Results just published to 10th March (;ast Wednesday) 2.8 million tests in secondary school kids, 1324 positives- 0.048% or 1 in 2086. Lowest rate ever observed
Government figures would have predicted around 10,000.
Will post more analysis shortly
Sens=50.1% Spec 99.7% Prevalence of 0.5%
of 2,762,775 tests we would expect 6921 true positives and 825 false positives - nearly 6 times more test positives than have been reported.
To get down to the 1324 positives actually observed, either the prevalence has to be 0.036% (1 fourteenth of the expected rate) - 36 per 100,000
Or the sensitivity of the test has to be a pathetic 3.6%
Of course it could be a bit of both, and higher spec would change it slightly but nowhere near explain it.
Great that @ab4scambs shows some MPs understand the laws of probability (beginning to doubt that there was one) but this justification why we don't need to PCR kids who have positive LFT sadly starts with a fatal flaw
This is the second time I have tweeted this as one decimal place went for a wander in my first set of tweets. Nothing else changes. Thanks to @d_spiegel for spotting it.
2/8
It presumes that the prevalence to use for Covid infection in these calculations is that in the general population - 0.5% or 1 in 200. And then shows that 30% of those who are LFT+ and then PCR - will still have Covid infection. Can you spot the error?
3/8
Can we give @DHSCgovuk and @educationgovuk a lesson in probablilty? This is A level stuff - if there are Year 12 and 13s in isolation please try it (you can do it with Venn diagrams or a Tree diagram) and send your full workings to @GavinWilliamson@MattHancock@SMHopkins
(a) In 1,000,000 children of which 0.1% have Covid-19, if a test gives +ve results with probability 0.5 in those with Covid-19 and -ve results with probability 0.999 in those without, how many +ve results would you get, and how many of these would actually have Covid-19?
For Further Maths geeks:
(b) If those +ve on the first test and tested with a second test which gave -ve results in those without disease with probability 0.990, how many will not have Covid-19 infection AND have a +ve result on the 1st test AND have a +ve result on the 2nd test?
So are Lateral Flow Tests are becoming more useful?
Eh – No
Last week 2,764,845 tests done (new record high) and 4,353 were positive. That’s 0.16% (new record low).
So probably lots are false positives. Lots of money spent– little found
In secondary school 663,332 were tested, only 328 positive. Testing has move than doubled on previous week, numbers detected have not.
We are now down to 0.05% being positive – that is only 1 in every 2000 tested – another record low.
Given what we know about the infection rates from ONS and REACT – these data raise serious concerns that the LFTs are not doing the job that we expect. Many more cases should have been detected.
The mistake being made is to think that all that matters is that false positives are rare. However, if true positives are even rarer then we are in trouble. Test positivity data from Test-and-Trace (1 in 1500 positive) raises serious concerns that is the case.
2/8
If 1 in 100 pupils had Covid-19, we would be fine. Five out of every six test positives would be true positives. But it looks like we are somewhere between 1 in 1,000 and 1 in 10,000 (we don’t know).
This is a real lesson in LFTs not working well as "tests to enable". Lessons from two outbreaks in sporting teams. Clear evidence that the undetectable infectious period can be longer than hoped, and -ve tests increase risk by disinhibition.
Sorry @sbfnk I don't see how this analysis takes us forwards. We need to know the +ve predictive value, not specificity, and we cannot get that without verifying LFT+ves with PCR. Your analysis only tells us that the specificity must be =< observed total +ves, not by how much.
Last week total +ves in staff and students was 0.07%, so we know specificity was >=99.93% (we don't need to do any maths to conclude that). So we know it is between 99.93% and 100% but have absolutely no clear where. Without that knowledge we cannot compute the PPV.
If it was 99.93% that means none of the +ves were real cases. If it was 100% then all +ves would be real cases. So we can't tell whether the PPV was 0% or 100% or where it is inbetween. No maths will solve it, only PCR verification.