Bayes Theorem: Difference between revisions

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imported>Robert Badgett
imported>Robert Badgett
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==Calculations==
==Calculations==
 
{{main|Sensitivity and specificity}}
{| class="wikitable" align="center"
|+ Two-by-two table for a diagnostic test
!colspan="2" rowspan="2"| || colspan="2"| Disease||
|-
| Present || Absent||
|-
| rowspan="3"|'''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===
The sensitivity and specificity of diagnostic tests are 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)."<ref name="MeSH_SnSp">{{cite web |url=http://www.nlm.nih.gov/cgi/mesh/2007/MB_cgi?term=Sensitivity+and+Specificity |title=Sensitivity and specificity |accessdate=2007-12-09 |author=National Library of Mediicne |authorlink= |coauthors= |date= |format= |work= |publisher= |pages= |language= |archiveurl= |archivedate= |quote=}}</ref>
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:<math>\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 )</math>
 
:<math>\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 )</math>
 
===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."<ref name="MeSH_PV">{{cite web |url=http://www.nlm.nih.gov/cgi/mesh/2007/MB_cgi?term=Predictive+value+of+tests |title=Predictive value of tests |accessdate=2007-12-09 |author=National Library of Mediicne |authorlink= |coauthors= |date= |format= |work= |publisher= |pages= |language= |archiveurl= |archivedate= |quote=}}</ref>
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:<math>\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 )</math>
 
:<math>\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 )</math>


==References==
==References==

Revision as of 07:02, 9 December 2007

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".[1]

Calculations

For more information, see: Sensitivity and specificity.


References

  1. ↑ National Library of Medicine. Bayes Theorem. Retrieved on 2007-12-09.
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