by Tom Chivers
Thursday, 7
October 2021
Factcheck
07:30

PCRs are not as reliable as you might think

Government policy on testing is worryingly misleading
by Tom Chivers
Swabs away! (Photo by Sean Gallup/Getty Images)

There’s been a bit of a Covid outbreak in our neighbourhood, including our eldest child (he’s fine). All the cases were first detected with rapid, at-home “lateral flow” tests, or LFTs.

It is currently government policy that if you get a positive LFT, but then you do the traditional, more accurate PCR and it’s negative, you don’t have to self-isolate any more: you can go back to school or work or whatever. If our child’s LFT had been followed up by a negative PCR, he would be back in school.
But I am pretty sure that many – perhaps most – of the people who get a negative result on their PCR “confirmation” will in fact have Covid, but will go back into work or school falsely reassured that they do not.

Here’s my reasoning. This is just Bayes’ theorem: remember that getting a positive result on a 99% accurate test does not mean that there’s a 99% chance you have the disease.

Let’s say about 1% of people who do an LFT have Covid. It’ll actually be more than that — about one person in 85 in England has the disease, more in the other three nations, and if you’re doing an LFT you may have reason to think you have it — but let’s go with it. 

Imagine you test one million people. Of those one million people, 10,000 will have the disease, and 990,000 will not.

According to the Government’s own figures, LFTs only give a false positive result at most one time in every 1,000. There’s some argument about how often they give false negatives, but this Cochrane review suggests (with caveats) about one time in three.

So you test your million people. Of the 10,000 who have the disease, LFTs correctly tell you that 6,700 do, but wrongly tell you that 3,300 don’t. Of the 990,000 who don’t have the disease, they correctly tell you that 989,010 don’t. But they wrongly tell you that 990 do. That means that you get a total of 7,690 positive results. But now you go and “confirm” them with PCR tests.

What we need to know now is how often PCRs give false negatives. According to this paper, it’s about one time in three; according to this one, it’s one time in 10. The Office for National Statistics’ infection survey relies on this paper, which says one time in 20. (False positives are so rare that we can ignore them.)

If we take the ONS figure of 5%, then of our 6,700 people who got a true LFT positive, your PCR will wrongly tell 335 of them that they’re disease-free. If we take the largest figure of 30%, it’ll wrongly reassure 2,010 of them.

Given that it will also correctly identify the 990 false positives, that means that — depending on how accurate we think PCR testing is — between 25% and 67% of everyone given the all-clear by a PCR after a positive LFT actually have the disease. 

The problem may be even worse than that. I was using conservative estimates of Covid prevalence among the people tested — and among schoolchildren, the prevalence is higher still, around 4% of kids in secondary and 2.6% of primary. (Possibly because we keep telling people to send their kids back to school despite a positive LFT.) For children, the risk of a false negative on PCR after a true positive will be even higher.

There is, I think, a tendency to assume that PCRs outrank LFTs. But that’s not how it works: both have some chance of being right and some chance of being wrong, in either direction. A negative PCR definitely does not mean you are safe to go back into the office or school. It may be government policy, but you should be extremely careful about ignoring a positive LFT, no matter what the “confirmation” test says. Perhaps the risk is worth it — in our mainly vaccinated population, Covid is less deadly than it used to be — but let’s not pretend that it isn’t there.

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Peta Seel
Peta Seel
11 months ago

Covid is less deadly than it used to be — but let’s not pretend that it isn’t there.”
No-one is pretending it isn’t there, bar a few nutcases of course. In fact, with an infection survival rate of over 99% and an average age of death at over 80, it has never been that deadly except to a small minority at whom it was most likely developed to be targeted. What is more, the inventor of the PCR test stated categorically that it is not a diagnostic tool. Sadly he died just before the Covid outbreak which quite possibly changed the course of history.
With the advent of the vaccines coinciding more or less with that of the Delta variant we will probably never know how much less virulent it is, but the way viruses adapt would indicate that it is.
Please find another drum to beat, this one has been beaten to death. The virus is here to stay, the vulnerable can have protection from the vaccines. The next problem may well be how much damage is being done by vaccinating those who are not vulnerable, especially the very young like your children Tom.

Lloyd Byler
Lloyd Byler
11 months ago
Reply to  Peta Seel

there are many viruses here to stay.. so?
show me one in the last 70 years that was a pandemic?

Fran Martinez
Fran Martinez
11 months ago
Reply to  Lloyd Byler

Aids, flu every few years, etc. Unless you only call it ‘pandemic’ if the msm calls it so.

Last edited 11 months ago by Fran Martinez
George Glashan
George Glashan
11 months ago

Another episode of : Imaginary Numbers with Tom Chivers

“Let’s say

but let’s go with it

Imagine 

suggests (with caveats) about one time in three

it’s about one time in three;

according to this one, it’s one time in 10

which says one time in 20.

If we take

If we take the largest figure of 30%

depending on how accurate we think”

Chivers can you do a Baysian analysis on the accuracy of predictions in articles that claim to use Bayes Theorem based on imaginary numbers?

Last edited 11 months ago by George Glashan
Andrea X
Andrea X
11 months ago
Reply to  George Glashan

I don’t think that is the issue at all. He is just trying to give a ballpark figure.

George Glashan
George Glashan
11 months ago
Reply to  Andrea X

thanks Andrea, respectfully i disagree. Chivers conclusion is valid, tests do give false positives and false negatives, but Unherd weren’t going to pay for a 100 word article that states the obvious. All the “working out” before that is pure fiction and whatever the ballpark figure is , its meaningless.
To be fair to Chivers this is less mince than his last Bayesian Theorem article where he “calculated” he didn’t have Covid.

Last edited 11 months ago by George Glashan
Andrea X
Andrea X
11 months ago
Reply to  George Glashan

To me, as I said in the other comment, the question he should be answering is first and foremost why he is testing his healthy child. The rest is just fluff.

Alka Hughes-Hallett
Alka Hughes-Hallett
11 months ago
Reply to  Andrea X

He has most likely vaccinated his children too. Madness

Lloyd Byler
Lloyd Byler
11 months ago
Reply to  Andrea X

He needs something to write about, its his job.

Alka Hughes-Hallett
Alka Hughes-Hallett
11 months ago
Reply to  George Glashan

He is utterly lost – this poor man needs help. I wonder how he occupied himself before Covid!

Listen Tom, keep you child at home if you are confused about the testing. Do your bit you think necessary if you fear Covid so much. We the public have stopped reading your confusing articles.

Lloyd Byler
Lloyd Byler
11 months ago

Pity these confused moron writers!

Mark Burbidge
Mark Burbidge
11 months ago

From the early days of this chaos, it has been public knowledge that PCR tests are not diagnostic. So why do the authorities insist on them ? Is it because they can be manipulated ?

Caroline Watson
Caroline Watson
11 months ago

Why does it matter? If your child is ill, keep them at home. If not, send them to school. Above all, stop the pointless testing!

Andrea X
Andrea X
11 months ago

My question to the author is, WHY do you test your child? What is it you are actually hoping to accomplish, in our “mainly vaccinated country”, especially if your child is fine to start with?
And, even more importantly, you keep testing them after writing this article?

Last edited 11 months ago by Andrea X
Adam Bacon
Adam Bacon
11 months ago

No s**t Sherlock. Where have you been for the last 18months Tom?

Steve Bouchard
Steve Bouchard
11 months ago

what about the false positives of the PCR tests? Seems to me we need to get on with life and stop spreading the fear. How about spreading the news to boost your immune system to fight off all respiratory viruses?

Lloyd Byler
Lloyd Byler
11 months ago

“Lies, damned lies, statistics and hearsay”
(There’s your four kind of lies)

Why is it so damn difficult to follow investigative reporters such as Jon Rappoport and Sheryl Atkinson who have decisively debunked all late 20th and this century’s pandemics?
They have done far more than the gobbly-gook hypothesis that this author and many others have spit out from a brain fart.

But instead you believe the fully debunked statisticians who get mainstream air and print exposure?

What happened to human curiosity, wherein we are at least wondering why there is so much difference of ‘facts’ out there even from the mainstream quack news? Dr. Antone Quack Fauci himself said that running the PCR lab test above 25 cycles is useless, but note that the FDA recommends running them at 40 cycles; and now a whistleblower has come out on PV saying the labs are running the tests as high as 57!

What the flying freaking hell is WRONG with you people?

In August of 2020, the CDC came out and said that 94% of the “positive” tests are indeed false and the person has so little viral particles on them they couldn’t possibly be contagious.. but, the local, national and international press said not a peep (I watched closely)!

That is when I knew the ‘fix’ was in and the road to truth is going to be very difficult.

Not only are you damn cotton-picking journalists pissing me off.. you frigging scare me!

Jeremy Bray
Jeremy Bray
11 months ago

People are not good at accepting uncertainty and few are statistically competent. Statistics should be taught in school once children have a proper grasp of maths. Statistics are not intuitive indeed often counter-intuitive.

Prashant Kotak
Prashant Kotak
11 months ago

Correct, they are not. The vaccines though, pretty much all of the western ones anyway, are. Effective enough to prevent serious consequences in most people, but not the illness itself. They take most of the edge off the illness for most people.

But the numbers in the UK are telling the hell of a story. The daily infection rate is hovering around the 35K per day mark, and has been (give or take) for at least six weeks. They show no signs of abating. That 35K per day number translates to circa 12 million cases per annum – basically the entire country infected at least once over three years or so (assuming there are large numbers, children etc, who have been infected but symptomless and so not showing up in the official stats).

And assuming the UK is not unique, across the globe this has still got several years to play out – with unpredictable consequences. This says to me there is still a lot unknown and not really understood or explained, and in all honesty these big holes in knowledge are not really discussed, and so to me at least the chance of one or more black swan type events in the immediate future, perhaps in economic or political arenas if not medical, is very very real.

Last edited 11 months ago by Prashant Kotak
Lloyd Byler
Lloyd Byler
11 months ago
Reply to  Prashant Kotak

Infection rate of what, exactly?

Neven Curlin
Neven Curlin
11 months ago

including our eldest child (he’s fine)”

Of course he is, you silly ‘journalist’.

Hardee Hodges
Hardee Hodges
11 months ago

The LFT is intentionally biased toward positivity. If results are negative and you have no symptoms, you are most probably negative. If LFT positive you may (not are) infected so a PCR is needed for confirmation along with clinical observation. The LFT is designed so that the early asymptomatic condition can be recognized earlier. PCR tests are way more sensitive with the cycle count used as surrogate for infectious particles. A low number of amplification cycles suggests heavy load of particles which may be infectious. Cycle counts higher than 30 suggest a mild infection, perhaps, and need clinical verification. Any cycle count as the person recovers is likely false given shedding over a prolonged period. The PCR sees matched particles which may or may not be actually infectious. It’s simply a surrogate for a real test using active cultures to verify infectivity. The gold standard is that culture but it takes even more time and costs more. Statistics about the various tests are meaningless without confirmation via cultures. Each sample depends a lot on when in the infection stage it was collected. Reliance on any of these simplified surrogates requires clinical confirmation.

Jeffrey Chongsathien
Jeffrey Chongsathien
11 months ago

18 months behind the curve. Unherd, why haven’t you fired this clown?

Paul Temperate
Paul Temperate
11 months ago

Thanks Tom, I always find your articles interesting. I see other commenters take issue with your acceptance of most of the mainstream view of covid (or willingness to question even a part) and your use of sophisticated Mathematical ideas in a relatively unsophisticated way. Personally I find your perspective challenges my ideas on both sides of most issues and the math gives a starting point for exploring an idea with at least a hint of rigor (or at least basis other than preconceived feelings). Look forward to more.