In medicine and statistics, sensitivity and specificity mathematically describe the accuracy of a test that reports the presence or absence of a medical condition. If individuals who have the condition are considered "positive" and those who do not are considered "negative", then sensitivity is a measure of how well a test can identify true positives and specificity is a measure of how well a test can identify true negatives:
Sensitivity (true positive rate) is the probability of a positive test result, conditioned on the individual truly being positive. Specificity (true negative rate) is the probability of a negative test result, conditioned on the individual truly being negative. If the true status of the condition cannot be known, sensitivity and specificity can be defined relative to a "gold standard test" which is assumed correct. For all testing, both diagnoses and screening, there is usually a trade-off between sensitivity and specificity, such that higher sensitivities will mean lower specificities and vice versa. A test which reliably detects the presence of a condition, resulting in a high number of true positives and low number of false negatives, will have a high sensitivity. This is especially important when the consequence of failing to treat the condition is serious and/or the treatment is very effective and has minimal side effects. A test which reliably excludes individuals who do not have the condition, resulting in a high number of true negatives and low number of false positives, will have a high specificity. This is especially important when people who are identified as having a condition may be subjected to more testing, expense, stigma, anxiety, etc.
The terms "sensitivity" and "specificity" were introduced by American biostatistician Jacob Yerushalmy in 1947. There are different definitions within laboratory quality control, wherein "analytical sensitivity" is defined as the smallest amount of substance in a sample that can accurately be measured by an assay (synonymously to detection limit), and "analytical specificity" is defined as the ability of an assay to measure one particular organism or substance, rather than others. However, this article deals with diagnostic sensitivity and specificity as defined at top.
Application to screening study Imagine a study evaluating a test that screens people for a disease. Each person taking the test either has or does not have the disease. The test outcome can be positive (classifying the person as having the disease) or negative (classifying the person as not having the disease). The test results for each subject may or may not match the subject's actual status. In that setting:
True positive: Sick people correctly identified as sick False positive: Healthy people incorrectly identified as sick True negative: Healthy people correctly identified as healthy False negative: Sick people incorrectly identified as healthy After getting the numbers of true positives, false positives, true negatives, and false negatives, the sensitivity and specificity for the test can be calculated. If it turns out that the sensitivity is high then any person who has the disease is likely to be classified as positive by the test. On the other hand, if the specificity is high, any person who does not have the disease is likely to be classified as negative by the test. An NIH web site has a discussion of how these ratios are calculated.
Definition
Sensitivity Consider the example of a medical test for diagnosing a condition. Sensitivity (sometimes also named the detection rate in a clinical setting) refers to the test's ability to correctly detect ill patients out of those who do have the condition. Mathematically, this can be expressed as:
A negative result in a test with high sensitivity can be useful for "ruling out" disease, since it rarely misdiagnoses those who do have the disease. A test with 100% sensitivity will recognize all patients with the disease by testing positive. In this case, a negative test result would definitively rule out the presence of the disease in a patient. However, a positive result in a test with high sensitivity is not necessarily useful for "ruling in" disease. Suppose a 'bogus' test kit is designed to always give a positive reading. When used on diseased patients, all patients test positive, giving the test 100% sensitivity. However, sensitivity does not take into account false positives. The bogus test also returns positive on all healthy patients, giving it a false positive rate of 100%, rendering it useless for detecting or "ruling in" the disease. The calculation of sensitivity does not take into account indeterminate test results. If a test cannot be repeated, indeterminate samples either should be excluded from the analysis (the number of exclusions should be stated when quoting sensitivity) or can be treated as false negatives (which gives the worst-case value for sensitivity and may therefore underestimate it). A test with a higher sensitivity has a lower type II error rate.
Specificity Consider the example of a medical test for diagnosing a disease. Specificity refers to the test's ability to correctly reject healthy patients without a condition. Mathematically, this can be written as:
A positive result in a test with high specificity can be useful for "ruling in" disease, since the test rarely gives positive results in healthy patients. A test with 100% specificity will recognize all patients without the disease by testing negative, so a positive test result would definitively rule in the presence of the disease. However, a negative result from a test with high specificity is not necessarily useful for "ruling out" disease. For example, a test that always returns a negative test result will have a specificity of 100% because specificity does not consider false negatives. A test like that would return negative for patients with the disease, making it useless for "ruling out" the disease. A test with a higher specificity has a lower type I error rate.
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