An experimental test of a theoretical foundation for rating-scale valuations

A major advantage of using a rating scale in health-utility measurement is its practical applicability: the method is relatively easy to understand, and various health states can be assessed simultaneously. However, a theoretical foundation for rating-scale valuations has not been established. The primary aim of this paper is to present a theoretical foundation for rating-scale valuations based on the theory of measurable value functions and to provide a consistency test to see whether rating-scale valuations do indeed elicit a measurable value function. If rating-scale valuations elicit a measurable value function, then Dyer and Sarin have shown how they are related to von Neumann-Morgensterm (vNM) utilities. The appropriate technique to measure vNM utilities is the standard gamble. Torrance has suggested that rating-scale valuations and standard-gamble valuations are related by a power function. A secondary aim of this paper is to examine the relationship between rating-scale valuations and standard-gamble valuations hypothesized by Torrance. An experiment was designed to test consistency of rating-scale valuations and the relationship between rating-scale valuations and standard-gamble valuations. The experiment tested whether rating-scale valuations are independent of the context in which they are elicited, as they should be if they elicit points on a measurable value function. 80 Swedish and 92 Dutch respondents participated in the experiment. The results showed that rating-scale valuations depend on the number of preferred alternatives in the task and thus violate a basic property of measurable value functions. The estimation of the power function did not result in stable results: parameter estimates varied, in some cases there was indication of misspecification, and in most cases there was indication of heteroskedastic errors. The implications of these findings for the common use of rating-scale valuations in cost-utility analysis are serious: the dependency of the rating-scale valuations on the other health states included in the task casts serious doubts on the validity of the rating-scale method.