This is a continuation of my ‘A Beginner’s Guide to False Positives’ from two days ago. In that post I described how false positives can swamp true positives when the prevalence of the disease or condition in question is low. This was the situation in Britain with Covid for quite a few months. However, more recently the percentage of tests that are positive has increased, so I thought I should take a look at the situation in regards to the latest figures.
(I should point out that, as we have recently seen, Public Health England, which handles this data, has proven itself to be less than competent, so we should take this data with a large handful of salt.)
Here’s a quick and dirty graph (click to enlarge) that I did tracking the recent changes in percentage of tests that are positive (data from https://coronavirus.data.gov.uk/). There’s various issues with this data (eg. the inclusion of antibody tests, although the numbers for that are small) so, even forgetting our more general suspicions about any data that comes from PHE, it’s not going to be very accurate, but it will illustrate the general picture.
Take 30 September, for example, the day the percentage was highest (5.63% positive). On that day we had 184,624 tests done, of which 10,387 were positive. If the false positive rate is about 0.9%, as Matt Hancock intimated – in fact, let’s say 0.8%, as some people have claimed – then we should expect 1477 false positives. As we had 10,387 positives, then we must have had 8909 true positives. It appears, then, that we are back to a situation where the true positives swamp the false positives, rather than the opposite situation that we had over summer, in which case the relevance of false positives is diminished. This is also indicated by the fact that the percentage of positive tests on that day, 5.63% is far higher than the false positive rate (0.9%).
However, things aren’t quite that simple. Over summer, the percentage of tests that were positive apparently went down to 0.4%. Logic tells us that that’s the false positive ceiling. It can’t be any higher than that. Or rather, it can’t be any higher at that time. It could be higher at other times, though, unless the false positive rate cannot change. Can it change? Is it fixed? It’s fixed if all the things it depends upon never change, or never deviate very much from an approximate level. But we know that one of the ways a false positive can be produced is if it gets a very similar bit of RNA. So it’s possible that false positives could increase over autumn and winter as other viruses circulate. So it’s possible that some of the increase we are seeing in the rate of positive tests is due to the rate of false positives increasing.
Possible, but how likely? Looking into this, the scientists who work in this area are very insistent that the PCR tests are tailored very specifically for SARS-CoV-2, and they make sure that they can’t be triggered by other coronaviruses, or flu, or any other virus, except in fluke circumstances. I’m going to accept that, at least provisionally.
I don’t mean that I’m entirely convinced. Years ago I used to be friends with some really, really top molecular biologists and they used to be pretty scathing about all the things that go wrong in their field, especially when you’ve got clueless Research Assistants doing the grunt work. How things are supposed to work in theory is one thing, how they work in practice is another thing altogether. You’ve also got SAGE papers that won’t commit to any more than 5% as a false positive ceiling, and you’ve got this recent Lancet paper saying “The current rate of operational false-positive swab tests in the UK is unknown; preliminary estimates show it could be somewhere between 0·8% and 4·0%.”
So maybe there are more false positives than the government lets on, and maybe not; that’s not something that can be decided on just by finding a few internet links. (Feel free to knock yourself out talking about what you’ve found in comments, although I’m not going to take seriously any Off-Guardian-type nonsense about Koch’s Postulates.)
On the other hand, we’ve got this graph from Christopher Bowyer, which indicates that the rate of hospital admissions per 1000 positive test has not gone down since the summer (after decreasing markedly over summer), If a lot, or all, of the recent rise in the positive test rate is due to colds causing false positives then this rate should have decreased since summer. But it hasn’t.
There’s also the issue of false negatives. The false negative rate is sometimes estimated to be higher than the false positive rate, which blunts the false positive-style critique.
Besides, the crux of my lockdown scepticism does not depend on claiming that Covid is now completely gone, which I doubt is true anyway. I think it’s very unlikely that the recent increase in positive tests is not being driven at least partly by an increase in SARS-CoV-2. So to some extent I think the focus on false positives is barking up the wrong tree. The case against lockdown applies even if (as seems likely) Covid is increasing again.
But there are some other serious issues with PCR tests that I want to look at (eg. the cycle numbers, dead fragments, and the large numbers of asymptomatic positives), which I’ll do in a further post.