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Recall Bayes' theorem.
Standard textbooks show how to derive it from a few basic principles
of probability theory. But where does it come from?
Bayes' theorem comes
in two equivalent forms:
- One
uses the probability of disease
- Another uses the
odds of disease
The likelihood ratio
is a characteristic of diagnosis-related information, whether
it be a test or a finding from the history or physical examination.
It is expressed as follows:
| Likelihood
ratio =
| p
[test result if disease present]
p [test result if disease absent]
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Because physicians
often express test results as either positive or negative, there
is:
- A
likelihood ratio for a positive test result (LR+), and
- A likelihood ratio
for a negative test result (LR-).
The formula for the
likelihood ratio for a positive test result is:
| LR+
=
| sensitivity
1 - specificity
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The formula for the
likelihood ratio for a negative test is:
| LR-
=
| 1
- sensitivity
specificity
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The likelihood ratio
is generally a better descriptor than sensitivity or specificity
because it more directly describes the effect of a test result
on the odds of disease.
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