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

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

Calculations

Likelihood ratios are relatived to sensitivity and specificity.

The positive likelihood ratio (LR+) meaures the probability 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 probability 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.

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