subjective and 2) it assumes that decision makers have well-defined options and are more rationale and dispassionate than they typically are. Variable subjective utility can be illustrated by two patients who view the same condition with very different utility. Arthritis of the fingers may ruin the career of a professional musician but may not have such severe consequence for a college professor. In scenarioswhere two patients have the same condition but different utilities, there may no single course of ideal action. This notion can be very disconcerting to both patients and clinicians. In addition, the average clinician must make decisions under time-pressure and stress and generally use a series of shortcuts or "heuristics" to assist in decision making. Bayes' TheoremDespite the limitations of classical decision making, using information to make better decisions is clearly desirable. One of the key ways of reducing uncertainty in medicine is through the performance of diagnostic tests. Diagnostic tests include visual inspection, lab results, imaging studies as well as a large range of medical exams and equipment. Before any such diagnostic test, there is a prior probabilitythat a patient has a given condition (Coiera, 2003). Unless there is other information
about why a patient may have a condition, such as genetic predisposition, this may often be the prevalence of a condition in the population. After a diagnostic test is performed and a positive result is received, the chances that a patient has a given condition have clearly increased. We often call this resulting likelihood as the posterior probabilityand its calculation depends on Bayes Theorem (Coiera, 2003). This theorem is a formula which relies on three key pieces of information: the test’s sensitivity, the test’s specificity and the priorprobability, which is often substituted with the disease prevalence. The most common form of Bayes’ Theorem (or Law, Rule or Formula) is shown below:Figure 2.10 Bayes’ Theorem, where P means "probability of" and the vertical bar means "given that"Using this form of Bayes’ Theorem, here is how the three key pieces of information contribute to the formula:P ( B | A) is generally the sensitivity of a testP ( A ) is the prior probability, which is often substituted with prevalenceP ( B ) is the chance that a positive test is received, which is often estimated as the inverse of a test’s specificity for rare conditionsAn important implication of Bayes Theorem is that clinicians should be very careful in testing for rare conditions unless there is a strong belief that a patient has the condition or there is a test which yields very few false positives. Otherwise, the vast majority of positive results will be false and lead to unnecessary stress and costs. Part of this thinking can be summarized in the adage "When you hear hoofbeats, think of horses not zebras." Research has found that clinicians often overestimate the probability of disease given a positive result (Eddy, 1982). A visual representation of this scenario can be reviewed by a video Explaining Bayesian Problems Using Visualizations .
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