Generalized Risk-Adjusted Cost-Effectiveness (GRACE) aims to incorporate risk appetite into standard cost-benefit analysis (CEA) methods. Whereas traditional CEA assumes individual risk neutrality, GRACE allows risk appetite to affect value. That is, a health gain in a healthier state is more valuable than an equivalent health gain in a healthier state. But a key parameter in estimating GRACE is knowing the risk-averse estimates of quality-of-life outcomes.
A recent NBER working paper by Mulligan et al. (2023) provide a way to do this. Individuals have certain quality of life and risks. The survey asks which one an individual prefers. Repeat this process with different specific values. Using this approach, the authors calculated the certainty equivalent for each condition as the midpoint for certain outcomes between two adjacent rows where respondents switched from preferring a risky treatment to preferring a treatment with a specific outcome.
Once the certainty equivalent is known, an individual’s utility function can be estimated. The baseline approach used expected utility theory, assumed that reference health status was unimportant, and that the authors pooled data from all respondents and questions. In addition, the authors estimate utility using expo-power and the constant relative risk aversion (CRRA) utility function (see formula below).
Using this approach, the authors found that:
…the individual exhibits a risk-seeking preference at low fitness levels, shifts to a risk-averse preference when health equals 0.485 (measured on a scale of 0 to 1), and becomes most risk-averse when health is perfect (relative risk aversion coefficient = 4.36). Risk preference estimates imply an empirical premium for disease severity: for patients with severe health status (health equals 0.5), the value per health unit is three times higher than for perfectly healthy patients. They also suggested that the therapeutic value of conventional CEA was more than two-fold overestimated for the mildest disease. The use of traditional CEA both overstimulates innovation in mild disease treatment and inhibits innovation in severe disease treatment.
Note that these results are sensitive to specifications. The expo power function is parabolic in that mild and very severe disease is overestimated and fairly severe disease is underestimated. However, for CRRA, the relationship is monotonic (more severe means higher willingness to pay). The authors explain that the reversal of the switch between risk aversion and risk preference at the lowest quality-of-life scores may be due to the encoding of gambling as gains and losses (as postulated by prospect theory).
One of the benefits of this method is that the authors used a health status of 0 to 100 in order to quantify quality of life. In practice, however, respondents may have a good understanding of what quality of life at age 50 means. People can use actual health status, but individual assessments of these health status may vary.
This is the key and I certainly recommend reading the full article here.
