John M. Miyamoto

Parameter Estimates for a QALY Utility Model

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 patients 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.

A multiplicative model of the utility of survival duration and health quality.

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.

Incorporating risk attitude into Markov-process decision models: importance for individual decision making

Most decision models published in the medical literature take a risk-neutral perspective. Under risk neutrality, the utility of a gamble is equivalent to its expected value and the marginal utility of living a given unit of time is the same regardless of when it occurs. Most patients, however, are not risk-neutral. Not only does risk aversion affect decision analyses when tradeoffs between short- and long-term survival are involved, it also affects the interpretation of time-tradeoff measures of health-state utility. The proportional time tradeoff under- or overestimates the disutility of an inferior health state, depending on whether the patient is risk-seeking or risk-averse (it is unbiased if the patient is risk-neutral). The authors review how risk attitude with respect to gambles for survival duration can be incorporated into decision models using the framework of risk-adjusted quality-adjusted life years (RA-QALYs). They present a simple extension of this framework that allows RA-QALYs to be calculated for Markov-process decision models. Using a previously published Markov-process model of surgical vs expectant treatment for benign prostatic hypertrophy (BPH), they show how attitude towards risk affects the expected number of QALYs calculated by the model. In this model, under risk neutrality, surgery was the preferred option. Under mild risk aversion, expectant treatment was the preferred option. Risk attitude is an important aspect of preferences that should be incorporated into decision models where one treatment option has up-front risks of morbidity or mortality. Key words : risk attitude; Markov models; patient preferences; quality-adjusted life years. (Med Decis Making 1997;17:340-350)

What should be reported in a methods section on utility assessment

BACKGROUND The measurement of utilities, or preferences, for health states may be affected by the technique used. Unfortunately, in papers reporting utilities, it is often difficult to infer how the utility measurement was carried out. PURPOSE To present a list of components that, when described, provide sufficient detail of the utility assessment. METHODS An initial list was prepared by one of the authors. A panel of 8 experts was formed to add additional components. The components were drawn from 6 clusters that focus on the design of the study, the administration procedure, the health state descriptions, the description of the utility assessment method, the description of the indifference procedure, and the use of visual aids or software programs. The list was updated and redistributed among a total of 14 experts, and the components were judged for their importance of being mentioned in a Methods section. RESULTS More than 40 components were generated. Ten components were identified as necessary to include even in an article not focusing on utility measurement: how utility questions were administered, how health states were described, which utility assessment method(s) was used, the response and completion rates, specification of the duration of the health states, which software program (if any) was used, the description of the worst health state (lower anchor of the scale), whether a matching or choice indifference search procedure was used, when the assessment was conducted relative to treatment, and which (if any) visual aids were used. The interjudge reliability was satisfactory (Cronbachs alpha = 0.85). DISCUSSION The list of components important for utility papers may be used in various ways, for instance, as a checklist while writing, reviewing, or reading a Methods section or while designing experiments. Guidelines are provided for a few components.

Preference elicitation via theory refinement

We present an approach to elicitation of user preference models in which assumptions can be used to guide but not constrain the elicitation process. We demonstrate that when domain knowledge is available, even in the form of weak and somewhat inaccurate assumptions, significantly less data is required to build an accurate model of user preferences than when no domain knowledge is provided. This approach is based on the KBANN (Knowledge-Based Artificial Neural Network) algorithm pioneered by Shavlik and Towell (1989). We demonstrate this approach through two examples, one involves preferences under certainty, and the other involves preferences under uncertainty. In the case of certainty, we show how to encode assumptions concerning preferential independence and monotonicity in a KBANN network, which can be trained using a variety of preferential information including simple binary classification. In the case of uncertainty, we show how to construct a KBANN network that encodes certain types of dominance relations and attitude toward risk. The resulting network can be trained using answers to standard gamble questions and can be used as an approximate representation of a persons preferences. We empirically evaluate our claims by comparing the KBANN networks with simple backpropagation artificial neural networks in terms of learning rate and accuracy. For the case of uncertainty, the answers to standard gamble questions used in the experiment are taken from an actual medical data set first used by Miyamoto and Eraker (1988). In the case of certainty, we define a measure to which a set of preferences violate a domain theory, and examine the robustness of the KBANN network as this measure of domain theory violation varies.

Multiattribute Utility Theory Without Expected Utility Foundations

Methods for determining the form of utilities are needed for the implementation of utility theory in specific decisions. An important step forward was achieved when utility theorists characterized useful parametric families of utilities and simplifying decompositions of multiattribute utilities. The standard development of these results is based on expected utility theory which is now known to be descriptively invalid. The empirical violations of expected utility impair the credibility of utility assessments. This paper shows, however, that parametric and multiattribute utility results are robust against the major violations of expected utility. They retain their validity under nonexpected utility theories that have been developed to account for actual choice behavior. To be precise, characterizations of parametric and multiattribute representations are extended to rank-dependent utility, state-dependent utility, Choquet-expected utility, and prospect theory.

A characterization of quality-adjusted life-years under cumulative prospect theory

Quality-adjusted life-years (QALYs) are the most common utility measure in medical decision analysis and economic evaluations of health care. This paper presents an axiomatization of QALYs under cumulative prospect theory (CPT), currently the most influential model for decision under uncertainty. Because the set of health states need not be endowed with a natural topology that is connected, we first show how existing CPT characterizations can be extended to a class of outcome sets for which no connected natural topology is given. We then characterize QALY models with linear, power, and exponential utility for duration. Finally, we define loss aversion for multiattribute utility theory and characterize the QALY models under general and constant loss aversion. The measurement of QALYs belongs to the general field of multiattribute utility theory. Hence, our results can be generalized to other multiattribute decision contexts and they thereby contribute to the development of multiattribute utility theory under cumulative prospect theory.

Generic Analysis of Utility Models

It is now firmly established that expected utility (EU) theory and subjective expected utility (SEU) theory are descriptively invalid (Kahneman and Tversky, 1979; Luce, 1988b;MacCrimmon and Larsson, 1979; Slovic and Lichtenstein, 1983; Weber and Camerer, 1987). Descriptive utility theory is undergoing extensive revision, stimulated by empirical findings that challenge existing theories, and by new theories that more adequately account for the cognitive processes that underly preference behavior (Becker and Sarin,1987; Bell, 1982; Kahneman and Tversky, 1979; Loomes and Sugden, 1982; Luce, 1988a,1990; and Narens, 1985; Quiggin, 1982). Although these developments are undoubtedly salutory for the theory and practice of decision making, it might appear that in the short term they undermine the usefulness of multiattribute utility theory (MAUT), or at least that part of MAUT that is built upon EU or SEU assumptions. (Henceforth, I will refer only to SEU theory., noting that EU theory can be construed as a special case of SEU theory.) A substantial part of MAUT methodology is based on preference assumptions that characterize classes of utility models under the assumption that SEU theory is valid (Keeney and Raiffa, 1976; von Winterfeldt and Edwards, 1986). The strong evidence against the descriptive validity of SEU theory might appear to undermine or even invalidate those parts of MAUT methodology that assume SEU theory in deriving implications from patterns of preference. A major goal of this chapter is to show that this is in fact not the case.

An axiomatization of the ratio/difference representation

Abstract If ≥ r and ≥ d are two quaternary relations on an arbitrary set A , a ratio/difference representation for ≥ r and ≥ d is defined to be a function f that represents ≥ r as an ordering of numerical ratios and ≥ d as an ordering of numerical differences. Krantz, Luce, Suppes and Tversky (1971, Foundations of Measurement . New York, Academic Press) proposed an axiomatization of the ratio/difference representation, but their axiomatization contains an error. After describing a counterexample to their axiomatization, Theorem 1 of the present article shows that it actually implies a weaker result: if ≥ r and ≥ d are two quaternary retations satisfying the axiomatization proposed by Krantz et al. (1971), and if ≥ r′ and ≥ d′ are the relations that are inverse to ≥ r and ≥ d , respectively, then either there exists a ratio/difference representation for ≥ r and ≥ d , or there exists a ratio/difference representation for ≥ r′ and ≥ d′ , but not both. Theorem 2 identifies a new condition which, when added to the axioms of Krantz et al. (1971), yields the existence of a ratio/difference representation for relations ≥ r and ≥ d .

Compositional Anomalies in the Semantics of Evidence

Publisher Summary This chapter explores that semantic theory plays a central role in the normative and descriptive theory of deductive inference, but its role in the study of inductive inference has been much less prominent. The disparity is both odd and understandable. It is odd because deductive and inductive reasoning both rely heavily on linguistic representations and semantic theory is the natural tool for investigating inference within propositional structures. The axiomatic theory of subjective probability specifies further properties of belief strength that characterize so-called coherent beliefs; if strength of belief is coherent in this sense, then there exist numerical probabilities that represent the belief strength ordering and satisfy the mathematical laws of probability. A theory of semantics relates three aspects of language: (1) the syntactic structure of propositions, that is, a specification of how complex propositions are built from simpler parts, (2) the semantic structure of propositions, that is, a specification of the relation between propositional structure, reference, and truth values, and (3) inference rules that define inferential relations in terms of syntactic and semantic structure. The chapter considers variety of empirical results that illustrate concretely the relationship between strength of belief, propositional structure, and the structure of evidence. Many of the phenomena discussed in the chapter are characterized as compositional anomalies-they are cases in which observed relations in belief strength conflict with the semantic structure of propositions, or at least with well-established theories of this semantic structure.