[Cerium]

If a given test has a 1% chance of returning true, even when the actual result is false, then from a sample of say 1000 tests we would expect at least 10 trues, in addition to any actual true results. If the chance of having the disease in the general population is low (say 1 in a thousand for this example) then we would expect 11 true results in our thousand samples. Of which 91% are incorrect results - false positives.

[japhyr]

So then you'd want to know if the cause of a false positive is random, or specific to the individual, right? If it's random, then how much would a retest change your certainty that an initial positive was a true positive?

ie, if someone was a false positive the first time would they still have a 1% chance of getting another false positive, or is it possible there's something about that individual that will always give them a positive result?

[andrewseanryan]

Would I be correct with the following:

If the false positive rate is higher than the expected rate of disease in a given community, then the majority of positive tests will be false positives.

Does this relate to COVID in any way? Since the rates among affected communities seem to be growing rapidly. Would appreciate your thoughts.

[usrusr]

Looking at growth rate with false positives is a bit of a mindbender: if you limit your testing to the potential contacts of a positive (false or not), you could get a "false R0" virtual epidemic from testing alone, if and only if you test more contacts per positive than 1/false positive rate. Unfortunately, actual hospitalizations and and deaths rule out a virtual epidemic so this is not a hope to cling to.

[AnthonyMouse]

> Unfortunately, actual hospitalizations and and deaths rule out a virtual epidemic so this is not a hope to cling to.

Not necessarily. In theory all the deaths could have some other cause, i.e. some fraction of people with a different underlying fatal condition had false positive tests for this coronavirus and then died of the other condition.

That's probably not what's happening, but it's theoretically possible. (It's also probable that some of the reported deaths are that, but who knows what percentage.)

[hanche]

If the false positive rate is p and the false negative rate is q, and the infection rate is r, then you will have p·(1-r) false positives (as proportion of the tested population) and (1-q)·r true positives. Your hypothesis p>r is not enough to settle which of those two numbers is bigger.

(Edited to fix a silly mistake: The phone rang while I was posting, so I ended up being hasty.)

Edit the 2nd: Even in the simplified case q=0, you can't easily tell.

[ses1984]

Does 1% error rate mean it's positive 1% of the time or wrong 1% of the time?

[9HZZRfNlpR]

How does it relate to universal Healthcare? I'm not an American so maybe I'm missing something.

[AnthonyMouse]

A "fallacy that seems universal with healthcare folks" is not expected to be related to universal healthcare.

[9HZZRfNlpR]

Yes, that was rather embarrasing. Sorry about that.