Han Bleichrodt

Income-related inequalities in health: some international comparisons

This paper presents evidence on income-related inequalities in self-assessed health in nine industrialized countries. Health interview survey data were used to construct concentration curves of self-assessed health, measured as a latent variable. Inequalities in health favoured the higher income groups and were statistically significant in all countries. Inequalities were particularly high in the United States and the United Kingdom. Amongst other European countries, Sweden, Finland and the former East Germany had the lowest inequality. Across countries, a strong association was found between inequalities in health and inequalities in income.

Life-cycle preferences over consumption and health: when is cost-effectiveness analysis equivalent to cost–benefit analysis?

This paper studies life-cycle preferences over consumption and health status. We show that cost-effectiveness analysis is consistent with cost-benefit analysis if the lifetime utility function is additive over time, multiplicative in the utility of consumption and the utility of health status, and if the utility of consumption is constant over time. We derive the conditions under which the lifetime utility function takes this form, both under expected utility theory and under rank-dependent utility theory, which is currently the most important nonexpected utility theory. If cost-effectiveness analysis is consistent with cost-benefit analysis, it is possible to derive tractable expressions for the willingness to pay for quality-adjusted life-years (QALYs). The willingness to pay for QALYs depends on wealth, remaining life expectancy, health status, and the possibilities for intertemporal substitution of consumption.

Characterizing QALYs by Risk Neutrality

This paper shows that QALYs can be derived from more elementary conditions than thought hitherto in the literature: it suffices to impose risk neutrality for life years in every health state. This derivation of QALYs is appealing because it does not require knowledge of concepts from utility theory such as utility independence. Therefore our axiomatization greatly facilitates the assessment of the normative (non)validity of QALYs in medical decision making. Moreover, risk neutrality can easily be tested in experimental designs, which makes it straightforward to assess the descriptive (non)validity of QALYs.

Standard gamble, time trade-off and rating scale: Experimental results on the ranking properties of QALYs

This paper compares the relative performance of quality adjusted life years (QALYs) based on quality weights elicited by rating scale (RS), time trade-off (TTO) and standard gamble (SG). The standard against which relative performance is assessed is individual preference elicited by direct ranking. The correlation between predicted and direct ranking is significantly higher for TTO-QALYs than for RS-QALYs and SG-QALYs. This holds both based on mean Spearman rank correlation coefficients calculated per individual and based on two social choice rules: the method of majority voting and the Borda rule. Undiscounted TTO-QALYs are more consistent with direct ranking than discounted TTO-QALYs.

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-Morgenstern (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. Key words: QALYs; rating scale; cost-utility analysis; medical decision making. (Med Decis Making 1997;17:208-216))

A Quantitative Measurement of Regret Theory

This paper introduces a method to measure regret theory, a popular theory of decision under uncertainty. Regret theory allows for violations of transitivity, and it may seem paradoxical to quantitatively measure an intransitive theory. We adopt the trade-off method and show that it is robust to violations of transitivity. Our method makes no assumptions about the shape of the functions reflecting utility and regret. It can be performed at the individual level, taking account of preference heterogeneity. Our data support the main assumption of regret theory, that people are disproportionately averse to large regrets, even when event-splitting effects are controlled for. The findings are robust: similar results were obtained in two measurements using different stimuli. The data support the reliability of the trade-off method: its measurements could be replicated using different stimuli and were not susceptible to strategic responding.

Time preference, the discounted utility model and health

The constant rate discounted utility model is commonly used to represent intertemporal preferences in health care program evaluations. This paper examines the appropriateness of this model, and argues that the model fails both normatively and descriptively as a representation of individual intertemporal preferences for health outcomes. Variable rate discounted utility models are more flexible, but still require restrictive assumptions and may lead to dynamically inconsistent behaviour. The paper concludes by considering two ways of incorporating individual intertemporal preferences in health care program evaluations that allow for complementarity of health outcomes in different time periods.

Non-hyperbolic time inconsistency

The commonly used hyperbolic and quasi-hyperbolic discount functions have been developed to accommodate decreasing impatience, which is the prevailing empirical finding in intertemporal choice, in particular for aggregate behavior. However, these discount functions do not have the flexibility to accommodate increasing impatience or strongly decreasing impatience. This lack of flexibility is particularly disconcerting for fitting data at the individual level, where various patterns of increasing impatience and strongly decreasing impatience will occur for a significant fraction of subjects. This paper presents discount functions with constant absolute (CADI) or constant relative (CRDI) decreasing impatience that can accommodate any degree of decreasing or increasing impatience. In particular, they are sufficiently flexible for analyses at the individual level. The CADI and CRDI discount functions are the analogs of the well-known CARA and CRRA utility functions for decision under risk.

QALYs and HYEs: Under what conditions are they equivalent?

The paper examines what restrictions have to be imposed on the individuals preference structure for QALYs and HYEs to yield identical results. It is shown that using QALYs involves imposing three additional restrictions. Empirical evidence suggests that these restrictions cannot be expected to hold in all applications. The main problem in using HYEs appears to be practical. An alternative index is proposed, that may help to bridge the gap between QALYs and HYEs by combining to some extent the advantages of the two measures.

Resolving Inconsistencies in Utility Measurement Under Risk: Tests of Generalizations of Expected Utility

This paper explores inconsistencies that occur in utility measurement under risk when expected utility theory is assumed and the contribution that prospect theory and some other generalizations of expected utility can make to the resolution of these inconsistencies. We used five methods to measure utilities under risk and found clear violations of expected utility. Of the theories studied, prospect theory was the most consistent with our data. The main improvement of prospect theory over expected utility was in comparisons between a riskless and a risky prospect (riskless-risk methods). We observed no improvement over expected utility in comparisons between two risky prospects (risk-risk methods). An explanation for the latter observation may be that there was less distortion in probability weighting in the interval [0.10, 0.20] than has commonly been observed.