Likelihood ratio

From Citizendium, the Citizens' Compendium

Jump to: navigation, search

Main Article

Talk

Related Articles ^[?]

Bibliography ^[?]

External Links ^[?]

This is a draft article, under development and not meant to be cited but you can help to improve it. These unapproved articles are subject to a disclaimer.

[edit intro]

In diagnostic tests, the likelihood ratio is the likelihood that a clinical sign is in a patient with disease as compared to a patient without disease.

$\text{Likelihood ratio} = \frac{\mbox{probability of test result with disease}}{\mbox{probability of same result without disease}}$

$\text{Likelihood ratio} = \frac{\mbox{sensitivity}}{1 - \mbox{specificity}}$

To calculate probabilities of disease using a likelihood ratio:

$\text{Post-test odds} = \text{Pre-test odds} * \text{Likelihood}\ \text{ratio}$

Comparing likelihoods (or odds) is different than comparing percentages. (or probabilities).

$\text{Odds}=\frac{\text{probability}}{(1-\text{probability})}$

The likelihood ratio is an alternative to sensitivity and specificity for the numeric interpretation of diagnostic tests. In a randomized controlled trial that compared the two methods, physicians were able to use both similarly although the physicians had trouble with both methods.^[1]

Calculations

Likelihood ratios are related to sensitivity and specificity.

The positive likelihood ratio (LR+) measures the likelihood of a finding being present in patient with the disease. A large LR+, for example a value more than 10, helps rule in disease.^[2]

$\text{LR+} = \frac{\text{sensitivity}}{(1-\text{specificity})}$

The negative likelihood ratio (LR-) measures the likelihood of a finding being absent in patient with the disease. A small LR-, for example a value less than 0.1, helps rule out disease.^[2]

$\text{LR-} = \frac{(1-\text{sensitivity})}{\text{specificity}}$

References

↑ Puhan MA, Steurer J, Bachmann LM, ter Riet G (August 2005). "A randomized trial of ways to describe test accuracy: the effect on physicians' post-test probability estimates". Ann. Intern. Med. 143 (3): 184–9. PMID 16061916.
↑ ^2.0 ^2.1 McGee S (August 2002). "Simplifying likelihood ratios". J Gen Intern Med 17 (8): 646–9. PMID 12213147.