Likelihood ratio

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.

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.

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

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.

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