Positivity Criterion and Cutoff Values

A Clinical Example

A clinical example that illustrates the above principles is the tuberculin skin test, used to determine whether individuals have been exposed to tuberculosis (TB) and developed so-called latent disease, which would necessitate medical treatment. Tuberculin skin testing is performed by injecting a small amount of purified tuberculin extract under the skin. The test is read 48 hours later by seeing if redness and swelling (also called induration) develops and, if so, how large an area of induration. Figure 1 shows a hypothetical distribution of results in which the horizontal axis represents the amount of induration in millimeters (mm). The top distribution describes test results in a population without latent TB, while the bottom distribution describes results for patients with latent TB. Each vertical line represents a different potential positivity criterion. For any criterion, all the patients to the left of the line are deemed to have a negative test result, and those to the right of the line are deemed to have a positive result. The line representing each cutoff divides the distributions into four quadrants. In the top distribution describing patients without disease, those to the left of the cutoff who have a negative test result are the true negatives (TN), while those to the right who have a positive result are false positives (FP). In the bottom distribution describing those with disease, those to the right who have a positive result are true positives (TP), while those to the left are false negatives (FN). As the criterion moves to the right (from A to B to C), the proportion of patients with true-negative test results increases, while the proportion with true-positive results decreases. Since the area under each distribution is unity, the true-negative area corresponds to the specificity, while the true-positive area corresponds to the sensitivity. Thus, moving to the right in [Page 891]the figure, specificity increases while sensitivity decreases. The American Thoracic Society has updated the guidelines for the interpretation of TB skin tests to account for the principles described above. The old guidelines simply used 10 mm of induration as the cutoff for all patients. The new guidelines are as

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