3: Likelihood Ratios

← Back to Module

One of the most common ways we use Bayesian analysis in medicine is through likelihood ratios.

Post-test odds = Pre-test odds × LR

Positive likelihood ratio

LR+ describes how much a positive test increases the probability of disease. Larger values create stronger upward movement.

LR+ = sensitivity / (1 - specificity)

Negative likelihood ratio

LR- describes how much a negative test decreases the probability of disease. Smaller values create stronger downward movement.

LR- = (1 - sensitivity) / specificity
Scale showing how positive likelihood ratios increase diagnostic probability
Scale showing how negative likelihood ratios decrease diagnostic probability

Example of likelihood ratios in diagnosing MI

Positive likelihood ratios (+LR):

  • Chest pain radiating to both arms: 7.1
  • Positive troponin I: 9 to 25 depending on the degree of elevation and delta

Negative likelihood ratios (-LR):

  • Sharp or stabbing chest pain: 0.3
  • Negative troponin I (0/2 hours): 0.02