Sensitivity and specificity

The sensitivity and specificity of diagnostic tests are based on Bayes Theorem and defined as "measures for assessing the results of diagnostic and screening tests. Sensitivity represents the proportion of truly diseased persons in a screened population who are identified as being diseased by the test. It is a measure of the probability of correctly diagnosing a condition. Specificity is the proportion of truly nondiseased persons who are so identified by the screening test. It is a measure of the probability of correctly identifying a nondiseased person. (From Last, Dictionary of Epidemiology, 2d ed)."

Successful application of sensitivity and specificity is an important part of practicing evidence-based medicine.

Calculations

Two-by-two table for a diagnostic test

		Disease
		Present	Absent
Test result	Positive	Cell A	Cell B	Total with a positive test
	Negative	Cell C	Cell D	Total with a negative test
		Total with disease	Total without disease

Sensitivity and specificity

${\mbox{Sensitivity of a test}}=\left({\frac {\mbox{Total with a positive test}}{{\mbox{Total }}without{\mbox{ disease}}}}\right)=\left({\frac {\mbox{Cell A}}{{\mbox{Cell A}}+{\mbox{Cell C}}}}\right)$

${\mbox{Specificity of a test}}=\left({\frac {\mbox{Total with a negative test}}{{\mbox{Total }}without{\mbox{ disease}}}}\right)=\left({\frac {\mbox{Cell D}}{{\mbox{Cell B}}+{\mbox{Cell D}}}}\right)$

Predictive value of tests

The predictive values of diagnostic tests are defined as "in screening and diagnostic tests, the probability that a person with a positive test is a true positive (i.e., has the disease), is referred to as the predictive value of a positive test; whereas, the predictive value of a negative test is the probability that the person with a negative test does not have the disease. Predictive value is related to the sensitivity and specificity of the test."

${\mbox{Positive predictive value}}=\left({\frac {{\mbox{Total }}with{\mbox{ disease and a positive test}}}{\mbox{Total with a positive test}}}\right)=\left({\frac {\mbox{Cell A}}{{\mbox{Cell A}}+{\mbox{Cell B}}}}\right)$

${\mbox{Negative predictive value}}=\left({\frac {{\mbox{Total }}without{\mbox{ disease and a negative test}}}{\mbox{Total with a negative test}}}\right)=\left({\frac {\mbox{Cell D}}{{\mbox{Cell C}}+{\mbox{Cell D}}}}\right)$

Summary statistics for diagnostic ability

While simply reporting the accuracy of a test seems intuitive, the accuracy is heavily influenced by the prevalence of disease. For example, if the disease occurred with a a frequency of one in one thousand, then simply guessing that all patients do not have disease will yield an accuracy of over 99%.

Area under the ROC curve

The area under the ROC curve, or c-index has been proposed. The c-index varies from 0 to 1 and a result of 0.5 indicates that the diagnostic test does not add to guessing.

Sum of sensitivity and specificity

This easy metric is called S+T. It varies from 0 to 2 and a result of 1 indicates that the diagnostic test does not add to guessing.

Threats to validity of calculations

Various biases incurred during the study and analysis of a diagnostic tests can affect the validity of the calculations. An example is spectrum bias.

Poorly designed studies may overestimate the accuracy of a diagnostic test.