The Validity of QALYs under Non‐Expected Utility

Abstract

This paper examines applications of non-expected utility in the health domain. The most widely used utility model in health economics, the time-linear QALY model, assumes (i) separability of quality of life and life duration, and (ii) linearity of the utility for life duration. We perform new tests, which are robust to violations of expected utility, of these two assumptions. The data support separability, but show that the utility for life duration is concave rather than linear. The finding of concave utility may not be surprising in itself. The contribution of this paper is to demonstrate this empirically without being invalidated by violations of expected utility. It has by now been widely recognised that expected utility is not valid as a descriptive theory of decision under uncertainty. The descriptive violations of expected utility have led to the emergence of several non-expected utility theories. The increasing importance of non-expected utility makes it necessary to reassess applications that were previously based on expected utility. Examples of such reassessments include Karni and Safra (1989), Crawford (1990) and Dekel et al. (1991) for game theory, Machina (1995) and Wakker et al. (1997) for insurance theory and Cubitt and Sugden (1998) for the evolution of preferences. See Starmer (2000) for a review. The present paper examines applications of non-expected utility in the health domain. We focus on the main utility model in health economics, the quality-adjusted life-years (QALY) model, and present new theoretical foundations for, and empirical tests of this model under non-expected utility. QALYs provide a simple way to combine the two dimensions of health, life duration and health status, into a single utility index. They are intuitively appealing, which facilitates communication to policy makers, and analytically tractable, which explains their widespread use in practical studies. A disadvantage of QALYs is that they only represent individual preferences over health under strong assumptions. If these assumptions do not hold, then the use of QALYs may lead to incorrect policy recommendations. To gain insight into the validity of QALYs, it is necessary to assess the restrictiveness of the assumptions that the QALY model imposes. In the most common version of the QALY model, the time-linear QALY model, the utility of the health outcome of spending t years in health state q is equal to tV(g), where V is a utility function over health states. That is, in the time-linear QALY model the utility for duration is linear. It is well known that under expected utility, linearity of utility implies risk neutrality. As it turns out, risk neutrality with