What is a QALY Worth? Admissible Utility Functions for Health, Longevity, and Wealth

Health risks are commonly quantified using either of two alternative measures, willingness to pay (WTP) and quality-adjusted life years (QALYs). The relationship between these measures is of interest for comparing benefit-cost analysis (which uses WTP) with cost-effectiveness analysis (which uses QALYs), identifying a threshold for determining which health interventions are cost-effective, and estimating WTP for health improvement from expected QALY gains. WTP and QALYs rest on different theoretical foundations. Utility functions that are consistent with both concepts are derived. Some commonly used utility functions (e.g., expected present value of period utility) are inconsistent with these assumptions except in special cases. The admissible utility functions imply that an individual’s marginal WTP per QALY is not constant but depends on baseline and incremental QALYs, wealth, and aversion to longevity risk, which implies that cost-effectiveness analysis using a fixed threshold value per QALY is inconsistent with individuals’ preferences. Moreover, the admissible utility functions imply that value per statistical life is weakly increasing in future health and life expectancy, in conflict with empirical evidence. These results suggest that QALYs are not a valid measure of individuals’ health and longevity preferences.