Monday, 21 September 2020

Is there really a dramatic rise in Covid-19 cases?

There's a handy 'dashboard' at

The chart for 'Cases' shows an apparently dramatic increase, from about 800 new cases per day in July to nearly 4,000 now (late September).

To interpret this properly, you have to also look at the chart for 'Testing'. The number of tests carried out has increased from about 100,000 to over 200,000. So the percentage of positive tests has increased from 0.8% to 1.8%. I am perfectly aware that there are a lot of false positives, so let's round that 1.8% down to 1% for sake of argument.

These tests have two quite distinct purposes:

1. Back in March/April, they would only do tests on people who were displaying symptoms, who had been admitted as patients, or who had good reason to assume they might have contracted it. About half of tests came back positive. That was important to know, so that they knew how to treat patients or who should self-isolate.

2. Nowadays, lots of people are being tested, whether they have any symptoms or not. As far as I can see, the people being tested are a fairly random cross section of the general population. So the relevance of these tests is telling us what percentage of the general population have contracted the virus. We know that the tests throw up a lot of false positives, but that doesn't matter if you are interested in the general trend rather than trying to pin down an exact but entirely unascertainable number. And that trend appears to be going ever so slightly upwards.

But what do we really care about here? We care about large numbers of preventable deaths and the NHS being "swamped". Neither of those things are happening, daily deaths have been in the 10 to 20 range for three months; daily admissions to the NHS are just over one hundred; and the total number of patients in hospitals is just over 1,000 (none of the Nightingale hospitals were ever used AFAIAA). The NHS has over one million staff, just quite how many does it take to look after one covid-19 patient?

If 1% of the general population has covid-19 at any point in time, that means 700,000 people have it. Of those, only 100 will be hospitalised and 10 or 20 will die every day. Assuming the illness comes and goes in two weeks (and you're either recovered or dead), that's a death rate of about 0.3%, which is so close to zero as to be meaningless.

Assuming two weeks to be a fair guess, that means about 50,000 new infections per day in the UK. Multiply that by nine months and that means about one-fifth of us have had it (and most won't even have realised). I'm not sure what the cut-off point for 'herd immunity' is, but it's only a matter of time, isn't it, vaccine or not?


View from the Solent said...

your 10 to 20 deaths per day is too high.
See Hector Drummond's blog at
It's been 8 or lower deaths 'with Covid19' since end July.
Hector's is a good source of analyses of official figures. Facts rather than government-induced hysteria.

Mark Wadsworth said...

VFTS, that's quite possibly true. Round it down to 0.2% fatality rate. Or 0.1%.

Like I say, the numbers are so low as to be meaningless. I'm sure that some people who break a leg end up dying of complications, but that number is a tiny fraction of a % and not indicative of anything and not something you should be panicking about if you break a leg.

Lola said...

MW. Thanks for doing that. It is almost exactly as I expected.

Dr Evil said...

The false positive rates for Covid-19 antibody testing is 2% at the three week mark. It is on the NICE website

Mark Wadsworth said...

L, I'm here to inform and entertain!

Dr E, 2% of all tests = false positive (appalling) or 2% of all positives are false (very good)?

Lola said...

Dr E. Well, as NICE 'guidance' nearly killed me, I'm not a fan...

Andrew Carey said...

Hancock has said that .8% of +ve test outcomes from the PCR test are false positives. Yes, I know he's not using the false positive rate the way you or I or anyone with a mathematical background is using it, but he was pretty clear to me the sense in which he was using it.
We can work out a rough bound on the FPR as you or I would use it which is lower than 1 in 2500. That because from the ONS infection survey there were a couple of weeks when that was the proportion coming back +ve from the PCR swab test. That would assume that in the worst case there were no +ves in the sample and all the +ves reported were false.

Mark Wadsworth said...

AC, if Hancock says that then he's lying. I accept that it is an unknowable figure, so that's a) spurious accuracy and b) mathematically more or less impossible.

Assuming approx. 2% of those tested have it, and 'sesnsitivity' is 100%, then 'specificity' would have to be 99.984%. No test is that accurate.

Andrew Carey said...

We can deduce that the True Positive Rate is at least 99.96% (2499/2500). I'm not sure what you mean by specificity in inverted comments though.
And there are some tests which are that accurate. Most of the ones I can think of are trivial though - boy/girl, dead/alive.
I can accept there will be human error in the administration of the tests and there are likely people texted by the contact tracers to say they were +ve when the test was -ve and vice-versa.

Mark Wadsworth said...

AC, I looked this up

Sensitivity = how many positives are correctly identified as positive
Specificity = how many negatives are correctly identified as negative

From what I've read, the specificity something like 99% because it identifies dead/dormant virus remnants.

So if they test 1,000 people who are all negative, it will throw up 10 positives anyway.

So if 1% actually have it, then approx 2% will get shown as positive, so half of them are false positives

But like I said, we'll never know.

Bayard said...

"Most of the ones I can think of are trivial though - boy/girl, dead/alive."
Not these days they ain't, unless you are talking babies for the first one.

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