Here’s an interesting extract from the official UK government website:
What is the UK operational false positive rate?
The UK operational false positive rate is unknown. There are no published studies on the operational false positive rate of any national COVID-19 testing programme.An attempt has been made to estimate the likely false-positive rate of national COVID-19 testing programmes by examining data from published external quality assessments (EQAs) for RT-PCRassays for other RNA viruses carried out between 2004-2019 . Results of 43 EQAs were examined, giving a median false positive rate of 2.3% (interquartile range 0.8-4.0%).
Why are false positives a problem?
DHSC figures  show that 100,664 tests were carried out on 31 May 2020 (Pillar 1 and 2 RT-PCR tests). 1,570 of those tests were positive for SARS-CoV-2 (1.6%). The majority of people tested on that day did not have SARS-CoV-2 (98.4% of tests are negative). When only a small proportion of people being tested have the virus, the operational false positive rate becomes very important. Clearly the false positive rate cannot exceed 1.6% on that day, and is likely to be much lower. If the operational false positive rate was 0.4%, 400 of the 1,570 positive tests would be false positives. That would represent 400 people being isolated when they are well, and much wasted effort in contact tracing. It is possible that a proportion of infections that we currently view as asymptomatic may in fact be due to these false positives.Unless we understand the operational false positive rate of the UK’s RT-PCR testing system we risk overestimating the COVID-19 incidence, the demand on track and trace, and the extent of asymptomatic infection. (https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/895843/S0519_Impact_of_false_positives_and_negatives.pdf)
This is easy to translate. There are no reliable figures for the false positive rate of PCR testing for COVID-19 in real life (the article actually says in lab settings it is around 5%), but the best estimate is 2.3%, with error bars between 0.8% and 4%. But the positive test rate in UK (in May) was only 1.6%.
The article rightly says that the false positive rate therefore can’t logically be more than 1.6%, but then says “it is likely to be much lower,” and out of the air conjures a figure of 0.4% to show how badly this will skew policy-guiding case figures. The truth is, though, that there’s no reason why the fale positive rate should be much lower, except wishful thinking: the false positives are anywhere between 0% and 1.6%, that is to say there is a wider range of error than what is being measured. For all the testing proves, there may in fact have been no actual cases of COVID-19 at all.
Fast forward to today. Testing is at far higher rates than in May, but hospitalisations and deaths are almost negligible. Taking today’s official figures, the positive test rate is now only 0.7%, or a quarter of what the best guess false positive rate was back in May. As far as PCR testing goes, there is every likelihood that, in the absence of symptoms, any positive test result is false, and that the virus is nowhere to be seen. How would we know if it had disappeared completely, based on such a test?
But hold on, you will (sensibly) say. Some people are still getting ill and dying, and a proportion of positive tests will be of people with mild COVID symptoms: they at least must be true positives. Furthermore, the number of “cases” is varying, suggesting more than a background false positive rate.
To take the second first, the number of tests is also varying: the figures suggest that the tiny decrease in cases in the last few days correlates with a slightly lower rate of testing. And given the low number of positives, variations might be partly explained by the many other variables of different labs, different sample populations, and other things which are not revealed by government statistics. In other words, there are too many variables to assume that true positives are varying up or down.
But it is true that there are still 767 people in hospital, far fewer in ICUs, and 12 deaths daily. It’s not unlikely that all or most of those are genuine COVID cases. But it’s a pretty paltry number from an epidemiological point of view. However, amongst those with lesser symptoms, with positive tests at only 0.7%, or around 1500 a day in a population of 70 million, there are also going to be clinical false positives at a high rate.
The “key” symptoms of COVID are pretty non-specific. To have a fever, a dry cough and loss of smell in the middle of a major epidemic probably means you’ve caught the plague, more likely than not. But when numbers are so low, any number of other viruses will cause similar symptoms. Furthermore, if you’re tested randomly, say after you and your mates get sick after returning from Greece, a (false) positive test is likely to get your sore throat attributed to Coronavirus by default, even if it’s not typical.
I only know, personally, one person who thought she’d had COVID during the peak of the outbreak (that in itself is odd in a “worldwide pandemic,” though I am in the least-affected part of Britain). It was in the days before widespread testing. When we finally met up, her description of her symptoms didn’t seem particularly pathognomonic of COVID, but her assumption is easy to understand. If she’d had a positive PCR test, with an error range larger than the actual positives being found, my clinical impression would, surely, have been dismissed by patient and officialdom alike.
The only other case in someone I knew involved her reporting a loss of smell and, because she in a care situation, she was tested and found positive, leading to all the usual panic and quarantine. She was otherwise well, and was a solitary “case.” Is it really sound science to say that a solitary loss of smell + unreliable test = genuine diagnosis?
But the simple fact remains: government policy here (and no doubt in your country too) is being guided by a test with an unknown false-positive rate that is probably larger than the actual percentage of positive tests. Under such circumstances, the whole testing rigmarole is entirely useless, and given its effect on society, likely to be very harmful. Using horoscopes would be no less scientific.
How am I wrong here?
Postscript: I haven’t mentioned the false-negative rate, which the article I cited says is equally unknown, but probably in the same kind of ballpark. If so, there may be a few more real cases than we are seeing, by a percent or two. But there may still, in theory, be no cases at all.