Sensitivity & Specificity
How well a test detects disease when it is present (sensitivity) and excludes it when it is absent (specificity).
Sensitivity = TP / (TP + FN) — the proportion of people with disease the test correctly calls positive. Specificity = TN / (TN + FP) — the proportion of people without disease it correctly calls negative. Both are intrinsic properties of the test, not of the population.
| Disease + | Disease − | |
|---|---|---|
| Test + | 80True positive | 30False positive |
| Test − | 20False negative | 870True negative |
Sensitivity reads down the Disease + column · specificity down the Disease − column
The 2×2 of test result (rows) against true disease status (columns), splitting every patient into one of four outcomes — true positive, false positive, false negative, true negative. Here Sn = 80 / (80 + 20) = 80% and Sp = 870 / (870 + 30) = 97%.
Sensitivity is read down the “Disease +” column (of those who truly have it, how many test positive); specificity is read down the “Disease −” column. PPV and NPV are read across the rows and depend on prevalence — so the same test behaves very differently as disease becomes rarer.
You pick a test by purpose: a highly sensitive test to safely rule out and discharge, a highly specific test to rule in before committing to treatment. Sn and Sp don’t move with prevalence — but they can shift with case-mix (spectrum bias), so figures from a sick referral cohort may not hold in your undifferentiated ED.
Sensitivity = TP / (TP + FN)Specificity = TN / (TN + FP)- SnNOUT (sensitive, Negative → rules OUT) · SpPIN (specific, Positive → rules IN)
Ottawa Ankle Rules — a decision rule designed to exclude clinically significant ankle/mid-foot fracture and cut needless x-rays. In Bachmann et al.’s meta-analysis (BMJ 2003; 27 studies, 15,581 patients) pooled sensitivity approached 100% (only 47 / 15,581, 0.3%, false negatives) while specificity was modest (~26–32%); applying the rule reduces unnecessary radiographs by 30–40%. High sensitivity / low specificity is exactly why a positive rule still needs imaging — it rules out, it does not rule in.
- Confusing Sn/Sp with PPV/NPV — predictive values are prevalence-dependent; Sn/Sp are not.
- Misapplying SnNOUT/SpPIN — a sensitive test rules out on a negative; a specific test rules in on a positive.
- Ignoring spectrum bias — Sn/Sp can shift with the disease-severity mix of the population tested.
Quick check
A test is 99% sensitive and the patient tests negative — is the diagnosis excluded?
Answer: Largely yes for ruling out (SnNOUT), but factor in pre-test probability — with a very high pre-test probability the few false negatives still matter, so a negative result does not fully exclude disease.
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