Bayes Theorem

Bayes Theorem is defined as "a theorem in probability theory named for Thomas Bayes (1702-1761). In epidemiology, it is used to obtain the probability of disease in a group of people with some characteristic on the basis of the overall rate of that disease and of the likelihoods of that characteristic in healthy and diseased individuals. The most familiar application is in clinical decision analysis where it is used for estimating the probability of a particular diagnosis given the appearance of some symptoms or test result".

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

${\mbox{Sensitivity of a test}}=\left({\frac {\mbox{Total with a positive test}}{{\mbox{Total }}with{\mbox{ disease}}}}\right)$

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

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

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