Hayley Mcclain

2022-11-09

"The population, for a disease D, has a true rate of T%"
"Some Test ST, has false positive rate of FP% and a false negative rate of FN%."
"T, FP, and FN are elements of the set of real numbers."
Was the number T determined by some 100% accurate and possibly expensive test?

Phiplyrhypelw0

Expert

The problem for which 𝑇, 𝐹𝑃 and 𝐹𝑁 are the input data usually asks for a calculation of the probability that a patient actually has disease 𝐷 given that they test positive.
The source of those numbers is not part of the problem. 𝑇 might come from data kept by departments of health, hospitals and insurance companies. You could get it by giving that hypothetical perfect test to a large random sample of the population, but that's not a likely source for the number. 𝐹𝑃 and 𝐹𝑁 result are found by actually trying the test on people who for some other reason you know do or don't have the disease.
Many people are surprised by the answer when 𝑇 is small, which is (much) less than 𝐹𝑁 since then most of the positives will be false positives.

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