How prevalence changes predictive values
- Concept
The same test's positives are right more often where the disease is common and less often where it is rare.
What it is
Sensitivity and specificity belong to the test, but predictive values also depend on how many diseased people are in the group tested. When prevalence falls, healthy people are so numerous that even a small percentage of false positives outnumbers the true positives: PPV falls and NPV rises. That is why a test that works very well in a referral hospital can produce mostly false positives when it screens the general population.
Worked example
- Data: a test with 95% sensitivity and 90% specificity is used in two places, with 1,000 people in each.
- Referral clinic, prevalence 40%: 400 diseased (380 TP, 20 FN) and 600 healthy (540 TN, 60 FP).
- Clinic: PPV = 380 / 440 ≈ 86.4%; NPV = 540 / 560 ≈ 96.4%.
- General population, prevalence 2%: 20 diseased (19 TP, 1 FN) and 980 healthy (882 TN, 98 FP).
- Population: PPV = 19 / 117 ≈ 16.2%; NPV = 882 / 883 ≈ 99.9%.
- Reading: with the same test, 86 of every 100 positives are real in the clinic and only 16 in the general population.
The same test (sensitivity 95%, specificity 90%) at two prevalences
| Setting | Prevalence | PPV | NPV |
|---|---|---|---|
| Referral clinic | 40% | 86.4% | 96.4% |
| General population | 2% | 16.2% | 99.9% |
Markers
- PPV
- NPV
- prevalence
In practice
- Screening programmes target age or risk groups where prevalence is higher, so positives are more reliable.
- A positive result in someone without risk factors calls for more caution and confirmation than the same result in a patient with symptoms.
Common pitfalls
- Assuming a test with 95% sensitivity and 90% specificity has a PPV of 95% everywhere.
- Forgetting that the prevalence in the clinic acts as the pre-test probability.
- Blaming the test for a change in PPV that actually comes from the population tested.
Test yourself
Think of the answer, then tap the question to see it.
If prevalence falls, what happens to PPV and NPV?
PPV falls and NPV rises.
Does a test's sensitivity change when it moves from a hospital to the community?
In principle no, because it is calculated only among diseased people; it can change if the spectrum of patients differs (milder cases).
Why does screening only high-risk groups improve the PPV?
It raises the prevalence in the group tested, so a larger share of positives are true.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Sensitivity, Specificity, and Predictive Values: Foundations, Pliabilities, and Pitfalls in Research and Practice (Frontiers in Public Health, 2017); Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests - Guidance for Industry and FDA Staff (U.S. Food and Drug Administration, 2007).
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Representative model, for educational purposes only.