So, thinking about surveillance in e.g. schools.

If your choice is to test all the students monthly -- e.g. 3% of them per day -- with a molecular test that has a couple day turnaround... This works pretty much only well enough to detect rampant, uncontrolled spread, and will not break a transmission chain very often.

Or to test all the students weekly -- 14% per day -- with an antigen test that returns results in 30 minutes... Even if there's some false negatives, you'll still interrupt many transmission chains and effectively lower Rt.

This is wrong. Too false positive and people will start ignoring the results. Thats what happened in the current climate. You need consistently good days otherwise over the long haul people will distrust and ultimately not follow.

You mean false positives? This assay doesn't false positive that much-- specificity is estimated to be 96-97%.

That's a false positive every day in a normal-sized school.

It isn't quite that bad, because the tests aren't independent. You end up with a few people who are disproportionately likely to test positive and can adjust appropriately your testing strategy for them.

And even if that wasn't the case-- you keep a few people home (them + close contacts) until followup molecular testing returns a negative. Yes, it's a big hassle-- you're "falsely" forcing 10% of the student body into remote learning, but probably better than remaining closed.

Yes. And then it’s not just one kid. It’s the entire class plus teacher. It would be a fire drill per day. And then they would need to take the tests every day until they are cleared. It’s not feasible.

Yes thank you I corrected.

As I understand it, these tests rarely produce a false positive, but often produce a false negative. So a positive test result on 6 occurrences is a much stronger signal than a negative result on 8 days. If you get a positive result from a rapid test, you should either self isolate or take a PCR test to confirm.

Think about what you would do if you wake up with cold or flu symptoms these days - there's a chance you don't have covid, but you still need to be extremely careful. These rapid tests should be thought of as a more effective version of the "do I have symptoms" test everybody does subconsciously every day.

Sensitivity of these tests is 95%, but specificity is 97%. So it can definitely be wrong in both directions.

Some rapid tests go as high as 99.97% specificity.

Large scale testing is likely aimed at public health, where the goal is to lower Rt < 1. Missing some positives is tolerable. Also, the antigen tests are more sensitive when the person is most likely to be contagious.

With n multiple tests you are much more likely to approach the mean of positive results, which for an actually positive patient is (1-p1)n and for an actually negative patient is p2n, where p1 and p2 are false result probabilities. If p1, p2 << 1 then the means are sufficiently apart that you can compute the probability of getting your result (whatever that is) under the actual positive/negative scenario and one probability will be significantly higher than the other.

Assuming the tests are independent, which is unrealistic. If the antigen test is positive because it's cross-reacting to the common cold or because of something unique to you, then testing more tells you nothing.

It depends on the error rate of the test. If it's close to 50/50 then obviously the test is worthless. But these tests are much more reliable than that, so a population scale the wrong results will be corrected with more testing.

I don't have the analysis in front of me, but I encourage you to listen to that TWiV episode yourself and listen to the panel of virologists discussing this. They were initially skeptical also, but after questioning the plan's author they were eventually convinced and became excited because the plan could actually work.

Its not randomly unreliable but its significantly more unreliable when you have low viral load. (As it happens thats also when you're much less likely to be infectious)