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Value Health. 2019 Jul;22(7):785-791. doi: 10.1016/j.jval.2019.03.003. Epub 2019 May 17.

A New Method to Determine the Optimal Willingness to Pay in Cost-Effectiveness Analysis.

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University of Rochester, Rochester, NY, USA. Electronic address:



To provide a new approach to estimate optimal willingness to pay (WTP) for health technology assessment (HTA).


This analysis specified utility as a function of income and calibrated it using estimates of relative risk aversion, from which the optimal WTP (K) can be determined using Garber and Phelps' results (1997).


This analysis used the highly flexible Weibull utility function, calibrated with estimates of relative risk aversion (r*) derived from multiple data sources. The analysis centered on r* = 1 and conducted sensitivity analysis on r* and key Weibull parameters. For a range of income (M), graphs demonstrated how K/M and K vary with M. Results were compared with estimates of K and K/M from alternative models. Extrapolation from a representative individual to population-wide health plans was discussed.


Using r* = 1 and central values of other key parameters, K/M (at average income for developed nations) was approximately 2× annual income. Both K and K/M rose with income. Sensitivity analysis showed that results depend moderately on the chosen value of r* and specific Weibull utility function parameters. At average income, the optimal K/M ratio (2×) was modestly lower than many standard recommendations (typically 3× average income) and substantially lower than estimates using value-of-statistical-life approaches.


The new model, although not yet perfected, provides a different way to identify the WTP cutoff for HTA. Extrapolation to more than twice the calibration income ($50 000) is advised against. Analysis of other approaches to estimate the optimal K reveal potential upward biases.


cost-effectiveness analysis; cost-effectiveness cutoff; health technology assessment; willingness to pay


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