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AKT Statistics Guide · Part 3 · Chapter 9The Prevalence Trap: PPV & NPV
Your patient’s test came back positive — how worried should you be? That answer depends on prevalence, and it is the single most important diagnostic idea for GP practice.
Where this shows up in the AKT
- Interpreting what a result actually means for the individual patient in front of you.
- Screening low-risk populations — and the false-positive problem that follows.
- The classic trap of treating sensitivity and PPV as the same thing. They are not (Chapter 8).
Sensitivity and specificity start from a question you can only ask in a study: if I already know who has the disease, how does the test behave? Predictive values flip it round and start from the result. They follow directly from sensitivity and specificity — but, crucially, they also depend on how common the disease is.
Start from the result, not the disease
Where sensitivity and specificity begin with known disease status, predictive values begin with the test result:
Positive predictive value (PPV)
- PPV = TP / (TP + FP) — of everyone who tests positive, the proportion who genuinely have the disease.
Negative predictive value (NPV)
- NPV = TN / (TN + FN) — of everyone who tests negative, the proportion who are genuinely clear.
Sensitivity and specificity are fixed properties of the test. PPV and NPV are not — they move with prevalence. That single fact is what trips candidates up, so let us see it happen.
Worked example — same test, two settings
A coeliac-disease test is 90% sensitive and 95% specific. The test never changes. Only the population does.
Hospital clinic — prevalence 10%
1,000 patients, 100 with the disease, 900 without:
| Disease + (100) | Disease − (900) | Total | |
|---|---|---|---|
| Test + | 90 | 45 | 135 |
| Test − | 10 | 855 | 865 |
- PPV = 90 / 135 = 67% — two-thirds of the positives are real.
- NPV = 855 / 865 = 99% — a negative here is very reassuring.
GP population — prevalence 1%
Same 1,000 patients, but now only 10 have the disease and 990 do not:
| Disease + (10) | Disease − (990) | Total | |
|---|---|---|---|
| Test + | 9 | 49.5 | 58.5 |
| Test − | 1 | 940.5 | 941.5 |
- PPV = 9 / 58.5 ≈ 15% — now only about one positive in seven is real.
Same test. In hospital, two-thirds of positives are true; in GP, roughly one in seven. Most of your positive results are now false positives. The test did not get worse — the maths of low prevalence did this. (The decimal cells are an artefact of scaling to 1,000; the proportions are what matter.)
Why this matters clinically
- Do not trust a positive test on its own when prevalence is low — the pre-test probability matters (Chapter 10).
- This is why a hospital-grade test can perform poorly when imported into GP without thought: same test, far lower prevalence.
- PPV rises with prevalence, so we target screening at higher-risk groups; NPV rises as prevalence falls.
- Screen a low-risk population for a rare disease and you drown in false positives — which is exactly why every screening programme needs a confirmatory test before anyone is told they are ill.
The traps that cost marks
A new test for coeliac disease has a sensitivity of 90% and a specificity of 95%. In a GP population where the prevalence of coeliac disease is 1%, a patient tests positive. Which statement is most accurate?
- The patient almost certainly has coeliac disease
- The test has ruled the disease in
- Most positive results will still be false positives
- The test is not sensitive enough for primary care
Reveal answer
C — most positive results will still be false positives. Even with excellent sensitivity and specificity, a low-prevalence setting like GP massively reduces the PPV. At 1% prevalence the PPV here is only about 15%, so most positives are false alarms — the classic Prevalence Trap. The test characteristics are fine; it is the population, not the test, that makes a lone positive untrustworthy.
Lock it in
- PPV = TP / (TP + FP): of the positives, who truly has it. NPV = TN / (TN + FN): of the negatives, who is truly clear.
- Both depend on prevalence — sensitivity and specificity do not.
- Low prevalence drives PPV down: even a great test yields mostly false positives in a low-risk group.
- So target testing at higher-risk groups, and confirm before you alarm.
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