Dr Mike Yeadon, a senior research scientist who was the head of R&D at Pfizer, told Julia Hartley-Brewer on TalkRADIO on Wednesday that she should ask the Secretary of State for Health what the false positive rate is the next time he’s on her show. Well, Matt Hancock appeared on her show Friday morning and she put the question to him. His answer was “less than one percent”.

As Julia pointed out on Twitter, that wasn’t as reassuring as he hoped.

Matt Hancock told me on @talkRADIO that the False Positive Rate of Covid tests in the community is “under 1%”. Sounds good, doesn’t it? WRONG!

An FPR of 0.8% when the virus prevalence is so low means that at least 91% of “Covid cases” are FALSE POSITIVES.

This FPR means that thousands of the people testing positive for coronavirus in the community are NOT in fact currently infected with Covid and they CANNOT infect others with the virus. That’s why the “rising Covid cases” is not translating into mass deaths.

Oxford Uni Prof @carlheneghan has already shown that, even an FPR as low as 0.1% in community testing returns over 55% false positives.

The Government is planning to lockdown our country again when there is no evidence of a second wave. 

We cannot allow this to happen.

You can read Julia Hartley-Brewer’s Twitter thread here.

One alarming thing about Hancock’s reply to Julia’s question is that he appears to think the false positive rate, or FPR, is the percentage of people among those who’ve tested positive who are, in fact, negative. After telling Julia that the FPR was “less than one per cent”, he went on to say: “Under one percent means that for all the positive cases the likelihood of one being a false positive is very small.” No, Health Secretary. The FPR is the percentage of all the people you’ve tested who are found, falsely, to be positive. And when the prevalence of infection is low, that means the likelihood of a positive test result being a false positive is very high.

The smarter a person is, the more effortlessly they are able to believe whatever is in their best interests to believe

To illustrate this, let’s suppose that 11 in 10,000 people in England have the virus, which is what the latest ONS Coronavirus Infection Survey estimates (week of Sept 4 – 10). So according to the Health Secretary’s understanding, if the PCR test has an FPR of 0.8% and you test 10,000 people and 91 test positive, that means that 0.8% x 91 are false positives, i.e. less than one person in the 10,000 is a false positive; one out of the 91 who tested positive. But in fact the numerator is all the people you’ve tested – that’s who the FPR applies to – not just those who’ve tested positive. So, the number of false positives is 0.8% x 10,000, i.e. 80 people. To be clear, 80 of the 91, not one out of the 91, are recorded as positive when they are not. Which leaves exactly 11 “true” positives. Just one in 9 of those getting a positive result actually carry the virus. In other words, because the Health Secretary appears not to understand what an FPR is, he’s over-estimating the number of true positives by at least 700%.

But the number of people who should self-isolate – and hand over the details of those they’ve been in contact with to NHS Test and Trace – is actually much lower than 11 in 10,000 because about half of those 11 will be “cold positives”, i.e. people who test positive because they have fragments of the virus still in their systems even though they’ve long since ceased to be infectious. And 40% of the remainder will be asymptomatic – and, according to the World Health Organisation, cases of asymptomatic secondary transmission are “very rare”. That brings the total of people who should be self-isolating per 10,000 to about three. That’s a far cry from the 91/10,000 Hancock thinks should be self-isolating. Scaling that up by the population of England, that’s about 16,800 people, or 0.03%. Less a “second wave”, more a barely perceptible ripple.

Some people will think the Health Secretary knows exactly how many of the people testing positive each day are false or cold positives, but is keeping this knowledge from the public for nefarious reasons. After all, it’s easier to dismiss concerns about false positives if you pretend the numerator is just those people who’ve tested positive rather than everyone you’ve tested.

But what would be his motive for dismissing those concerns if he knows they’re well-founded? Might it be that it would discredit his whole approach to managing the pandemic, which is test, test and test again, and make his landmark achievement of carrying out 100,000 tests in one day a few months ago – which saved him from Boris’s axe – seem less impressive? Because he doesn’t want to undermine public confidence in the Government and its public health agencies? Because he’s hoping to get a job with AstraZeneca when he leaves office?

I suspect his answer to Julia Hartley-Brewer wasn’t deliberately misleading; rather, he has misled himself because actually getting to grips with the FPR and thinking through its implications is much more politically perilous that saying things like, “Under one percent means that for all the positive cases the likelihood of one being a false positive is very small.”

Less a ‘second wave’, more a barely perceptible ripple

As I’ve said before on my daily blog Lockdown Sceptics, the fact that senior politicians and public health panjandrums say things that we know not to be true doesn’t mean they’re lying to us. Rather, they’re lying to themselves because it’s in their interests to do so. And the root cause of this self-deception isn’t stupidity – or a poor grasp of statistics, as in this case. On the contrary, the smarter a person is, the more effortlessly they are able to persuade themselves to believe whatever it is that’s in their best interests to believe. Hancock is one of Robert Musil’s “rightly blended personalities” as described in The Man Without Qualities:

And indeed the most coldly calculating people do not have half the success in life that comes to those rightly blended personalities who are capable of feeling a really deep attachment to such persons and conditions as will advance their own interests. 

The tragedy of our age is that these “rightly blended personalities” are the ones that rise to the top in politics.