Abstract
Diagnostic tests are important clinical tools. Bayes’ theorem and Bayesian approach are important methods for interpreting test results. The Bayesian factor, the so-called likelihood ratio, has not always been well-understood. In this article, we try to discuss the likelihood ratio and its value for a specific test result, a positive or negative test result, and a range of test results, along with their graphical representations.
Highlights
First described in 1763, Bayes’ theorem, named after Reverend Thomas Bayes, is one of the cornerstones of methods used for interpreting diagnostic test results
The slope of the tangent line to the receiver operating characteristic (ROC) at the solid circle, the point corresponding to a test value r (FBS = 98 mg/dL in our example) in Figure 1, is the likelihood ratio of having an fasting blood sugar (FBS) of 98 mg/dL
likelihood ratio (LR)(+) is clearly, the slope of the line segment joining the origin of the unit square to the point on the ROC curve corresponding to the test cut-off value, r
Summary
First described in 1763, Bayes’ theorem, named after Reverend Thomas Bayes (an English statistician and philosopher), is one of the cornerstones of methods used for interpreting diagnostic test results. The slope of the tangent line to the ROC (grey short dashed line) at the solid circle, the point corresponding to a test value r (FBS = 98 mg/dL in our example) in Figure 1, is the likelihood ratio of having an FBS of 98 mg/dL.
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