Just to clarify, the linked article isn't really talking about false positives. It's talking about people who are carrying the virus, but perhaps aren't contagious due to it being only small amounts.

"False positive" isn't really an accurate term there.

If there's no virus, you're not going to be able to amplify it. A too-high threshold may detect non-contagious levels of virus (still a concern, if you're in the early pre-symptomatic days of an infection) or non-infectious virus particles left over post-infection.

Doesn't this presuppose that the only thing the test can detect is the virus itself and not things that highly, but not perfectly, correlate to it?

Not really, no. They specifically pick genomic sequences believed to be unique to SARS-CoV-2; they're specific enough to distinguish between SARS-CoV-2 and the other known coronaviruses, let alone less related viruses.

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This article doesn't mention PCR tests, so perhaps we're being smart enough to accept the often-more-relevant-for-infection-control antigen tests for this purpose. (I'd not yet bet on it, given how bureaucracies have made almost every wrong choice so far, but: maybe?)

But also: if PCR false-positives are a concern, the cycle standard can be reduced, or the reporting expanded to include the cycle on which a test turned positive, so that "positive" tests that are likely dubious/marginal/past-infection can distinguished from "blazing active infection".

The rapid antigen tests have a significant problem with false-negatives: the BMJ reported that Innova tests have 49% sensitivity.

That makes it pointless to use as a border control - for every two cases, at least one gets through. (Or, potentially much worse, under this system: I throw away my positive tests and show whatever false negative one I have).

You ideally want to be conservative and permit some false positives at an effective border control, because you don't want to risk infectious cases getting through and causing an untraceable national breakout.

Even tiny sensitivity would be better than nothing – or something that's so slow & expensive it's impractical.

But other antigen tests purport to have 90%+ sensitivity.

And the kinds of "PCR positives" they miss are often cases that are no longer infectious, anyway: lingering viral fragments, rather than live full-virus shedding.

So: ideal for border-control & creating other internal gradients that help suppress the worst active cases. The perfect should not be the enemy of the very good.

> Even tiny sensitivity would be better than nothing

Not if you imagine that one case on a plane = potential super-spreading event, the plane touches down and then newly infected people go in every direction.

Your hypothetical test with tiny sensitivity is pointless, in this regard: it has a (less than) tiny chance of preventing each risky passenger. In my view, any kind of low-sensitivity testing before departure is theatre: it won't make any difference in preventing new infection from breaking out.

The government of the country that I am in agrees, and requires a negative PCR test.

Well at least false positives are much better than false negatives.

How easy is it to find out the cycle threshold the provider use?