I went and dug out using the wayback machine the original CDC guideline for the RT-PCR test for SARs CoV2 that was published back in February. The clearest most comprehensive description I've seen. This will give people a very good idea of just how many steps are involved in the test process, steps which can fail for various reasons discussed in the document, and the interpretation section at the end of the page give a very good idea of just how open to misreading the final results curve interpretation stage is. Just add some HCOV's like 229E or OC43 to the sample and, well, the curve can get very ambiguous.

https://www.cdc.gov/coronavirus/2019-ncov/lab/rt-pcr-detection-instructions.htm l"> https://web.archive.org/web/20200212234329/https://www.cdc.gov/coronavirus/2019-ncov/lab/rt-pcr-detection-instructions.html

This page looks like it was rewritten many times after the debacle from February through April due to a dodgy reagent distributed as part of the test kits the CDC sent out to the states. As a result outside of Washington state, where the guys in UW went rogue and set up their own testing process much to the chagrin of the CDC and FDA regulators, most states in the US only started any kind of reliable testing in late April / early May. And in the case of California there were still very serious problems with testing well into July.

Thats why I consider the real world testing accuracy to be at best 95%, both sensitivity and specificity, and those are the kind of numbers that should be slotted into the PPV and NPV equations.

Some more discussion on testing accuracy here.

https://www.medrxiv.org/content/10.1101/2020.04.16.20067884v3

The change appears to have been on 6th September.

A further observation is that, on this date, the rate of testing suddenly increased about three-fold. That is approximately the same as the increase in cases/tests from 0.5% to 1.4%.
Could someone in the know say whether tripling the rate of tests would approximately correspond to the tripling of positives? And would false positives also triple at the same time?

I have no data to support this hypothesis, and I truly wish someone does (but I doubt it), but I would not be surprised to see an increase in False Positive Rate as the number of tests increase due to

: increased stress on over-worked labs
: reduced quality control perhaps due to inadequate training by all the people running tests
: change in demographics of people tested
: errors in stats, e.g. some multiple tests for individuals reported as seperate people
: less structured follow-up on "positive" cases to absolutely confirm they were "sick" because maybe they are too busy doing tests (sigh)
: etc.

I have no data to support this hypothesis, and I truly wish someone does (but I doubt it), but I would not be surprised to see an increase in False Positive Rate as the number of tests increase due to

: increased stress on over-worked labs
: reduced quality control perhaps due to inadequate training by all the people running tests
: change in demographics of people tested
: errors in stats, e.g. some multiple tests for individuals reported as seperate people
: less structured follow-up on "positive" cases to absolutely confirm they were "sick" because maybe they are too busy doing tests (sigh)
: etc.

Your possible causes are, I suspect, also-rans. I expect to see some direct correlation if someone can only confirm from a technical perspective.
There is motive here. Boris Johnson wants to increase testing to 500,000 per day by the end of October. If he is found to have pushed this through at the expense of testing accuracy (already low), and consequently punishes the rest of the population via lock-down measures, this could bring down the government.

Not sure if it was discussed elsewhere but here is a another way of thinking of the problem of false positives and a mass testing regime not accounting for them. If the infection rate drops from 1% of the sample population to 0.1% , a factor of ten, using the example above of 1000 people tested the total number of positives only declines from 60 to 51, but the number of true positive declines from 10 to 1. The number of false positives remaining the same.

So the total positives from testing only declines about 15%, the number of true positives declines 90%, and the percentage of false positives goes up to 98%.

This is a big problem because the typical new infection rate curve for a novel infectious agent has a drop off from first peak of up to one order of magnitude. So even if the novel infectious agent has reached the equilibrium point in the population and the new infection rate is just at background level there will be little evidence of this from mass testing due to uncorrected false positives. Because mass testing will only show a decline of 15%/20% from peak and still very high levels of "positives", almost all false.