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Prevalence-Adjusted PPV Calculator

Use Bayes theorem to convert a test’s sensitivity and specificity into predictive values at any disease prevalence.

Sensitivity

Specificity

Disease prevalence

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How it works

PPV = (Se·p) ÷ (Se·p + (1−Sp)·(1−p)) · NPV = (Sp·(1−p)) ÷ (Sp·(1−p) + (1−Se)·p) · p = prevalence

This is Bayes theorem applied to diagnostic testing: it takes a test’s fixed sensitivity and specificity and folds in the pre-test probability (prevalence) to give the post-test probability of disease. The striking lesson is how much prevalence matters — a highly accurate test can still yield a PPV near 30% when it screens a low-prevalence population, because true cases are swamped by false positives. Raising prevalence, as happens when you test symptomatic rather than general populations, sharply improves the PPV.

Worked example

A test with 95% sensitivity and 90% specificity screening a population with 5% prevalence: PPV = (0.95 × 0.05) ÷ (0.95 × 0.05 + 0.10 × 0.95) = 0.0475 ÷ 0.1425 = 33.3%. Despite the strong test, two-thirds of positives are false alarms because the disease is rare.

Sources: Bayes' theorem — Wikipedia

Frequently asked questions

Why is the PPV so low even with a 95% accurate test?

When only 5% of those tested actually have the disease, the many healthy people generate a large absolute number of false positives (10% of them here). Those false positives outnumber the true positives from the small diseased group, so most positive results are wrong.

How can I raise the positive predictive value?

Test a higher-prevalence group (for example, people with symptoms or risk factors), use a more specific test to cut false positives, or confirm positives with a second independent test. All three raise the share of positives that are true.

What is the base-rate fallacy?

It is the mistake of judging a positive result by the test’s accuracy alone while ignoring how rare the condition is. This calculator corrects for it by combining prevalence with the test characteristics through Bayes theorem.

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Educational statistics tool, not medical advice.