"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?

Question

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

Phiplyrhypelw0 · Accepted Answer

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&#039;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&#039;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.