Parametric models of the utility of survival duration: Tests of axioms in a generic utility framework

Abstract

The risk posture of a utility function is, roughly speaking, a measure of the curvature of the utility function with respect to an objectively quantified dimension like money or survival duration. Risk posture with respect to survival duration is critically important in the normative decision analysis of medical therapy selection because medical choices often involve therapies that differ in their trade-offs between short- and long-term survival, e.g., between surgical and nonsurgical treatments. Power utility functions and exponential utility functions are potentially useful in the normative analysis of medical decisions because they provide simple representations of risk posture with respect to survival duration. The present study formulates and tests axiomatic characterizations of power and exponential utility models within a theoretical framework called the generic utility theory. The formalizations generalize the work of J. W. Pratt on parametric characterizations of risk attitude. An experiment is reported in which the hypotheses that the utility of survival duration is a linear, exponential, logarithmic, or power function are tested. The experiment illustrates how to apply statistical criteria to the empirical test of preference axioms. Experimental results show that the linear, exponential, logarithmic, and power utility models are all violated by a substantial proportion of subjects. Qualitative analyses of the pattern of violations suggest that the linear and exponential utility models are a better approximation of subjects' preference than the logarithmic and power utility models. The formalizations and experimental tests are carried out within the generic utility theory because the assumptions of this theory are consistent with important “strong” utility theories, including expected utility theory, subjective expected utility theory, the dual bilinear model, and prospect theory. Investigations of utility models within the generic utility framework are interpretable from the standpoint of stronger theories, but are not committed to the hypothesis that a particular strong utility theory is valid.