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Any facts on false positives?
With mandatory testing for athletes participating in contact youth sports, there is a tremendous fear of false positives impacting individuals and their teams. Are there any studies that show the rates of false positives for the various tests? I found this from MIT:

And the CDC's commentary is fairly wishy washy, the % of false positives rise when the overall rates of Covid decrease (no kidding). The real question is how many false positives as a percent of tests taken. The MIT study seems to get there. . . .
I dug into this shortly after your posting but didn't quite get to a finished result.  From the MIT article, follow the links to the referenced reports.  There you'll see the procedure and results of testing of various PCR testing kits.

Basically, it seems the tests are very specific.  Apparently different PCR test kits may detect different parts of the virus so it is possible that false positives might differ for different test vendors.  Although one report suggests that other coronaviruses might give false positives, none of the reports that I saw talk about actual false positives, where the result would be repeatable.  None showed any false positives.

The testing that was being done had results of Positive, Negative, Inconclusive, and Invalid.

It seemed to me that the more likely cases for a false positive would be from mishandling of the sample, perhaps contaminating it at collection or in processing, or by some labelling or data entry error.   Those kinds of errors are not something where the statistics seem reliable.   For instance, if sports team A and sports team B had different people doing collection and different labs, I wouldn't expect a 0.01% false positive rate for one team to apply to the other team.

I think it would have been instructive to include known false and positive samples with each group of samples to get some idea of FP and FN samples.  I expect the labs run those on their own (or, as part of what is required of them).

There is one researcher who has been studying & publishing on COVID false-positive rates.  He indicates that FP rates are somewhere roughly in the 0.5% range.  As he points out, when positive rates get low, the percent of the positives that are false goes up.
November 2020 short article  Unfortunately, he talks of studies that provide his external quality assessments but gives no references.
August 2020 paper  
May 2020 paper  At that time, there were no external quality assessments for COVID PCR tests.

Currently, Santa Clara County is showing 1.7% positive rates.  If 0.5% of the true negatives have results as false positives, then that is a significant percentage of the positive rates.  

However, we don't know whether two or three samples are being.  If the errors are independent on different samples, then taking & processing two samples results in FP rate of 0.5% dropping to 0.0025%.  If the errors are not independent, then this redundancy doesn't help.
Thanks. Makes good sense, though seems that .5% is fairly high, especially looking at the rate at MIT. With the testing positivity rate of 2.9% in CoCoCo, then the % of total of false positives would be very significant. Anecdotally, my daughter's school has been testing weekly of late (over 300 per week), with no positives over the last few weeks. Two indeterminate, but that's it.
If you don't mind me asking, is that 300 just staff, or is it just students, or both? What level school (pre-K, K-6, 7-12, college)? Is that a sampling of the set of people (random or, say, test 1/4 each week) or basically a full set? Is it voluntary or expected of all (perhaps with some exceptions)? How are the tests being financed?

I'm just curious.
Voluntary, though athletes are expected to test by state mandate (at least for purple tier contact sports). If you travel out of state, it's requested as well, before you come back to school (hybrid at the moment). It's a Catholic High School, 9-12. Staff and students, though I think they only mentioned the number of kids tested and cleared. Allegedly, financed by health insurance or the state, and free to the kids--importantly, the county has been encouraging people to get tested often to keep the rates down and to control the spread, so we're doing our part. I think my daughter has been tested four or five times and has the option for an antibody test as well. All have been negative so far, including one blood draw for the antibody test.

Hoping she stays negative, two more swim meets then water polo starts up. Appears that she will be the starting varsity goalie as a Freshman. . . .

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