A utility-theoretic approach to the aggregation of willingness to pay measured in decomposed scenarios: development and empirical test.

For cost-benefit analysis, health technologies with multiple effects should be valued in a single scenario by a holistic willingness-to-pay (WTP) measure. Recent studies instead used decomposed scenarios in which respondents report their WTP for each individual effect. Evidence can be found that the sum of such decomposed WTPs overestimates the holistic WTP, i.e. the holistic WTP is sub-additive. This sum of decomposed WTPs can lead to wrong conclusions on the efficiency of health technologies. This is also relevant in decision making about new technologies that are valued separately in different surveys. To date, no utility-theoretical and empirically validated aggregation function for decomposed WTPs exists. Within an expected utility model, this paper identifies as a reason for sub-additivity--beside risk aversion with respect to wealth--a negative influence of better health on the marginal utility of wealth, i.e. marginal utility of wealth is smaller in better health states. Assuming mutual utility independence of health and wealth, a theoretically founded aggregation function covering these two impacts is derived. In a contingent valuation study, 92 patients with diabetes were asked to state their WTP for reductions of the risk of several diabetic complications in decomposed as well as in holistic scenarios. The patients had preferences with a significant negative influence of health on the marginal utility of wealth. Sub-additivity occurred and theoretically founded aggregation could considerably lower the degree of overestimation. These results suggest that the theoretically founded aggregation function might reduce problems of sub-additivity that can be economically relevant. Further empirical testing of the approach is indicated.