PPV & NPV
Given a test result, how likely is disease? — the bedside question, and it moves with prevalence.
PPV = TP / (TP + FP) — the probability a patient has disease given a positive test. NPV = TN / (TN + FN) — the probability a patient is disease-free given a negative test. Unlike sensitivity and specificity (intrinsic to the test), predictive values depend on prevalence — the pre-test probability in the population you are testing.
| Disease + | Disease − | |
|---|---|---|
| Test + | 80True positive | 30False positive |
| Test − | 20False negative | 870True negative |
PPV reads across the Test + row (80/110 ≈ 73%) · NPV across the Test − row (870/890 ≈ 98%)
1,000 patients, 10% truly diseased. The same test (Sn 80%, Sp 97%) yields PPV = 80 / 110 ≈ 73% and NPV = 870 / 890 ≈ 98%. Predictive values are read across the rows — from a result back to the probability of disease — whereas Sn/Sp are read down the columns.
Now drop prevalence to 1% (same test). Of 1,000 patients only 10 have disease: ~8 true positives but ~33 false positives, so PPV collapses to ~20% while NPV climbs toward ~99.8%. Identical test, very different bedside meaning — because predictive values bake in the pre-test probability of the people you are testing.
PPV/NPV answer what the clinician actually asks: “my patient’s test is positive — do they have it?” In a low-prevalence ED population, even an excellent test throws up many false positives, so a positive result is often a false alarm. Conversely a high NPV is what licenses a safe rule-out and discharge.
PPV = TP / (TP + FP)·NPV = TN / (TN + FN)- Both depend on prevalence (pre-test probability); Sn/Sp do not
- ↓ prevalence → ↓ PPV, ↑ NPV · high Sn underpins a high NPV (rule-out)
D-dimer for PE — the Christopher Study (JAMA 2006; 3,306 patients). In patients with a “PE unlikely” Wells score, a negative D-dimer ruled out PE: the 3-month VTE rate after this combination was just 0.5% (overall NPV of the algorithm ~99.5%). But D-dimer’s PPV is poor — it is raised by infection, malignancy, pregnancy and age, so a positive result is non-specific. Excellent NPV makes D-dimer a rule-out test; its low PPV in a low-prevalence ED means a positive result mandates imaging, not a diagnosis.
- Prevalence dependence — quoting a PPV without stating the population/pre-test probability it came from.
- Confusing PPV/NPV with sensitivity/specificity — predictive values read across rows; Sn/Sp read down columns.
- Base-rate neglect — assuming a positive test in a low-prevalence setting means disease is probable.
Quick check
Does PPV change with disease prevalence?
Answer: Yes — for the same test, a lower prevalence (lower pre-test probability) produces a lower PPV, because false positives make up a larger share of the positives; NPV rises in the same setting.
Ready to build your plan? EMF Premium gives you all 40,000+ questions, 20 mocks and 1,215 OSCE stations from £29/month — or a one-off 3- or 6-month pass.