Bayesian Diagnostic Test Simulator

Population & test

Disease prevalence 1.0%

Sensitivity (true-positive rate) 90%

Specificity (true-negative rate) 95%

Bayesian result

PPV — P(disease | test+)

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NPV — P(healthy | test−)

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Diseased (of 10,000)

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Positive tests

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True positives

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False positives

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False negatives

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True negatives

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Every one of the 10,000 squares on the right is one simulated person, coloured by their real (disease status) × (test result) outcome — computed from the sliders above, not illustrated.

How it works

Bayes' theorem converts a test's known accuracy into the number that actually matters to a patient: given a positive result, what's the real chance of having the disease? Sensitivity and specificity describe the test in isolation; the positive predictive value (PPV) also depends on how common the disease is in the population being tested — prevalence.

PPV = (sensitivity·p) / (sensitivity·p + (1−specificity)·(1−p))
NPV = (specificity·(1−p)) / (specificity·(1−p) + (1−sensitivity)·p)

Prevalence (p) — fraction of the population that truly has the disease. Lower it and watch PPV collapse even with a highly accurate test.
Sensitivity — of everyone who truly has the disease, the fraction the test correctly flags positive. Raising it shrinks false negatives (missed cases).
Specificity — of everyone who is truly healthy, the fraction the test correctly clears. Even a small drop here floods a rare-disease screen with false positives, because healthy people vastly outnumber sick ones.

The grid is a natural-frequency diagram: instead of abstract percentages, it shows 10,000 concrete people split by real outcome. At low prevalence the orange "false positive" block is often larger than the red "true positive" block, even for a 95%+ accurate test — the classic, well-documented reason a single positive screening result is not, by itself, a diagnosis.

True positive (sick, test+) False positive (healthy, test+) False negative (sick, test−) True negative (healthy, test−)