v:30:y:2021:i:7:p:1697-1702
    DOI: 10.1002/hec.4268

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    References listed on IDEAS

    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. Dimitris Christelis & Dimitris Georgarakos & Tullio Jappelli & Maarten van Rooij, 2020. "Consumption Uncertainty and Precautionary Saving," The Review of Economics and Statistics, MIT Press, vol. 102(1), pages 148-161, March.
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    5. Linda Ryen & Mikael Svensson, 2015. "The Willingness to Pay for a Quality Adjusted Life Year: A Review of the Empirical Literature," Health Economics, John Wiley & Sons, Ltd., vol. 24(10), pages 1289-1301, October.
    6. Donald Meyer & Jack Meyer, 2005. "Relative Risk Aversion: What Do We Know?," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 243-262, December.
    7. Karl Claxton & Steve Martin & Marta Soares & Nigel Rice & Eldon Spackman & Sebastian Hinde & Nancy Devlin & Peter C Smith & Mark Sculpher, 2013. "Methods for the estimation of the NICE cost effectiveness threshold," Working Papers 081cherp, Centre for Health Economics, University of York.
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    Cited by:

    1. Darius N. Lakdawalla & Charles E. Phelps, 2022. "A guide to extending and implementing generalized risk-adjusted cost-effectiveness (GRACE)," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 23(3), pages 433-451, April.

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