There’s a snarky piece about Julia Hartley-Brewer under the BBC’s “Reality Check” banner claiming she got her facts wrong about the False Positive Rate. In fact, the BBC journalists who’ve written the hatchet job – Simon Maybin and Josephine Casserly – are the ones who’ve got their facts wrong.
Julia’s sin was to claim that nine out of 10 “cases” could be false positives. The journalists say that is categorically untrue.
Could it be true that 90% of positive results from tests in the community – that means tests not carried out in hospitals – are false? The answer is “no” – there is no way that so-called false positives have had such an impact on the figures.
Actually, there is a way “so-called false positives” could have had that impact. Suppose the true community case rate is eight in 10,000. If the false positive rate is 0.8% – as estimated by this paper submitted to SAGE – then if you test 10,000 people, you’ll get 88 positive results, of which 80 are false positives and eight are true positives. Perhaps the true community case rate is now slightly higher than eight in 10,000 – the latest ONS infection study puts it at 21 in 10,000 – but even so there is certainly a plausible scenario in which 90% of the positive results from tests in the community are false.
The extraordinary thing is that these reality-checking sleuths then go on to admit this.
If you tested 1,000 people at random for COVID-19 in early September, for example, data from the Office for National Statistics (ONS) infection study suggests you should have expected one of them to actually have the virus.
With a false positive rate of 0.8% – a figure used by Ms Hartley-Brewer and within the broad range of what we think might be the actual rate for community testing – you would get eight false positives. So in that context, it’s true that roughly 90% of positives would be false.
But having admitted that there is a scenario in which 90% of positives could be false, they then go on to say that it’s no longer plausible because the people volunteering for community testing, as opposed to the people being sampled at random by the ONS, are much more likely to have the virus – the same point made by Tom Chivers in UnHerd and which James Ferguson comprehensively rebutted on Lockdown Sceptics.
Here’s what the reality checkers think is their killer point:
Figures for late September from Public Health England show that 7% of community tests were positive. That means if 1,000 people were tested with a false positive rate of 0.8%, eight would be false positives, but 70 would be true positives – the vast majority.
But hang on. They’re assuming that PHE’s 7% positive rate doesn’t include any false positives – hence their claim that if you test 1,000 people 70 would be true positives. But given that they’ve accepted there’s a false positive rate of 0.8%, it’s more likely that PHE is counting the false positives alongside the true positives when estimating the current rate of infection. That means that of the 70 people who test positive, eight are false positives, leaving 62 true positives.
Come on, reality checkers. If you’re going to chastise another journalist for not getting her facts right – even though she did – you need to get the facts straight yourself.
Stop Press: There’s an excellent letter in the Lancet by three doctors raising the alarm about false positives. I look forward to the BBC’s reality checkers doing a number on them.