Sensitivity and Specificity

In medicine, diagnostic tests are administered to patients to detect diseases so that appropriate treatments can be provided. A test can be relatively simple, such as a bacterial culture for infection, or a radiographic image to detect the presence of a tumor. Alternatively, tests can be quite complex, such as using mass spectrometry to quantify many different protein levels in serum and using this ‘protein profile’ to detect disease. Screening tests are special cases of diagnostic tests, where apparently healthy individuals are tested with the goal of diagnosing certain conditions early, when they can be treated most effectively and with higher success. For example, in the United States, annual screening mammograms are recommended for healthy women aged 40 years and older to facilitate early detection of breast cancer.

Whether for diagnosis or screening, the objective is to use some kind of a test to correctly classify individuals according to their true disease state. Sensitivity and specificity are two related measures used to quantify the performance of a screening or diagnostic test compared with the true condition or disease state. The test yields a binary result for each individual, positive for the presence of a condition or negative for its absence, which is compared with the true disease state for the same individuals. In practice, since the true disease state cannot always be identified with absolute certainty, a gold standard test that also yields a binary result (presence or absence of a condition) is considered the true status for an individual. For example, screening tests conducted among pregnant women to measure the chance of a child having birth defects usually take results from an amniocentesis as the gold standard, since the true status of the infant may not be determined until birth. In most cases, the amniocentesis results reflect the truth with extremely high probability.

A comparison of diagnostic or screening test results with the true disease state (or gold standard test results) can be displayed in a 2 × 2 table, as in Table 1.

Sensitivity, calculated as a/(a + c), gives the proportion of individuals who truly have the disease for whom the test gives a positive result. Sensitivity is also sometimes referred to as the ‘true positive fraction’ or ‘true positive rate.’ That is, among those individuals in whom the condition is truly present, sensitivity reflects how often the test detects it.

Specificity, calculated as d/(b + d), gives the proportion of those individuals who truly do not have the disease for whom the test gives a negative result—the true negatives. That is, for those individuals in whom the disease or condition is truly absent, specificity reflects how often the test gives a negative result. Closely related to specificity is the proportion of false-positive test results, which is calculated as b/(b + d)or1 − specificity. In the health sciences literature, sensitivity, specificity, and false-positive rate are usually reported as a percentage rather than as proportions (i.e., they are multiplied by 100).

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