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.

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