When will we beat the false positives?

Daily Telegraph headline today:

“Covid lockdown to continue until cases drop below 1,000 a day.”

It’s accompanied by a graphic projecting the current fall in UK cases to make April 7th the likely date. But there is reason to doubt this optimism.

Currently, the lates ONS daily positive-test figure is 10,625. But as has been the case throughout the pandemic, the denominator, ie the number of tests, has been completely variable. In fact the only purpose of recording the number of tests seems to be to say that we’re doing a lot of tests, and that more is better. The wide variation shows the meaninglessness of case number totals. So the current daily number of tests overall is 457,144. That is a 2.3% rate of positive cases.

The actual number of tests has dropped a little over February, but there is no way of knowing why that is. What is certain is that the way the stats are presented gives no idea either of the selection criteria of the sample, nor even of what proportion of the tests are PCRs, or LFTs, or even antibody tests. But what is also certain is that the majority are still PCRs, and that the false positive rate of COVID PCRs has still not been defined against a gold standard, even if the test itself were standardised to a particular number of amplification cycles, cross-checked with human DNA for sampling variations, and checked with a second test as per WHO recommendations… which they are not, and never have been.

All these things mean there is still a false positive rate of at least 1%, if one were foolish enough to accept Matt Hancock’s guess in parliament, or 1.6% if we take the rate of PCR positives over last summer, when it is likely that SARS-CoV-2 was completely quiescent. Remember that the false positive rate expected by the NHS in advance, based on other PCR tests, was 2.4% – close to the positive rate being reported now.

For the sake of being generous, let us assume the true PCR false positive rate is Hancock’s 1%. In that case if SARS-Cov-2 were to disappear entirely, then in order for positive cases to drop below 1,000 a day, it would be necessary to perform no more than 100,000 PCR tests per day – less than a quarter of the present rate. Conversely, if present levels of testing are maintained, cases will never drop below 4,500 per day, and lockdown will never be removed if the DT‘s reporting is accurate. That’s assuming all the current tests are PCRs, but see below.

In case anyone is inclined to argue that cases reached a far lower level than that last summer, then all one needs to do is to compare the level of testing then with the level of testing now:

Tests only reached 100,000 at the end of last June, when cases were still falling from the first epidemic. In fact, positives began to rise, slightly, only at the very end of August – the very time (purely coincidentally, of course) that the rate of positives rose above 1.6%, the more likely false positive rate.

One might optimistically assume that whatever SAGE or government source is behind the “below 1,000 a day cutoff for lockdown” policy reported exclusively by the DT would be totally cognisant of the false-positive problem. But if last summer’s failure to recognise the seasonality of Coronaviruses were not sufficient to show they have not got a grasp of basic statistics in relation to screening, then the scorn of actual specialists in screening programmes for the government’s testing program is good evidence.

It is difficult to make a prediction about what actually will happen to case-numbers, because of the lack of available data for the criteria for testing, and the mode and manner of testing, as already mentioned. All of the variations of those would tend to increase the false positive rate, and hence the final number of “cases.”

Only a massively increased reliance on lateral flow tests (LFTs) would also increase the false negative rate, but they still carry a significant false positive rate of apparently around 0.3%. Understanding the present situation is not helped by the fact that the ONS also publishes a chart showing that PCR testing capacity remains at around 800,000 tests daily, whereas the number actually done has been declining since the New Year to around 300,000 a day. Are most of the remaining 157,000 of the 457K tests currently occurring daily LFTS? We just don’t know.

But were we to assume that is the case, and that the levels of both tests remain the same as now, we could calculate that in the total absence of SARS-CoV-2, the number of positive “cases” would level off at no lower than (300,000 X 1% [PCR])+(157,000 X 0.3% [LFT]) = 3,471 daily. We would still be, according to the Telegraph‘s sources, in a pandemic as serious as that on 28th March last year, 12 days after lockdown started. If the PCR false positive rate is closer to 1.6%, that final minimum would be 5,271 daily.

It’ll be interesting to see whether either of those predictions hold, and if not what relation the actual figures bear to continued testing. But let’s hope the Telegraph has got its numbers badly wrong.