Likelihood Ratios

The likelihood of a particular test result in people with disease divided by the likelihood of that result in people without it. LR+ = Sn ÷ (1 − Sp); LR− = (1 − Sn) ÷ Sp. Combine with the pre-test probability — via the Fagan nomogram or odds — to get the post-test probability.

A Fagan nomogram — a straight line from a pre-test probability, through the LR, reaching the post-test probability. Here a 20% pre-test probability, pivoted through an LR+ of 10, lands at roughly 70%.

Anchor the pre-test probability on the left axis, pivot the line through the LR on the middle axis, and read the post-test probability where it lands on the right. A bigger LR+ (or a smaller LR−) swings the line further — the more it moves, the more the result has changed your mind.

LRs quantify a test’s value at the bedside and are prevalence-independent, so you can chain results and risk-stratify without recomputing predictive values for every population — ideal for the ED, where the same test is used across very different pre-test probabilities.

• LR+ = Sn ÷ (1 − Sp)
• LR− = (1 − Sn) ÷ Sp
• LR+ >10 or LR− <0.1 = large, often decisive shift · LR = 1 is useless

ESC 0/1-hour hs-cTn rule-out for AMI — meta-analysis of 32 studies, 30,066 patients with suspected MI (Chiang et al., Ann Intern Med 2022). A “rule-out” 0/1-h result gave sensitivity 99% (95% CI 98.5–99.5%) and LR− ≈ 0.01 — far below the 0.1 threshold, so it collapses the post-test probability of MI to near zero. (Rule-in: specificity 94%, LR+ ≈ 14.) LRs assume the result is interpreted at the same threshold used to derive them — a different assay, cut-off or sampling time invalidates the figure.

• Confusing LRs with predictive values (PPV/NPV depend on prevalence; LRs do not).
• Forgetting that an LR is useless without a pre-test probability to apply it to.
• Treating a near-1 LR as informative — it barely moves the line.