The Utility of Survival Duration and Health Quality: a Conjoint Measurement Analysis (Independence, Medical Decision Analysis, Risk Aversion, Patient Preferences).

Abstract

The utility of survival duration and health quality are studied within the framework of conjoint measurement theory. A cardinal utility representation, called a lower triangular, identical components (LTIC) additive matching representation, is axiomatized in terms of the certainty equivalents of fixed probability, two-outcome gambles. This representation is a weak theory of preference under risk in the sense that it is consistent with more general theories like expected utility theory or prospect theory, but it is restricted to only a subset of the preference judgments that are encompassed in these theories. Two parametric hypotheses concerning risk attitude with respect to survival duration are analysed axiomatically in terms of the LTIC additive representation. These hypotheses are, respectively, the hypothesis that the utility of survival duration is linear or exponential, and the hypothesis that it is power or logarithmic. A multiplicative utility representation for survival duration and health quality is also axiomatized. The main axioms for the parametric utility hypotheses were tested experimentally. Stimuli were even-chance gambles for survival duration with health quality assumed to be fixed at good health. Subjects were 38 psychology students who judged certainty equivalents for the stimulus gambles. Analyses of data from individual subjects showed that both parametric utility hypotheses were violated by a majority of subjects. The main axiom for the multiplicative utility representation is a special case of the assumption that survival duration is utility independent of health quality. This axiom was tested empirically in the judgments of 27 hospital patients. Subjects judged certainty equivalents of even-chance gambles for survival duration in different health states. The results show that the axiom is approximately valid, and are consistent with the exact validity of the axiom for the majority of subjects. The investigations presented here contribute to the conjoint measurement analysis of cognitive judgments and to the theory of preference under risk. They are of practical importance in the decision theoretic analysis of medical choices.