Just FYI, if you don’t have symptoms or direct contact with someone with COVID (basically if you don’t have a high probability of having COVID before you have the test) a positive test still probably means you don’t have COVID:

Sample numbers:

* Population of US: 3e8

* People that have COVID right now in the US: 1e5 (30x the confirmed cases right now)

* Disease rate: 3e-4

* FALSE POSITIVE RATE for COVID test: 1% (likely higher)

* TRUE POSITIVE RATE for COVID: 100% (definitely lower)

If you take the test, don’t have symptoms or direct contact, and then the test comes back positive for the disease, then under these pretty reasonable assumptions, the likelihood you have the disease is

P(actually have COVID| positive test) = 3e-4 /(1e-2(1-3e-4) +3e-4) = 2.9%

Whole this is a correct application of Bayes Rule, a risk adjusted perspective still indicates that you should act as if you do have the virus. This is because the probability of having the virus multiplied by the damage of an infected person spreading the disease is much higher than the false positive probability times the personal impact of self-quarantine.

Yea I agree that it’s still useful like you say as just a way to screen for “higher risk” individuals and have them isolate, but still food for thought.

Could you please cite a source for the false positive rate? Real time RT-PCR should be nowhere near that. Maybe if your sample handling is messed up, but that should be easy to optimize...

No reliable source at all, saw various people refer to larger numbers and thought that would be conservative. If the false positive rate is actually way lower, then this whole point is totally wrong and I would be happy to just delete this comment rather than misinform someone or discourage someone from getting tested if they should.

FPR: 1% P(covid|+) = 2.3%

FPR: 0.1% P(covid|+) = 23%

FPR: 0.01% P(covid|+) = 75%

FPR: 0.001% P(covid|+) = 97%

I didn't mean to imply that the number was necessarily wrong. I looked around for a reference but couldn't really find anything.

The thing is, real time RT-PCR works by detecting specific viral sequences. If those are chosen properly, the FP rate should be super low in principle. However, since the test is so sensitive, even tiny contaminations could lead to FPs. Therefore, I think the FP rate in practice will mostly depend on the sample handling professionalism of the lab doing the test.

But I don't have a good intuition for what that could mean in numbers, which is why a reference would have been interesting.

Nevertheless, your point is a really generally important one when testing ... pretty much in any situation, so I don't think you should retract it.

Yea -- that's very interesting and insightful. It sounds like false positive rate is hard to nail down in practice, but I think from what you say there's a good chance it's well below 1%.

I won't delete the comment for now, but generally I am trying to be wary of giving actual advice -- I do know stats, but I am not an epidemiologist and I definitely don't want to give out wrong information during a time like this.

I wish there were more testing kits available, I wouldn’t want to be a vector of infection if I have no symptoms but am still carrying the virus. Im in the US and testing kits are not a thing yet

Testing kits aren’t a thing in the US unless you have symptoms and can demonstrate contact with a confirmed case. :-/