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Nonexpected Utility Theories
Medical treatments offer health prospects. A health prospect represents a course of action with respect to one's health for which the outcome is generally uncertain. A surgery, initiation of a pharmaceutical treatment, and an exercise program are examples of health prospects. For simplicity of exposition, this entry considers only binary prospects, prospects involving two outcomes. Such binary prospects are all that is needed to measure health utility. Figure 1 shows a health prospect [.45: 24; 2] that offers different survival durations, 24 years and 2 years with associated probabilities .45 and .55 = −.45.
When utilities are known, it is a widely held view that expected utility is normative and is thus the appropriate approach for assigning value to a prospect such as that in Figure 1. This approach can then inform decisions about optimal treatments and cost-effectiveness.
Utilities, however, are generally not available without some sort of elicitation from a respondent. Elicitation of utility requires that numbers be associated with prospects such that preference for those prospects is faithfully described by the numbers. Behavioral research on choice strongly suggests that people typically do not make choices that conform to expected utility. Thus, when expected utility is used as a measurement tool, it is often the case that the numbers assigned to the prospects do not describe preference well. In addition, research has shown that the effects of expected utility violations are not limited to health utility measurements but also can influence willingness to pay for reductions in health risks and other contingent valuation responses. To address the problems associated with expected utility theory, nonexpected utility theories have been introduced. This entry focuses on the most important of these nonexpected utility theories and prospect theory, first proposed by Daniel Kahneman and Amos Tversky in 1979 and later refined by them in 1992.
Prospect Theory
Prospect theory relaxes those expected utility assumptions that are frequently violated by decision makers. An important advantage of prospect theory is that it offers improvements over expected utility in estimating the value of treatments for application in medical decision models. Once the prospect theory utilities are known, they can then be applied within normative medical decision models to identify treatments that maximize utility. A brief review of expected utility and its relation to prospect theory concepts facilitates an understanding of how prospect theory generalizes and improves expected utility.
Figure 1 A typical binary health prospect
Expected Utility
Expected utility evaluates prospects by multiplying the utility of each outcome by its associated probability and then summing over this product. For a binary health prospect [p: x; y], the expected utility is pU(x) + (1 − p)U(y), where U is a utility function and an interval scale. This shows that in expected utility, the decision weight assigned to an outcome is equal to its probability.
Nonexpected Utility and Transformation of Probability
Expected utility assumes that preferences are linear in probability. A change in probability from, say, .53 to .54 is given the same weight as a change from 0 to .01 or from .99 to 1. Empirical evidence suggests, however, that people are much more sensitive to the latter two changes than to the former. To model this, prospect theory allows for probability weighting. The probability weighting function w yields a nonlinear transformation of probabilities. The function w is a map from [0, 1] to [0, 1] that is increasing in its argument and for which w(0) = 0 and w(1) = 1. Empirical work suggests that the function w is often an inverse S shape such that small probabilities of the better outcome are overweighted and large probabilities of the better outcome are under-weighted, as in Figure 2. Incorporating probability weighting into expected utility implies that the prospect [p: x; y], x ≥ y should be evaluated
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- Basis for Making the Decision
- Acceptability Curves and Confidence Ellipses
- Beneficence
- Bioethics
- Choice Theories
- Construction of Values
- Cost-Benefit Analysis
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- Prospect Theory
- Range-Frequency Theory
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- Scaling
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- Stigma Susceptibility
- Support Theory
- Uncertainty in Medical Decisions
- Unreliability of Memory
- Value Functions in Domains of Gains and Losses
- Worldviews
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