True positive rate

Sensitivity and specificity are statistical measures of the performance of a binary classification test, also known in statistics as classification function:

Another way to understand in the context of medical tests is that sensitivity is the extent to which true positives are not missed/overlooked (so false negatives are few) and specificity is the extent to which positives really represent the condition of interest and not some other condition being mistaken for it (so false positives are few). Thus a highly sensitive test rarely overlooks a positive (for example, showing "nothing bad" despite something bad existing); a highly specific test rarely registers a positive for anything that is not the target of testing (for example, finding one bacterial species when another closely related one is the true target); and a test that is highly sensitive and highly specific does both, so it "rarely overlooks a thing that it is looking for" and it "rarely mistakes anything else for that thing." Because most medical tests do not have sensitivity and specificity values above 99%, "rarely" does not equate to certainty. But for practical reasons, tests with sensitivity and specificity values above 90% have high credibility, albeit usually no certainty, in differential diagnosis.

Sensitivity therefore quantifies the avoiding of false negatives, and specificity does the same for false positives. For any test, there is usually a trade-off between the measures – for instance, in airport security since testing of passengers is for potential threats to safety, scanners may be set to trigger alarms on low-risk items like belt buckles and keys (low specificity), in order to increase the probability of identifying dangerous objects and minimize the risk of missing objects that do pose a threat (high sensitivity). This trade-off can be represented graphically using a receiver operating characteristic curve. A perfect predictor would be described as 100% sensitive, meaning all sick individuals are correctly identified as sick, and 100% specific, meaning no healthy individuals are incorrectly identified as sick. In reality, however, any non-deterministic predictor will possess a minimum error bound known as the Bayes error rate.

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