# Likelihood ratios

What is a likelihood ratio?

The likelihood ratio provides a direct estimate of how much a test result will change the odds of having a disease, and incorporates both the sensitivity and specificity of the test.

The likelihood ratio for a positive result (LR+) tells you how much the odds of the disease increase when a test is positive.

The likelihood ratio of a positive test result (LR+) is sensitivity divided by (1- specificity)

 (LR+) = True positives Sensitivity False positives (1-Specificity)

The likelihood ratio for a negative result (LR-) tells you how much the odds of the disease decrease when a test is negative.

The likelihood ratio of a negative test result (LR-) is (1- sensitivity) divided by specificity.

 (LR-) = False negatives = (1- Sensitivity) True negatives (Specificity)

Interpretation of Likelihood Ratios

The further away a likelihood ratio (LR) is from 1, the stronger the evidence for the presence or absence of disease.

• LR >1 indicates that the test result is associated with the presence of the disease.
• LR <0.1 indicates that the test result is associated with the absence of disease.

© Dr Murad Ruf and Dr Oliver Morgan 2008, Dr Kelly Mackenzie 2017