Bayes Theorem: Difference between revisions
imported>Robert Badgett |
imported>Robert Badgett |
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| Present || Absent|| | | Present || Absent|| | ||
|- | |- | ||
| rowspan="3"|'''Test result''' || Positive || | | rowspan="3"|'''Test result''' || Positive || Cell A|| Cell B||Total with a positive test | ||
|- | |- | ||
| Negative|| | | Negative|| Cell C|| Cell D||Total with a negative test | ||
|- | |- | ||
| || Total with disease|| Total without disease|| | | || 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 } | :<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 )</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> | ||
:<math>\mbox{Positive predictive value}=\left (\frac{\mbox{Total }with\mbox{ disease and a positive test}}{\mbox{Total with a positive test}}\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 )</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 06:54, 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
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
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)."[2]
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."[3]
References
- ↑ National Library of Medicine. Bayes Theorem. Retrieved on 2007-12-09.
- ↑ National Library of Mediicne. Sensitivity and specificity. Retrieved on 2007-12-09.
- ↑ National Library of Mediicne. Predictive value of tests. Retrieved on 2007-12-09.