Likelihood ratios
Likelihood ratios (LRs) combine a test’s sensitivity and specificity into a single multiplier that converts a clinician’s pre‑test odds of disease into post‑test odds. LRs are preferred for applying diagnostic test results to patient care because they directly show how much a result changes probability and therefore whether it will alter management (rule in / rule out) (NICE methods).
Two measures
- LR+ (positive likelihood ratio): how much more likely a positive test result is in someone with the disease than in someone without it.
- LR- (negative likelihood ratio): how much more likely a negative test result is in someone with the disease than in someone without it.
LR = 1 means the test result does not change probability. LR
> 1 increases disease probability (useful to rule in). LR < 1 decreases probability (useful to rule out). Apply LRs to odds using Bayes’ theorem or use a nomogram.
Definitions and formulas
Algebraic
- LR+ = sensitivity / (1 - specificity)
- LR- = (1 - sensitivity) / specificity
From a 2 × 2 table
- Sensitivity = TP / (TP + FN)
- Specificity = TN / (FP + TN)
- LR+ = [TP / (TP + FN)] / [FP / (FP + TN)]
- LR- = [FN / (TP + FN)] / [TN / (FP + TN)]