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A disease affects 1% of the population. A new screening test has a sensitivity of 90% (it correctly identifies 90% of people with the disease) and a specificity of 95% (it correctly identifies 95% of people without the disease). 10,000 people are screened. (1) How many true positives and false positives would you expect? (2) If someone tests positive, what is the chance they actually have the disease? (3) What does this mean for a screening programme? You have 6 minutes.
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Understanding sensitivity, specificity and positive predictive value, and the counter-intuitive effect of low prevalence — central to evidence-based medicine.
A structure to build your own answer on — not a script.
Use natural numbers
Of 10,000: 1% = 100 have the disease; 9,900 don't.
True and false negatives/positives
90% of 100 = 90 true positives (10 missed). 5% of 9,900 = 495 false positives.
PPV
90 ÷ (90 + 495) = 90 ÷ 585 ≈ 15%.
Interpret
Most positives are false when prevalence is low; a positive screen needs confirmatory testing.
Implications
Anxiety, further tests, overdiagnosis vs benefit of early detection; prevalence matters (targeted screening).
A strong but not perfect answer. Read the notes to see why it works — then make your own version with your experiences.
I find it easiest to use actual numbers1. Of 10,000 people, 1% — so 100 — have the disease, and 9,900 don't.
Of the 100 with the disease, the test picks up 90%, so 90 true positives, and 10 are missed.
Of the 9,900 without the disease, 95% correctly test negative, so 5% test positive by mistake. 5% of 9,900 is 495 false positives.
So altogether, 90 plus 495 is 585 positive results, of which only 90 are real. 90 out of 585 is roughly 15%2. So if someone tests positive, there's only about a 15% chance they actually have the disease — even though the test sounds very accurate.
That seems surprising, but it's because the disease is rare3: a small error rate applied to a large number of healthy people produces more false positives than there are true cases.
For a screening programme, that means a positive screening result shouldn't be treated as a diagnosis — people need a confirmatory test, and they need to be told that clearly so they aren't unnecessarily frightened. False positives cause anxiety, further tests and sometimes harm. It also suggests screening works better in higher-risk groups: if 20% of people had the disease4, the proportion of positives that were real would be much higher.
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