Gamble Utilities Research Articles

Creating a Health Utility Value for Birdshot Chorioretinopathy

ABSTRACT Purpose To create a health utility value for birdshot chorioretinopathy (BCR) using Time Trade-Off (TTO) and Standard Gamble (SG) utilities. Method Adult BCR patients completed TTO, SG, EQ-5D-5L, and NEI VFQ-25 questionnaires and underwent a detailed history and clinical examination. Results A total of 28 BCR patients (9 M, 19 F; mean age 62 years, range 47–83) were included. There were 22 patients with a logMAR vision of 0.3 or better in both eyes. Mean TTO was 0.90 ± SD 0.18 (range 0.33–1.0) and mean SG was 0.94 ± SD 0.14 (range 0.5–1.0). TTO correlated with EQ-5D-5L index value (p = .024) and NEI VFQ-25 composite score (p = .015). Conclusions Of 28 patients with BCR, 11 would trade remaining life (mean 5.4 years), and 6 would take a risk of immediate death (mean 28% risk), in return for perfect vision in both eyes for the rest of their life.

UceWeb: a web-based collaborative tool for collecting and sharing quality of life data.

This work aims at building a platform where quality-of-life data, namely utility coefficients, can be elicited not only for immediate use, but also systematically stored together with patient profiles to build a public repository to be further exploited in studies on specific target populations (e.g. cost/utility analyses). We capitalized on utility theory and previous experience to define a set of desirable features such a tool should show to facilitate sound elicitation of quality of life. A set of visualization tools and algorithms has been developed to this purpose. To make it easily accessible for potential users, the software has been designed as a web application. A pilot validation study has been performed on 20 atrial fibrillation patients. A collaborative platform, UceWeb, has been developed and tested. It implements the standard gamble, time trade-off and rating-scale utility elicitation methods. It allows doctors and patients to choose the mode of interaction to maximize patients’ comfort in answering difficult questions. Every utility elicitation may contribute to the growth of the repository. UceWeb can become a unique source of data allowing researchers both to perform more reliable comparisons among healthcare interventions and build statistical models to gain deeper insight into quality of life data.

Sports gambling as consumption: Evidence from demand for sports lottery

Although the fact that sports lottery has become a prevalent phenomenon, it remains an under-researched area in sport management literature. Based on Conlisk's (1993) theory on the utility of gambling, an econometric model of demand for sports lottery gambling was constructed. The model assumes an experiential utility associated with sports lottery gambling, and proposes that rational consumers are mainly motivated by product attributes and marketing variables. The model is empirically examined by using a set of draw-to-draw sales data of a sports lottery in China. Time series analyses were conducted to analyze the determinants of sports lottery demand. This study revealed that ticket composition had considerable impact on the demand after partialling out information through the inclusion of an ex-post Prediction Difficulty Coefficient in the regression model. Eight percent of variance in the demand for sports lottery was found to be associated with ticket composition variables. The results provide additional evidence to the existing literature on sports gambling as consumption. The notion that nonmonetary activities associated with sports lottery gaming have a consumption value has considerable implications in terms of designing lottery products and delivering value to its consumers.

Probabilistic choice (models) as a result of balancing multiple goals

We conceptualize probabilistic choice as the result of the simultaneous pursuit of multiple goals in a vector optimization representation, which is reduced to a scalar optimization that implies goal balancing. The majority of prior theoretical and empirical work on such probabilistic choice is based on random utility models, the most basic of which assume that each choice option has a valuation that has a deterministic (systematic) component plus a random component determined by some specified distribution. An alternate approach to probabilistic choice has considered maximization of one quantity (e.g., utility), subject to constraints on one or more other quantities (e.g., cost). The multiple goal perspective integrates the results regarding the well-studied multinomial logit model of probabilistic choice that has been derived from each of the above approaches; extends the results to other models in the generalized extreme value (GEV) class; and relates them to recent axiomatic work on the utility of gambling.

Discrete Utility Jumps: The Value of Money in the Hand

Different theoretical explanations have been developed for seemingly inconsistent actions that deal with varying levels of time and risk: Allais Paradox, present-bias, dynamic inconsistency, risk aversion, prospect theory, and the utility of gambling, for example. This study develops a simple model of preferences that provides a unifying framework that accommodates these previously found phenomena. Our driving assumption is that preferences over riskier outcomes discontinuously depart from preferences under certainty. Decision-makers may discretely deem that a jump from no risk to some risk is fundamentally different than a marginal movement from some risk to more risk. Hence, risk may have two margins: the extensive margin is binary (risk either exists or does not) and the intensive margin is a continuum (if risk extends to this case then how intensive is that risk). Modeling attitudes towards risk as having these two separate margins reveals a preference mapping that explains these various phenomena while not departing so far from standard utility maximization.

Weighted entropies

Abstract We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem.

Functional Equations for Weighted Entropies

We find the continuous solutions of some functional equations arising from an axiomatization of weighted utility. The axiomatization itself will be presented in a subsequent paper. The results have potential applications to the “utility of gambling” problem.

Utility of Gambling when Events are Valued: an Application of Inset Entropy

The present theory leads to a set of subjective weights such that the utility of an uncertain alternative (gamble) is partitioned into three terms involving those weights—a conventional subjectively weighted utility function over pure consequences, a subjectively weighted value function over events, and a subjectively weighted function of the subjective weights. Under several assumptions, this becomes one of several standard utility representations, plus a weighted value function over events, plus an entropy term of the weights. In the finitely additive case, the latter is the Shannon entropy; in all other cases it is entropy of degree not 1. The primary mathematical tool is the theory of inset entropy.

Marker states and a health state prompt provide modest improvements in the reliability and validity of the standard gamble and rating scale in prostate cancer patients

To evaluate the combined effect of marker states and a prompt on the reliability and validity of direct utility assessment. In a structured interview, 141 prostate cancer (PC) patients provided rating scale (RS) and standard gamble (SG) utilities for their "own health" (RS-/SG-). Following self-completion of comparison instruments (two generic utility and one disease-specific psychometric), they answered a checklist of PC-related items (a prompt to consider self-health) and provided utilities for self-health and mild and severe PC marker states (RS+/SG+). The interview was repeated 5 weeks later, but without comparison instruments. Using Bayesian modeling, we computed and compared correlation coefficients to assess RS and SG test-retest reliability and validity and the effects of the prompt and marker states. RS and SG had acceptable test-retest reliability (intraclass correlation coefficients = 0.57-0.63). The prompt and marker states decreased the reliability of the RS by 0.01 (from 0.58 to 0.57) but increased the reliability of the SG by 0.05 (from 0.58 to 0.63). The probability that the reliability of the SG+ was greater than that of the SG- was very high (0.96). Correlations with comparison instruments were higher by 0.01-0.06 for RS+ vs RS-, and higher by 0.03-0.06 for SG+ vs SG-. The probabilities that the prompt and marker states improved validity ranged from 0.55 to 0.74 (RS), and from 0.61 to 0.70 (SG). A self-health description prompt and marker states modestly improved the reliability and validity of direct utility elicitation.

The Impact of Anchor Point on Utilities for 5 Common Ophthalmic Diseases

To elicit utilities on a perfect health and perfect vision scale for 5 common eye diseases. Cross-sectional observational preference study. We included 434 patients: 58 with diabetic retinopathy, 99 with glaucoma, 44 with age-related macular degeneration (AMD), 124 with cataract; 109 with refractive error. Standard gamble utilities were estimated using a computer-based preference assessment interview platform. Standard gamble utilities, a quality-of-life measure that examines the willingness to accept a risk of death or unilateral blindness in return for perfect health or perfect vision. Using the standard policy scale, where health equivalent to death is 0 and perfect health is 1, participants with asymptomatic diabetic retinopathy had a utility of 0.93. By comparison, symptomatic diabetics had a further utility loss of 0.14. Asymptomatic glaucoma participants had a utility of 0.92 with a decrease of 0.03 for early field loss and a further decrease of 0.03 with central field loss. Participants with AMD who had > or =20/100 better-eye visual acuity reported a utility of 0.89, whereas those with more severe AMD reported 0.76. However, neither clinical cataract opacity score nor refractive error correlated with utility. Adjustment for age and comorbidity did not alter these relationships. For the same participants, utilities measured with different anchor points-monocular blindness as 0 and perfect vision as 1-were lower, especially among participants with increased disease severity. The difference between utility assessed on this perfect vision-blindness scale and the perfect health-death scale ranged from 0.04 for those with severe refractive error to 0.19 for symptomatic diabetics and 0.37 for those with severe AMD. This paper elicits utilities with different anchor points from a previously unreported sample of 434 patients. Lower utility scores normally imply greater benefit with successful treatment or prevention of disease, but switching from the conventional policy scale to the perfect vision scale also consistently results in lower scores. Because most previous ophthalmic studies have used perfect vision as the upper anchor, the resulting utilities may not have been accurate.

Obese versus non-obese patients with type 2 diabetes: patient-reported outcomes and utility of weight change

ABSTRACTIntroduction: This study (1) used patient-reported outcome measures to assess and compare the health status of type 2 diabetes patients with and without obesity and (2) assessed the value of weight change among obese and non-obese subgroups, using standard gamble (SG) utility methodology.Methods: Among a sample with type 2 diabetes in the United Kingdom, individuals with obesity (BMI ≥ 30 kg/m2) were identified and compared to non-obese patients. Patients completed the EQ‑5D, Psychological General Well-Being Index, Appraisal of Diabetes Symptoms, and Diabetes Symptom Checklist – Revised (DSC‑R). SG interviews assessed the utility of the ‘basic’ type 2 diabetes health state anchored to respondents’ body weight, as well as health states with altered weight.Results: A total of 129 patients (74 obese; 55 non-obese) completed interviews (mean age 55.9 years; 64.3% male). Obese patients reported lower health status (EQ‑5D VAS; between-group difference: p < 0.001) and greater symptom impact (several DSC‑R scales, p < 0.05). Utilities of the basic health state were 0.86 (obese) and 0.91 (non-obese; p = 0.02). Hypothetical health states with higher weight received lower utilities, whereas reduced weight was associated with increased utility. There was a between-group difference in the disutility associated with 5% higher weight (obese 0.068; non-obese 0.051; p = 0.03).Discussion: Compared with non-obese patients, the obese group reported lower health status and greater symptom impact. SG interviews found an inverse relationship between weight and utility. Furthermore, obese patients with type 2 diabetes may value weight change differently than non-obese patients. Study limitations include the sample size and the use of a patient sample, rather than a sample selected from the general population. Overall, the results demonstrate that utilities can differ by patient subgroups, even among patients with the same diagnosis.

Utility of gambling I: entropy modified linear weighted utility

Behavioral axioms about preference orderings among gambles and their joint receipt lead to numerical representations consisting of a subjective utility term plus a term depending upon the events and the subjective weights. The results here are for uncertain alternatives, in much the same sense as Savage’s usage. Several open problems are described. Results for the risky case are in a second article.

Gambling and nonexpected utility: the perils of the power function

The use of the power utility function is problematic in expected utility theory. We show that, this is also the case in cumulative prospect theory, where the power function violates the assumption of loss-aversion at small stake levels, so that an optimal model of gambling is precluded. In the case of rank-dependent expected utility it has the counterfactual implication that agents will gamble all of their wealth at actuarially unfair odds.

It might be premature to reject the assumption of a power curve relationship between VAS and SG data: three comments on Stevens, McCabe and Brazier's ‘Mapping between VAS and SG data; results from the UK HUI Index 2 valuation survey’

In a recent paper in Health Economics, Stevens, McCabe and Brazier (Health Econ. 2006; 15: 527-533.) found that the cubic relationship between Visual Analog Scale (VAS) values and standard gamble (SG) utilities was superior to other functional forms in terms of explanatory power and predictive ability. Consequently, they question the reliance on the assumption of a power curve relationship, which was established, theoretically and empirically, in earlier works. This note argues that: (1) SMB's conclusions are incorrect. The estimated cubic function overfits the four data points, and is questionable with respect to the implied attitude toward relative risk. (2) The evaluation of the functional forms in terms of the individual predictions' mean absolute error is misleading and (3) correcting for heteroscedasticity improves the precision of the estimates and of the predictions.

The Utility of Gambling Reconsidered

The utility of gambling, which entails an intrinsic utility or disutility of risk, has been alluded to in the economics literature for over a century. This paper demonstrates that any utility of gambling almost unavoidably implies a violation of fundamental rationality properties, such as transitivity or stochastic dominance, for static choices between gambles. This result may explain why the utility of gambling, a phenomenon so widely discussed, has never been formalized in the economics literature. The model of this paper accommodates well-known deviations from expected utility, such as the Allais paradox and the coexistence of gambling and insurance, while minimally deviating from expected utility.

What constitutes success in preventive health care? A case study in assessing the benefits of hip protectors

The economic success of preventive health programs is typically assessed by the net health-related utility gain or loss to society relative to the cost. Issues relating to the positive or negative utility associated with participating in a preventive health program are often ignored. However, it is likely that calls for informed consumer choice and respect for patient autonomy will provide an impetus to examine utility associated with the process and outcomes of preventive health programs. In this paper, we outline the nature of the ex ante and ex post perspective in evaluing benefits and the presence of process utility and the utility of gambling in individual's utility function for preventive health care. The implications of including process attributes and psychological states when assessing benefits to society are discussed in relation to an empirical study on the value of external hip protectors for the prevention of hip fractures. We demonstrate that wearing hip protectors and the psychological outcomes of being a participant in the program can have a significant impact on individual's assessment of the benefits. Furthermore, point of reference plays a crucial role in their valuation. Individuals who did not consent to participate in a trial of hip protectors valued all states significantly lower than those who did participate in the trial. We argue that the utility associated with adherence to the intervention is an important issue for preventive health policy. From the viewpoint of applied welfare economics, evaluation of preventive health programs should allow for both process and outcome utility when assessing benefits. In this context, success might be viewed as maximising the opportunity for individuals to make an informed choice.

Testing interval independence versus configural weighting using judgments of strength of preference.

Judges made choices and raced strengths of preference between gambles composed of 50-50 chances to receive either of 2 monetary outcomes (x, y). Others judged how much they would pay to play their chosen gamble rather than the other gamble. Judged strengths of preference violated interval independence, because they depended on the value of a common outcome. For example, judges offered to pay an average of $44 to play ($74, $100) instead of ($8, $100) but offered to pay only $24 to play ($6, $74) instead of ($6, $8). Results violated the theory that utility of gambles is a nonconfigural average of the values of the outcomes and that strengths of preference are monotonically related to utility differences. Results can be explained by a configural weight model in which the lowest outcome receives greater weight.

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.

Progress in Utility and Risk Theory

I / Foundations of Utility and Probability.- The Foundations of the Theory of Utility and Risk. Some Central Points of the Discussions at the Oslo Conference.- II / One Utility Function or Two?.- Utility and Risk Preference Functions.- Neo-Cardinalism.- Prediction, Measurement, and Error of Utility: A Reply to Allais.- III / Prescriptive Versus Descriptive Decision Models.- Remarks to Professor Allais' Contributions to the Theory of Expected Utility and Related Subjects.- Decision-Aid and Expected Utility Theory: A Critical Survey.- IV / Aspects of Process Utility.- The Importance of What Might Have Been.- Relativity in Decision Theory.- The Utility of Gambling and of Outcomes: Inconsistent First Approximations.- Name Index.

An attempt to demonstrate utility of gambling

This experiment compared subjects' ( Ss') utilities for gambles with predictions of these utilities, based on Ss' utilities for the prizes of the gambles, and the SEU-model which does not allow for utility of gambling (UG). Since the gambles had only 2 possible outcomes equated in utility, it should not matter how Ss perceived the probabilities in the gambles. Under these conditions there was a majority of Ss who showed higher esteem for gambles than could be explained by the classical SEU-model. This was taken as indicative of positive UG. This conclusion is not cogent, however, since it had been impossible to match the 2 prizes of each gamble sufficiently close in utility. Some possible refinements are discussed which could be used in future studies.