This paper studies the implications of the “zero-condition” for multiattribute utility theory. The zero-condition simplifies the measurement and derivation of the Quality Adjusted Life Year (QALY) measure commonly used in medical decision analysis. For general multiattribute utility theory, no simple condition has heretofore been found to characterize multiplicatively decomposable forms. When the zero-condition is satisfied, however, such a simple condition, “standard gamble invariance,” becomes available.

Survival duration and health quality are fundamentally important aspects of health. A utility model for survival duration and health quality is a model of the subjective value of these attributes. We investigate the hypothesis that the utility (subjective value) of survival duration and health quality is determined by a multiplicative model. According to this model, there are separate subjective scales for the utility of survival duration and health quality. If F(Y) equals the utility of surviving Y years, and G(Q) equals the utility of living in health state Q, then the multiplicative model proposes that F(Y)G(Q) equals the utility of surviving Y years in health state Q. This model provides a simple explanation for several intuitively compelling relationships. First, the distinction between better-than-death and worse-than-death health states corresponds to the assignment of positive or negative utilities to different health states. Second, a zero duration of survival removes any reason to prefer one health state over any other, just as multiplying the utility of health quality by zero eliminates differences between the utilities of different health states. Third, the subjective difference between Y years in pain and Y years free from pain increases as Y increases as if the difference in utility between pain and no pain were being multiplied by the utility of surviving Y years. A critical prediction of the multiplicative model is the hypothesis that preferences between gambles for health outcomes satisfy a property called utility independence. Individual analyses revealed that most subjects satisfy utility independence, thereby supporting the multiplicative utility model. Some subjects appear to violate a fundamental assumption of utility theory: They appear to violate the assumption that a single utility scale represents both the ordinal preference relations between certain outcomes and the subjective averaging that underlies the utility of gambles. The violation is inferred from an inconsistency between preferences for multiattribute outcomes when they are viewed as certain outcomes and when they are viewed as the outcomes of gambles.

This paper discusses a utility model for quality adjusted life years (QALY). According to this model, the utility of Y years of survival in health state Q is bYrH(Q), where b is a scaling constant and r and H(Q) are parameters. The parameter r is shown to be interpretable as a representation of a patient's risk attitude with respect to survival duration. The parameter H(Q) represents the proportionate reduction in the utility of survival when health state Q prevails. Methods are described for estimating these parameters from the results of an individual patient utility assessment. Results are then reported for empirical estimation of parameters r and H(Q) from the preference judgments of a sample of 46 coronary artery disease patients. In this empirical study, health state Q takes on two values--survival with angina pectoris and survival free from angina pectoris. Estimated values of parameters r and H(Q) are discussed in relation to the decision analysis of coronary artery bypass graft surgery. Finally, it is argued that the model deserves consideration as a medical utility model, despite some preliminary evidence that assumptions of the model are descriptively false, because it provides a simple representation of the utility of survival duration and health quality. These aspects of health outcomes are known to be critically important in the expected utility analysis of health decisions.

Quality-adjusted life years (QALY) utility models are multiattribute utility models of survival duration and health quality. This paper formulates six classes of QALY utility models and axiomatizes these models under expected utility (EU) and rank-dependent utility (RDU) assumptions. The QALY models investigated in this paper include the standard linear QALY model, the power and exponential multiplicative models, and the general multiplicative model. Emphasis is placed on a preference assumption, the zero condition, that greatly simplifies the axiomatizations under EU and RDU assumptions. The RDU axiomatizations of QALY models are generally similar to their EU counterparts, but in some cases, they require modification because linearity in probability is no longer assumed, and rank dependence introduces asymmetries between the domains of better-than-death health states and worsethan-death health states. Academic PressThis paper concerns the foundations of quality-adjusted life years (QALY) utility models. QALY utility models are widely used in the expected utility analysis of health decisions because they provide an outcome measure that integrates the duration and quality of survival. Before discussing the specifics of these models, it will be helpful to motivate the discussion by describing the role played by QALY utility models in health decision analysis Sox, Blatt, Higgins, 6 Marton, 1988; Gold, Siegel, Russell, 6 Weinstein,1996, Drummond, O'Brien, Stoddart, 6 Torrance, 1997.A typical application of the QALY model would involve the utility analysis of a decision in which a patient must choose between two or more therapies. One component of the analysis involves the construction of probability models for each therapeutic choice. Each such model describes the possible sequences of health states that could occur given a therapeutic choice and assigns probabilities to these Article ID jmps.1999.1256, available online at http:ÂÂwww.idealibrary.com on 201

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