Chapter 003. Decision-Making in Clinical Medicine (Part 7)

To understand conceptually how Bayes theorem estimates the posttest probability of disease, it is useful to examine a nomogram version of Bayes theorem (Fig. 3-2). In this nomogram, the accuracy of the diagnostic test in question is summarized by the likelihood ratio , which is defined as the ratio of the probability of a given test result (e.g., "positive" or "negative") in a patient with disease to the probability of that result in a patient without disease.For a positive test, the likelihood ratio is calculated as the ratio of the truepositive rate to the false-positive rate [or sensitivity/(1 –...
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Chapter 003. Decision-Making in Clinical Medicine (Part 7) Chapter 003. Decision-Making in Clinical Medicine (Part 7) To understand conceptually how Bayes theorem estimates the posttestprobability of disease, it is useful to examine a nomogram version of Bayestheorem (Fig. 3-2). In this nomogram, the accuracy of the diagnostic test inquestion is summarized by the likelihood ratio , which is defined as the ratio of theprobability of a given test result (e.g., positive or negative) in a patient withdisease to the probability of that result in a patient without disease. For a positive test, the likelihood ratio is calculated as the ratio of the true-positive rate to the false-positive rate [or sensitivity/(1 – specificity)]. Forexample, a test with a sensitivity of 0.90 and a specificity of 0.90 has a likelihoodratio of 0.90/(1 – 0.90), or 9. Thus, for this hypothetical test, a positive result is 9times more likely in a patient with the disease than in a patient without it. Mosttests in medicine have likelihood ratios for a positive result between 1.5 and 20.Higher values are associated with tests that are more accurate at identifyingpatients with disease, with values of 10 or greater of particular note. If sensitivityis excellent but specificity is less so, the likelihood ratio will be substantiallyreduced (e.g., with a 90% sensitivity but a 60% specificity, the likelihood ratio is2.25). For a negative test, the corresponding likelihood ratio is the ratio of thefalse negative rate to the true negative rate [or (1 – sensitivity)/specificity]. Thesmaller the likelihood ratio (i.e., closer to 0) the better the test performs at rulingout disease. The hypothetical test we considered above with a sensitivity of 0.9and a specificity of 0.9 would have a likelihood ratio for a negative test result of (1– 0.9)/0.9 of 0.11, meaning that a negative result is almost 10 times more likely ifthe patient is disease-free than if he has disease. Applications to Diagnostic Testing in CAD Consider two tests commonly used in the diagnosis of CAD, an exercisetreadmill and an exercise single photon emission CT (SPECT) myocardialperfusion imaging test (Chap. 222). Meta-analysis has shown a positive treadmillST-segment response to have an average sensitivity of 66% and an averagespecificity of 84%, yielding a likelihood ratio of 4.1 [0.66/(1 – 0.84)]. If we usethis test on a patient with a pretest probability of CAD of 10%, the posttestprobability of disease following a positive result rises to only about 30%. If apatient with a pretest probability of CAD of 80% has a positive test result, theposttest probability of disease is about 95%. The exercise SPECT myocardial perfusion test is a more accurate test forthe diagnosis of CAD. For our purposes, assume that the finding of a reversibleexercise-induced perfusion defect has both a sensitivity and specificity of 90%,yielding a likelihood ratio for a positive test of 9.0 [0.90/(1 – 0.90)]. If we againtest our low pretest probability patient and he has a positive test, using Fig. 3-2 wecan demonstrate that the posttest probability of CAD rises from 10 to 50%.However, from a decision-making point of view, the more accurate test has notbeen able to improve diagnostic confidence enough to change management. Infact, the test has moved us from being fairly certain that the patient did not haveCAD to being completely undecided (a 50:50 chance of disease). In a patient witha pretest probability of 80%, using the more accurate exercise SPECT test raisesthe posttest probability to 97% (compared with 95% for the exercise treadmill).Again, the more accurate test does not provide enough improvement in posttestconfidence to alter management, and neither test has improved much upon whatwas known from clinical data alone. If the pretest probability is low (e.g., 20%), even a positive result on a veryaccurate test will not move the posttest probability to a range high enough to rulein disease (e.g., 80%). Conversely, with a high pretest probability, a negative testwill not adequately rule out disease. Thus, the largest gain in diagnosticconfidence from a test occurs when the clinician is most uncertain beforeperforming it (e.g., pretest probability between 30 and 70%). For example, if apatient has a pretest probability for CAD of 50%, a positive exercise treadmill testwill move the posttest probability to 80% and a positive exercise SPECT perfusiontest will move it to 90% (Fig. 3-2). Bayes theorem, as presented above, employs a number of importantsimplifications that should be considered. First, few tests have only two usefuloutcomes, positive or negative, and many tests provide numerous pieces of dataabout the pa ...