Say we have a test for a disease we are comparing with the gold standard. You are given the prevalence of the disease, which is 1%, and sensitivity, 80%, and specificity, 90% and a total population of 1000.
Now how would you tell how likely is it to get a false positive result?
And you have a couple of answer options, including A. 10% and B. 93%
When I first saw this question, I remembered there's a thing called "false positive rate" and I had understood it would tell me how likely it is to get a false positive result with the test, and that it was calculated as 1 - Specificity. 1 - 0.9 = 0.1, so the answer should be A. 10%, but turns out I was wrong.
I got explained that to answer this question I first need the Positive Predictive Value and that, as the Positive predictive value is the probability of a positive result with the test being true, then its complement (1 - PPV) would be the probability of a positive test being false, which doing the math would be 93% (PPV is 7% for this test), and it makes sense (of course), but I still don't understand what then is the false positive rate supposed to mean?
So (1-PPV) means (1 - probability of getting a true positive) and then it is the probability of getting a false positive. But what is the false positive rate? What is that 10% you get doing 1-Specificity?