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)."

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."

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

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