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 (., "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 –. | 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 . 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 - specificity . For example a test with a sensitivity of and a specificity of has a likelihood ratio of 1 - or 9. Thus for this hypothetical test a positive result is 9 times more likely in a patient with the disease than in a patient without it. Most tests in medicine have likelihood ratios for a positive result between and 20. Higher values are associated with tests that are more accurate at identifying patients with disease with values of 10 or greater of particular note. If sensitivity is excellent but specificity is less so the likelihood ratio will be substantially reduced . with a 90 sensitivity but a 60 specificity the likelihood ratio is . For a negative test the corresponding likelihood ratio is the ratio of the false negative rate to the true negative rate or 1 - sensitivity specificity . The smaller the likelihood ratio . closer to 0 the better the test performs at ruling out disease. The hypothetical test we considered above with a sensitivity of and a specificity of would have a likelihood ratio for a negative test result of 1 - of meaning that a negative result is almost 10 times more likely if the 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 exercise .
