Medical Decision Making

Markov models are useful when a decision problem involves risk that is continuous over time, when the timing of events is important, and when important events may happen more than once. Representing such clinical settings with conventional decision trees is difficult and may require unrealistic simplifying assumptions. Markov models assume that a patient is always in one of a finite number of discrete health states, called Markov states. All events are represented as transitions from one state to another. A Markov model may be evaluated by matrix algebra, as a cohort simulation, or as a Monte Carlo simulation. A newer repre sentation of Markov models, the Markov-cycle tree, uses a tree representation of clinical events and may be evaluated either as a cohort simulation or as a Monte Carlo simulation. The ability of the Markov model to represent repetitive events and the time dependence of both probabilities and utilities allows for more accurate representation of clinical settings that involve these issues. Key words: Markov models; Markov-cycle decision tree; decision mak ing. (Med Decis Making 1993;13:322-338)

The physician's estimate of prognosis under alternative treatment plans is a principal factor in therapeutic decision making. Current methods of reporting prognosis, which include five-year survivals, survival curves, and quality-adjusted life expec tancy, are crude estimates of natural history. In this paper we describe a general- purpose model of medical prognosis based on the Markov process and show how this simple mathematical tool may be used to generate detailed and accurate assessments of life expectancy and health status. (Med Decis Making 3:419-458, 1983)

Cost-benefit analysis (CBA) provides a clear decision rule: undertake an intervention if the monetary value of its benefits exceed its costs. However, due to a reluctance to characterize health benefits in monetary terms, users of cost-utility and cost-effectiveness analyses must rely on arbitrary standards (e.g., < $50,000 per QALY) to deem a program "cost-effective." Moreover, there is no consensus regarding the appropriate dollar value per QALY gained upon which to base resource allocation decisions. To address this, the authors determined the value of a QALY as implied by the value-of-life literature and compared this value with arbitrary thresholds for cost-effectiveness that have come into common use. A literature search identified 42 estimates of the value of life that were appropriate for inclusion. These estimates were classified by method: human capital (HK), contingent valuation (CV), revealed preference/job risk (RP-JR) and revealed preference/non-occupational safety (RP-S), and by U.S. or non-U.S. origin. After converting these value-of-life estimates to 1997 U.S. dollars, the life expectancy of the study population, age-specific QALY weights, and a 3% real discount rate were used to calculate the implied value of a QALY. An ordinary least-squares regression of the value of a QALY on study type and national origin explained 28.4% of the variance across studies. Most of the explained variance was attributable to study type; national origin did not significantly affect the values. Median values by study type were $24,777 (HK estimates), $93,402 (RP-S estimates), $161,305 (CV estimates), and $428,286 (RP-JR estimates). With the exception of HK, these far exceed the "rules of thumb" that are frequently used to determine whether an intervention produces an acceptable increase in health benefits in exchange for incremental expenditures. Key words: cost-effectiveness analysis; cost-utility analysis; quality-adjusted life years; value of life. (Med Decis Making 2000;20:332-342)

Background. Basic numeracy skills are necessary before patients can understand the risks of medical treatments. Previous research has used objective measures, similar to mathematics tests, to evaluate numeracy. Objectives. To design a subjective measure (i.e., self-assessment) of quantitative ability that distinguishes low- and high-numerate individuals yet is less aversive, quicker to administer, and more useable for telephone and Internet surveys than existing numeracy measures. Research Design. Paper-and-pencil questionnaires. Subjects. The general public (N = 703) surveyed at 2 hospitals. Measures. Forty-nine subjective numeracy questions were compared to measures of objective numeracy. Results. An 8-item measure, the Subjective Numeracy Scale (SNS), was developed through several rounds of testing. Four items measure people's beliefs about their skill in performing various mathematical operations, and 4 measure people's preferences regarding the presentation of numerical information. The SNS was significantly correlated with Lipkus and others' objective numeracy scale (correlations: 0.63—0.68) yet was completed in less time (24 s/item v. 31 s/item, P < 0.05) and was perceived as less stressful (1.62 v. 2.69, P < 0.01) and less frustrating (1.92 v. 2.88, P < 0.01). Fifty percent of participants who completed the SNS volunteered to participate in another study, whereas only 8% of those who completed the Lipkus and others scale similarly volunteered (odds ratio = 11.00, 95% confidence interval = 2.14—56.65). Conclusions. The SNS correlates well with mathematical test measures of objective numeracy but can be administered in less time and with less burden. In addition, it is much more likely to leave participants willing to participate in additional research and shows much lower rates of missing or incomplete data.

The area under the ROC curve is a common index summarizing the information contained in the curve. When comparing two ROC curves, though, problems arise when interest does not lie in the entire range of false-positive rates (and hence the entire area). Numerical integration is suggested for evaluating the area under a portion of the ROC curve. Variance estimates are derived. The method is applicable for either continuous or rating scale binormal data, from independent or dependent samples. An example is presented which looks at rating scale data of computed tomographic scans of the head with and without concomitant use of clinical history. The areas under the two ROC curves over an a priori range of false- positive rates are examined, as well as the areas under the two curves at a specific point.

Trust and confidence are critical to the success of health care models. There are two main methods for achieving this: transparency (people can see how the model is built) and validation (how well it reproduces reality). This report describes recommendations for achieving transparency and validation, developed by a task force appointed by the International Society for Pharmacoeconomics and Outcomes Research (ISPOR) and the Society for Medical Decision Making (SMDM). Recommendations were developed iteratively by the authors. A nontechnical description should be made available to anyone—including model type and intended applications; funding sources; structure; inputs, outputs, other components that determine function, and their relationships; data sources; validation methods and results; and limitations. Technical documentation, written in sufficient detail to enable a reader with necessary expertise to evaluate the model and potentially reproduce it, should be made available openly or under agreements that protect intellectual property, at the discretion of the modelers. Validation involves face validity (wherein experts evaluate model structure, data sources, assumptions, and results), verification or internal validity (check accuracy of coding), cross validity (comparison of results with other models analyzing same problem), external validity (comparing model results to real-world results), and predictive validity (comparing model results with prospectively observed events). The last two are the strongest form of validation. Each section of this paper contains a number of recommendations that were iterated among the authors, as well as the wider modeling task force jointly set up by the International Society for Pharmacoeconomics and Outcomes Research and the Society for Medical Decision Making.

This article describes the integrative model of behavioral prediction (IM), the latest formulation of a reasoned action approach. The IM attempts to identify a limited set of variables that can account for a considerable proportion of the variance in any given behavior. More specifically, consistent with the original theory of reasoned action, the IM assumes that intentions are the immediate antecedents of behavior, but in addition, the IM recognizes that environmental factors and skills and abilities can moderate the intention-behavior relationship. Similar to the theory of planned behavior, the IM also assumes that intentions are a function of attitudes, perceived normative pressure and self-efficacy, but it views perceived normative pressure as a function of descriptive as well as of injunctive (i.e., subjective) norms. After describing the theory and addressing some of the criticisms directed at a reasoned action approach, the paper illustrates how the theory can be applied to understanding and changing health related behaviors.

Decisions about medical treatments and the settings of health programs are not purely technical, but also involve issues of value such as the evaluation of trade-offs between quality of life (morbidity) and quantity of life (mortality). The most commonly used measure of outcome in such cases is the quality-adjusted life year (QALY). The authors show that QALYs, being a health status index, do not stem directly from the individual's utility function and thus only partly reflect the individual's true preferences. This might lead to the choice of the nonpreferred alternative due to the misrepresentation of the individual's preferences. Two examples illustrate this claim. An alternative measure of outcome, the healthy-years equiv alent (HYE), is described. This measure stems directly from the individual's utility function and thus fully reflects his/her preferences. It combines outcomes of both morbidity and mortality and thus can serve as common unit of measure for all programs, allowing com parisons across programs. Different ways of measuring the HYE are discussed. Key words: utility theory; economic evaluation; cost-effectiveness analysis. (Med Decis Making 1989;9:142-149)

The development of methods to measure willingness to pay (WTP) has renewed interest in cost-benefit analysis (CBA) for the economic evaluation of health care programs. The authors studied the construct validity and test-retest reliability of WTP as a measure of health state preferences in a survey of 102 persons (mean age 62 years; 54% male) who had chronic lung disease (forced expiratory volume <70%). Interview measurements in cluded self-reported symptoms, the oxygen-cost diagram for dyspnea, Short-Form 36 for general health status, rating scale and standard gamble for value and utility of current health state relative to death and healthy lung functioning, and WTP for a hypothetical intervention offering a 99% chance of healthy lung functioning and a 1% chance of death. WTP was elicited by a simple bidding game. To test for starting-point bias, the respondents were randomly assigned to one of five starting bids. All health status and preference measurements except WTP (controlling for income) showed significant (p < 0.05) differences between disease-severity groups (mild/moderate/severe). WTP was significantly (p = 0.01) associ ated with household income, but other health status and preference measures were not. The measure most highly correlated with WTP was standard gamble (r = -0.46). There was no association between starting bid and mean WTP adjusted for income and health status. The test-retest reliability of WTP was acceptable (r = 0.66) but lower than that for the standard gamble (r = 0.82). It is concluded that: 1) large variation in WTP responses may compromise this measure's discriminant validity; 2) there is some evidence of convergent validity for WTP with preferences measured by standard gamble; 3) there was no evidence of starting point bias; 4) the test-retest reliability of WTP is comparable to those of other preference measures. Key words: willingness to pay; health state preferences; economics. (Med Decis Making 1994;14:289-297)