RUTH B. HOPPE
DECISION
THEORY
AND HEALTH
RESOURCE
ALLOCATIONS*
ABSTRACT. If it can be agreed that health care resources are finite, it follows that choices between competing needs must be made. Cost utility analysis is an application of decision theory which has been proposed as a strategy for making difficult social decisions about health resource allocations. This method is heavily dependent upon the measurement of social utilities for various health outcomes. Recent work in cognitive psychology suggests that there are important sources of distortion in such measurement. Ethical implications of application of cost utility analysis to health resource allocations are discussed. Key words: Health care programs, Health expenditures, Health allocation, Cost containment,
Decision analysis, Cost utility analysis, Social utility, Social preferences.
INTRODUCTION The health care industry is one of our nation's largest, currently consuming over $285 billion annually or 9.1% of the gross national product [1]. This expenditure is not only large, it has undergone rapid recent growth. Total spending on health care rose from 5.9% o f the gross national product in 1965 to the current level of 9.1% [2]. The reasons for this growth are many, most notably inflation, advances in technology, an increasingly aged population which consumes per capita more health care resources than younger persons, and the nearly ubiquitous presence of third-party health insurance coverage which removes cost considerations from the locus of health resource consumption. Several solutions to this problem have been proposed. For example, the United States Congress has begun to grapple with regulatory versus competitive strategies for controlling costs. The traditional fee-for-service model has been challenged by government-assisted health maintenance organizations. Increases in hospital costs have been sharply curtailed by third party groups, using a variety of techniques. Health Systems Agencies have attempted to stem the tide of technology dissemination. These strategies, and others, emanate from either of two basic principles concerning the provision o f medical care. These principles have significantly different implications regarding the cost containing strategies that are adopted. The first principle holds that all beneficial medical care should be provided; that is, all services that are needed. The other principle asserts that there will be a limit set on the claim of medical care on the nation's resources. According to this principle, resources devoted to health care are finite and all needs will not be met. Rather, competing needs must be weighed against the limited resources made available for medical care [2].
TheoreticalMedicine 4 (1983) 193-205. 0167-9902/83/0042-019351.30. Copyright © 1983 by D. Reidel Publishing Company.
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Each of the two principles leads to a general cost containment objective. Under the first, needs-based principle which assumes all possible care should be delivered, cost containing strategies are devoted to eliminating inefficiency by identifying procedures and programs that confer no benefit. The focus is on identifying and curtailing unnecessary procedures and programs. No boundaries on total medical care expenditures are defined, no priorities for competing needs are set. Under the second principle where resources are assumed to be finite, choices between services or programs, none of which are unnecessary, must be made. Such cost containing strategies must, implicitly or explicitly, identify "some level of benefit, or benefit relative to cost, below which the value of the service is not sufficient to justify the resources required to provide it" (Russell 1982, p. 134). Since the 1960s we in the United States have tried to pursue the first objective: providing care whenever it is needed, without regard to the size or cost of the benefit. Indeed, the bulk of medical research has devoted itself to determining effectiveness not efficiency; that is, to documenting benefit, as opposed to measuring how large the benefit is relative to the expenditure of society's resources. However, more recently there has been a shift in the direction of the second objective, toward explicitly outlining the cost of health care programs, toward identifying and sometimes quantifying the benefits conferred, and toward balancing the cost and the benefits. Such efforts are now being applied to screening programs [3,4], individual patient decision making [5], vaccination programs [6], and dissemination of complex medical technology [7], among others. The methods used to compare the benefits of health programs and their costs will be the focus of the remainder of this paper. These methods will be described in some detail, and then some problems with their application will be outlined. It is important, however, to identify a conflict inherent in incorporating any cost containing strategy based on the principle of finite resources and the need to set priorities. This conflict has to do with rights and the precedence that claims based on such rights may have over societal priorities. The conflict is large or small depending upon how the scope of the right to health care is defined. If the right to health care is defined as having very broad scope to include preventive as well as corrective services, all care deemed as being possibly helpful, or all services rendered in a health care institution, including cosmetic surgery, it could result in a "blanket entitlement to all of the resources that might be conceivably applied to the problem of the individual patient" ([8], p. 301). On the other hand, a right to health care may be defined much more narrowly, not needing to provide everything for everyone, but pleading for equity in the distribution of resources that are recognized as finite and that must be allocated according to certain defined strategies. In the latter case, the
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patient and his physician advocate will be constrained "to operate within a schedule of social priorities devised by secondary decision makers, the ranking of which will be in conflict with the utilities of individual patients to some extent" ([8], p. 302). The physician would continue to seek out any resources that might benegit his patient, although he would be obliged to accept compromises when resource limits have been clearly defined by societal decision makers.
DECISION THEORY AND RESOURCE ALLOCATION If, then, we accept the contention that ultimately there must be a limit to the resources we are willing to make available for health care, complex decisions about resource allocation must be made. There remains the very difficult problem of developing guidelines or methods that can be used to develop solutions to health resource allocation problems. How should the last health care dollar be spent? On additional long-term care facilities? On dissemination of a new technology such as artificial hearts? On expanded neonatal care services? On more ambitious primary and secondary prevention programs? One alternative is to use systematic analysis based on the principles and techniques of decision theory. These methods require outcomes to be represented as numerical quantities (years of life, days of illness, cost of testing) to which are assigned values and probabilities of occurrence. The expected value of any action is the average of the values of the possible outcomes, weighted by their corresponding probabilities. The .expected value of one action can than be numerically compared to be expected value of an alternate decision choice. Decision theory holds that the action with the greatest expected value is the preferred choice. An example might be a choice between two actions, each with different impact on life expectancy [8] : Action 1 generates a 0.25 chance of living to age 40, a 0.05 chance of living to age 50, and 0.70 chance of living to age 60; and action 2 generates a 0.30 chance of living to age 40, a 0.10 chance of living to age 50, and a 0.60 chance of living to age 60. Which is the best decision? The expected value of action 1 is the weighted average of the various outcomes: 40 years(.25) + 50 years(.05) + 60 years(.70) ; 54.5 years. Similarly, the expected value of action 2 is 53 years. Hence, when the number of years of survival is the outcome of concern, action 1 is preferred. Advantages of such a method are its explicitness, its consistency and its coherence. In the above example, each additional year of life is assumed to have equal value or worth to the individual contemplating action 1 or action 2. Many health care decisions are not carefully enough examined with respect to this assumption; it is simply held that we all want to maximize length of life and the option which produces the greatest expected value with respect to length of
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life is seen as preferable. As we shall see later, this is not always the case. Some individuals under some circumstances, given the choice, opt for alternatives which seek to maximize the quality of a shorter amount of life, or for other reasons select alternatives which don't maximize quantity of life. In the context of individual medical decisions this underscores the importance of delineating 'who is the decision maker?' and 'whose values will get incorporated into the expected utility equation?'. In the context of healthy resource policy decisions, these same questions are relevant and must be examined carefully.
COST EFFECTIVENESS/COST BENEFIT ANALYSIS Cost effectiveness analysis (CEA) and its cousin, cost benefit analysis (CBA) are approaches which use many elements from decision theory, applied to the area of resource allocation decision making. These techniques are ways of making explicit the health benefits and resources used by health programs so that policy makers may choose between them. Cost effectiveness analysis expresses costs and benefits in different units and represents decisions as cost per unit of benefit (dollars per positive test, dollars per life saved) or vice versa (lives saved per dollar cost). Cost benefit analysis reduces costs and benefits to a common unit, usually dollars, wherein the decision can be viewed as producing positive or negative outcome based on the arithmetic difference of benefits and costs. Because cost benefit analysis requires that all outcomes be valued in economic terms (dollars), and because health outcomes deal with changes in life expectancy which, many feel, have unmeasurable monetary value, cost effectiveness analysis is more frequently applied to health resource decision making [9].
COST UTILITY ANALYSIS Furthermore, quality of life issues, beyond changes of life expectancy, are frequently found to be important aspects of any health-related decision. Methods for incorporating quality of life concerns into cost effectiveness analyses have been more recently developed. These are referred to as cost utility analyses or health status index analyses [10, 9]. Basic to this method is the expression of total health effects in a common unit which combines mortality and morbidity and incorporates the multiple dimensions of morbidity itself. For example, different health outcomes such as five years of extreme pain followed by death versus ten years of moderate pain followed by death need to be expressed in some common unit before they can be compared using cost utility analysis. The most frequently used unit has been the quality-adjusted life year (QALY),
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although it has undergone several modifications in specific terminology (Function Years, Value Adjusted Life Years, Well Years) [11]. All these terms are expressions for the output of health programs in years of life adjusted for quality lost due to disease or disability. Once the outcomes are expressed in common units, they may be assigned a utility or numerical expression of their relative value to the decision maker. These expressions can then be incorporated into an expected utility equation: Expected Utility -- (Probability or Risk) × (Value or Utility) × (Cost), where expected utility is measured in qualityadjusted life years. The differences in expected utility between various programs or decision outcomes can thus be compared. Discovering how a decision maker feels about the relative value of several health outcomes (e.g., immediate death, short-term life free of pain, long-term life with pain) becomes an important element of the decision making process.
ELICITING PREFERENCES FOR HEALTH OUTCOMES A number of techniques for the eficitation of preferences for various health states have been developed. Most frequently used are category scaling, basic reference gambles, and variations of the time trade-off technique. These elicitation procedures present the decision maker with descriptions, either written or oral, or both, of various outcome states he/she must evaluate within the framework selected. The states are then assigned a numerical value relative to all other possibilities. Conventionally, 1.0 is the value assigned to the most preferred state, 0.0 is assigned to the worst, and all other states have intermediate values. Torrance used these three measurement techniques with several samples of the general public to measure their preferences for ten different health states [12]. He concluded that his own time trade-off method provided the best combination of feasibility and reliability, although there is by no means complete agreement as to which technique best elicits individuals' utilities. Sackett and Torrance later applied this technique and the same ten health states to other population samples to make descriptive statements about the health state utilities of the general public [13]. The health states were felt to be familiar to the subjects, they spanned a range of times (3 months, 8 years, lifetime), and some were disease-slcecific (tuberculosis) while other were general (hospital confinement). Sackett and Torrance found very little difference in the elicited utilities between persons of different sex or social class. However, six of the 15 health states were significantly associated with age, with older subjects having lower utility for dialysis and kidney transplantation and higher utility for hospital confinement. Interestingly, Sackett and Torrance found the anticipated
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length of time spent in a health state to dramatically affect its utility: the longer durations of health state disabilities were associated with sharp dropoffs in utility, supporting the position that prolonging life is not always the best outcome. Finally, two other important variables were noted that have implications for how preferences are actually elicited. First, the presence or absence of a disease label (tuberculosis versus unnamed contagious disease) affected utilities, although in unpredictable directions. Similarly, akeady having the health state resulted in higher utility designations. The implications of these findings will be touched upon later in this paper.
MEASURING SOCIAL UTILITIES The entire process of preference elicitation and cost utility analysis is based on expected utility theory which holds that the "rational decision maker will prefer the prospect that offers the highest expected utility" ([8], p. 220). Such a process would appear to offer a method for social health resource allocation decision making. The model might work as follows: A representative sample of the general public could be selected. Using one of the standard methods, for example time-trade-off, these individuals' utilities for health states created by various health programs could be measured. Once measured, the individual utilities could then be aggregated into a social utility for each health outcome. Those programs producing outcomes with the highest expected utility would be financially supported by the nation's health dollars up to some predetermined limit. Programs which produce health outcomes of lower expected aggregate utility would not be supported. Such a process necessarily places a large burden on the planning group (or individual) to collect accurate and complete information about health programs and their likely outcomes. However, assuming that these data could be collected, there remain at least three problems with the process of social utility measurement.
THE FRAMING PROBLEM The first problem has to do with the methods used to elicit individual preferences. Before cost utility analysis based on the expected utility model can become prescriptive for societal decision making in health care, the expected utility model must first be shown to be descriptive of people's basic preferences. A developing body of evidence suggests that either expected utility theory does not accurately reflect people's choices and preferences, or that currently available methods for eliciting preferences introduce bias which invalidates the expected utility model [ 14].
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Several recent investigations [15-19] suggest that the way in which these problems and outcome states are presented (framed) affects people's choices in ways that are not defined as rational by expected utility theory. In other words, choices which are actuarially equivalent, but phrased differently produce wide swings in preference. For example, Tversky and Kahneman ([19], p. 453) posed the following problem to a group of students: "Imagine that an outbreak of an unusual disease is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. The outcomes of these programs are as follows: if Program A is adopted, 200 people will be saved. If Program B is adopted, there is a 1/3 probability that 600 people will be saved and 2/3 probability that no people will be saved. Which of the two programs do you favor?". Mathematically, these two options to have equal expected value of 200 lives. However, when this problem was posed to the students, 72 percent favored Program A. The traditional explanation of this phenomenon is that the students were risk averse; that is, for most people, the certain prospect of saving 200 lives is more attractive than risky prosper of equal expected value. A second problem was then posed to a different group of students. The 'cover' story was identical, but the outcomes were phrased differently: "If Program C is adopted 400 people will die. If Program D is adopted there is a 1/3 probability that nobody will die, and 2/3 probability that 600 people will die". In this problem, only 22% of the students chose Program C (in contrast to the behavior of the group of students who favored Program A, which is identical to Program C, although differently phrased). In the example of the second problem, the students appeared to be risk seeking: the uncertain choice was preferred over the certain one, again of equal expected value. These examples suggest a pattern that has also been demonstrated by other researchers [15, 18], namely, that choices involving gains (dollars, lives) demonstrate risk aversion and choices involving losses demonstrate risk taking. In Tversky and Kahneman's two problems, the different values of the students regarding gains and losses were elicited by seemingly trivial differences in the framing of the outcomes. Tversky and Kahneman concluded that the inconsistencies in the students' choices were "traced to the interaction of two sets of factors: Variations in the framing of acts, contingencies and outcomes, and characteristic nonlinearities of values and decision weights" ([19], p. 455). Similar factors have been demonstrated to affect patient decisions about health care options in recent work by McNeil and Pauker [16]. They first demonstrated that a group of patients with operable lung cancer had different preferences regarding immediate versus long-term survival. These patients were presented with a choice between two therapies: one, surgery, having immediate operative mortality of 10%, but a 5-year survival rate of 33%, and the other, radiation therapy, having virtually no peritreatment mortality, but a 5-year
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survival of only 22%. Decision analysis, which assumes linearity of the preference for years of survival, would define the surgical option in this example to have the highest expected value and hence to be preferred. However, ff survival preference is not linear, that is, if near-term survival has more value than long-term survival for any given patient, the decision tree will not adequately accomodate this fact and may point out an inappropriate treatment option. This is because for the first two years of treatment, the chances of being alive are better with radiation therapy, whereas after the first two years, the surgical option maximizes the chance of survival. McNeil and Pauker determined the relative importance to patients of long- and short-term survival by the use of an elicitation procedure which measured preference. Each patient was presented with a series of hypothetical gambles which ascertained how many years of guaranteed survival he would accept to avoid risk of a 50/50 chance of living out a normal life expectancy or dying immediately. The period of guaranteed survival is used as a means of assessing the importance of near-term versus far-term years of life for the patient. A utility curve for each patient can then be constructed which represents the relative value to that person of successive years of life (Figure 1). The straight line A represents the utility for a risk-neutral
Utility 1.0 A
0.5
Years Fig. 1. individual, namely, one for whom each additional year of life has equal value. Curve B is that for a risk averse individual, one for whom near-survival is valued over long-term survival. McNeil and Pauker interviewed patients with operable lung cancer and used their responses to the hypothetical gambles to derive an index of expected utility for each treatment option. They found that for most younger men, surgery was the better option, whereas for nearly half the older men, who more frequently valued near-term survival higher, radiation therapy
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was the preferred option. So, again the nonlinearity of values is demonstrated. Elicitation procedures, even for a seemingly straightforward quantity such as length of survival, are needed to provide the decision weights for formal analysis. But, as Slovic [18] has pointed out, the method assumes that elicitation procedures " . . . are unbiased channels that translate subjective feelings into analytically usable expressions". As we have seen (Tversky), the framing of such elicitation procedures may have profound impact on choice. In a more recent study, McNeil et al. [17] investigated how variations in the way information is presented to patients influences their choices between alternative therapies. They presented two different groups of respondents with data about surgical and radiation therapy for lung cancer which differed only in whether survival was characterized in life expectancy form (average number years lived after treatment) or cumulative probability form (chance of surviving after x period of time). Two other groups received identical input data, but had the characterization of outcomes varied in terms of percent surviving versus percent dying. A final pair of respondent groups received identical information except that in one group the treatments were specified as surgical or radiation, whereas in the other group the treatments were merely labeled Treatment A and Treatment B (similar to the Torrance study previously mentioned). These investigators found, for all three variables, significant differences in respondent choice, again suggesting that bias, or cognitive illusion, or both were affecting the expression of patients' preferences. (Significantly, there was no improvement in consistency when the respondent group was comprised of physicians as opposed to patients.) The results of these studies and other suggest that elicitation procedures that attempt in neutral fashion to ask the question 'What do I really want?' may actually play a role in answering the question. Any method which relies on such an elicitation process, such as expected utility theory, can therefore be called into question regarding reliability. To summarize, to the extent that seemingly trivial changes in the elicitation of individual preferences affects subsequent preference expression, the method is seriously flawed. As Tversky has put it, "when framing influences the experience of consequences, the adoption of a decision format is an ethically significant act" ([19], p. 455). Eraker and Polltser have recently summarized a larger body of research in behavioral decision theory which indicates other sources of distortions that can affect recommendations based on decision analysis [14].
THE AGGREGATING PROBLEM Having seen that the process of eliciting individual preferences may have some significant flaws, we next turn to the second problem with social utility
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measurement. This problem deals with the methods used to generate social, as opposed to individual, preferences. Assuming that a properly formulated theory of individual health utility can be derived, we must tackle the difficult problem of aggregating individual utility measures into a suitable societal decision-making model. Most sthdents of this field agree that judgements on social choice and of public policy are dependent upon the preferences of the members of society. What isn't agreed upon is the function which describes the specific nature of that dependence. Methods of going from individual orderings to social preference are called 'collective choice rules' [20]. The utilitarian model (see Harsanyi [21] and Torrance [22] ) is one, based on expected utility theory, in which individual utilities are aggregated with equal weights for each individual. Pawls [23] has proposed a collective choice rule based on the maximin principle which measures the welfare level of society by the utility of the worst-off individual. Other models have been set forth [20]. It may well be that no single social welfare function can be described which will provide choices over the total range of allocation alternatives. Indeed, Arrow has not only argued this, but has offered proof in his 'Impossibility Theorem' [24]. Sen has more succinctly described the problem: "while purity is an uncomplicated virtue for olive oil, sea air, and heroines of folk tales, it is not so for systems of collective choice" ([20], p. 94). Which social welfare function best represents health allocation decisions rests, at least in part, on whether health care, or portions of health care, is defined as a right. The conflict posed by balancing rights and social choices has already been outlined, if not answered. However, it needs to be appreciated that recommendations heretofore guided by formal analyses [3, 4, 7, 22, 6] rest on a utilitarian orientation where individual values are given equal weight. This may well be our social wish, but this assumption needs to be identified in the formal analytic process. Unfortunately, this rarely, if ever, happens. Another aspect of the aggregating problem is that of selecting a representative sample of society whose elicited, aggregated values would be used in the expected utility equation. This sample needs to be a representative cross section of the population whose collective values it represents. It must therefore be comprised of individuals whose values represent, in an appropriate proportion, the range of values to be found in that society. But it may not be possible to identify this range of values or even to fully identify those individual descriptors (e.g., age, sex, ethnic background, religion) which might serve to generate a sufficiently heterogeneous group (with respect to values). Furthermore, there will be members of society (the mentally infirm, neonates) whose values will not be able to be directly elicited or articulated.
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THE MORAL FRAMEWORK PROBLEM A third and f'mal problem with using social utility measurement to assist health allocation decision-making is more subtle than the framing and aggregating problems mentioned previously. This problem has to do with the moral framework in which our individual (and consequently social) values are embedded. It is possible that we might be able to reliably and consistently elicit preferences for various health states, asking individuals to make only self-regarding judgements. (In this way biases and prejudices emanating out of racism, sexism, ageism, etc. can be avoided.) We might then be able to agree on a specific social welfare function for aggregating these preferences. However, we would be left with the concern that the ranked health states, however accurately representative of that society's values, might still lead to selection of action alternatives that were nevertheless unjust. Consider the following example. Suppose a society existed where physical beauty held much higher social value than did creative skills. Appropriately elicited health state utilities from a representative sample of this society would be likely to reflect preference for those health states in which beauty rather than creative skills are preserved. These utilities would then be incorporated into an expected utility equation which would objectively designate a preferred course of action. Health care procedures or programs which maintained or restored the higher-valued physical attributes would receive higher priority for resource allocation. A procedure which maintained creative skills at the expense of marring physical beauty would have the lowest national priority rating. It is easy to see ho~v such a decision would accurately incorporate that society's collective values. What isn't so easy to see is how funding a health care procedure which maintains physical appearance over one which preserves creative skills is a fair or just allocation of that society's health care resources. This problem becomes more complex when one considers the fact that the moral framework from which individual values emanate is usually not made explicit and hence would not be made available for analysis. One advantage of formal decision analysis is seen to be its explicitness [9]. Action alternatives, probabilities of occurrence and values for each possible outcome are carefully displayed. However, such displays may generate a false sense of security that all relevant information has been presented, again because the moral framework from which the alternative actions spring is rarely made explicit.
CONCLUSION As was mentioned in the Introduction, the problems posed by expanded alternatives for health care and shrinking financial resources to support these alternatives
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is large and complex. Cost utility analysis, based on elements of formal decision theory, has many features which appear to make it desirable, at least as an aid to health resource allocation decision making. Foremost among these advantages are its explicitness and its ability to compare health actions with seemingly very different outcomes, each of which has varying utility or value to individuals. Some problems which relate primarily to ethical aspects of the application of the method have been outlined. It may well be that these problems can be significantly reduced by improved understanding and refinement of the elicitation process and by incorporating an 'ethical sensitivity analysis' into the method itself. However, these problems demand attention before cost utility analyses are applied, even as decision aids or guidelines, to health resource allocation decisions. Further, to the extent that some cost utility analyses are already being presented [22], their conclusions require examination from these ethical perspectives. RUTH B. HOPPE Michigan State University, College of Human Medicine, Department of Medicine, East Lansing, M1 48824, U.S.A,
NOTE * The author is indebted to Howard Brody, M. D., Ph.D., Norman Daniels, Ph.D., and Marilyn Rothert, R. N., Ph.D., for the helpful critique of this paper and its concepts.
BIBLIOGRAPHY [1] Gibson, R. M.: 1980, 'National heatth expenditures', Health Care Finance Review 3, 1-54. [2] Russell, L. B.: 1982, 'The role of technology assessment in cost control', in B. S. McNeil and E. G. Cravalho (eds.), Critical lssues in Medical Technology, Auburn House Publishing Company, Boston, pp. 129-138. [3] Berwick, D. M. and Domaroff, A. L.: 1982, 'Cost effectiveness of lead screening', New England Journal of Medicine 306, 1392-1398. [4] Holtzman, N. A., Meek, A. B. and Mellits, E. D.: 1974, 'Neonatal screening for phenylketonuria', American Journal of Public Health 64,775-779. [5] Weinstein, M. C.: 1980, 'Estrogen use in post-menopausal women - Costs, risks and benefits', New England Journal of Medicine 303,308-316. [6] Willems, J. S., Sanders, C. R., Riddiough, M. A., and Bell, J. C.: 1980, 'Cost effectiveness of vaccination against pneumococcal pneumonia', New England Journal of Medicine 303,553-559, 1980.
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Reiss, J. B., Burckhardt, J. and Hellinger, F.: 1982, 'Costs and regulation of new medical technologies: Heart transplants as a case study', in B. J. McNeil and E. G. Cravalho (eds.), Critical Issues in Medical Technology, Auburn House Publishing Company, Boston, pp. 399-418. Weinstein, M. C. and Fineberg, H. V. : 1980, ClinicalDecision Analysis, W. B. Saunders Company, Philadelphia, pp. 1--344. Weinstein, M. C. and Stason, W. B.: 1977, 'Foundations of cost-effectiveness analysis for health and medical practices', New England Journal of Medicine 296, 7 i6-721. Torrance, G. W.: 1976, 'Toward a utility theory foundation for health status index models', Health Services Research 11,349-369. Kaplan, R. M. and Bush, J. W.: 1982, 'Health-related quality of life measurement for evaluation research and policy analysis', Health Psychology 1,61-79. Torrance, G. W.: 1976, 'Social preferences for health states: An empirical evaluation of three measurement techniques', Soeio Economic Planning Sciences 10, 129- t53. Sackett, D. L. and Torrance, G. W.: 1978, 'Utility of health states as perceived by the general public', Journal of Chronic Diseases 31,697-704. Eraker, S. D. and Pohtser, Peter: 1982, 'How decision are reached: Physician and patient', Annals of Internal Medicine 97,262-268. Hershey, J. C., Kunreuther, H. C. and Schoemaker, P. J. H.: 1982, to appear in Management Science. McNeil, B. J. and Pauker, S. G.: 1982, 'Incorporation of patient values in medical decision making', in B. J. McNeil and E. G. Cravalho (eds.), CritiealIssues in Medical Technology, Auburn House Publishing Company, Boston, pp. 343-358. McNeil, B. J., Pauker, S. G., Sox, H. C. and Tversky, A.: 1982, 'On the elicitation of preferences for alternative therapies', New England Journal of Medicine 306, 12591262. Slavic, P., Fischoff, B. and Lichtenstein, S.: 1982, 'Response mode, framing, and information processing effects in risk assessment', to appear ha R. M. Hogarth (ed.), New Directions for Methodology of Social and Behavioral Science: The Framing of Questions and the Consistency of Response, Jossey-Bass, San Francisco. Tversky, A. and Kahneman, D.: 1981, 'The framing of decisions and the psychology of choice', Science 211, 453-458. Sen, Amartya K.: 1970, Collective Choice and Social Welfare, Holden-Day Incorporated, San Francisco, pp. 1-200. Harsanyi, J. C.: 1975, 'Nonlinear social welfare functions', Theory and Decision 6, 311-326. Torrance, G. W.: 1980, 'Multi-attribute utility theory as a method of measuring social preferences for health states in tongterm care', Presented at the Rand-UCLA Symposium on the Measurement of Value Preferences in Longterm Care, Los Angeles. Rawls, J.: 1971, A Theory of Justice, Harvard University Press, pp. 1-587. Arrow, K. J.: 1951, Social Choice and Individual Values, Wiley, New York, pp. 1-92.
