Monday, October 26, 2020
Home COVID-19 Maths, or myths: Do those scary Covid stats really add up?

Maths, or myths: Do those scary Covid stats really add up?

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THE media were in full doom and gloom mode last Thursday as they reported 6,634 new cases of Covid-19 that day and 37 deaths. But do those numbers mean what we assume they do? 

In order to answer that question, you need to know that the  government counts the numbers of cases  in two ways – according to the date the person was tested (what they call the specimen date) and according to the date the test was reported after processing in the lab.

Because of the workload in labs, it can take quite a while for tests to be processed, so the entries for the same date in the two lists are rarely the same.

The much-publicised 6,634 is the number of tests processed that day and the vast majority of those new cases weren’t tested on Thursday – they were tested one or more days previously – maybe as long ago as a week.

The number of people tested on Thursday who were positive won’t be known until all their tests are processed and could well be significantly lower than that headline figure. But 24-hour news wants facts now, so they use the number that’s available straightaway even if it could be misleading.  

Just like cases, deaths are counted in two ways – according to the date of death and according to the date the death is reported. 

The second set of numbers is available immediately and doesn’t change from day to day. The first one only becomes clear as the reported deaths are entered into the system, which can take a long time.

Once again, the media didn’t want to wait, so they announced the 37 deaths on Thursday without making clear that wasn’t the actual number of people who had died that day. 

Interestingly, the media know about this issue with reported deaths. That’s why there were no dramatic headlines when there were 0 deaths reported on July 30. Editors knew the final number for the day was likely to be higher and they didn’t want to end up with egg of their faces.

That was the right decision, because it is now clear that ten people died that day after testing positive (although, as always, it’s not clear if they died of something other than Covid-19).

It appears that the media know that numbers may be too low, but they don’t realise they may be too high. I hope the Government is better informed, but I’m not sure it is. 

Which way of recording is best? Recording deaths and positive tests on the day they are reported is simple and quick, but it doesn’t give such a clear picture of what’s happening as recording them for the day they actually happen.

If you are not careful, it can make you think there are trends that aren’t really there. For example, we were told last week that there was a huge backlog of tests waiting to be processed.

If processing is speeded up to clear the backlog, that could produce an artificial spike in the numbers of cases reported on the day that happens. However, it wouldn’t produce a spike in the numbers recorded on the day of testing. 

Earlier in the year, we didn’t put so much emphasis on case numbers – what mattered was how many people died. However, now deaths have dropped to well below 100 per day, the emphasis has switched to counting cases.

In the absence of any other obvious reason for doing this, you’d be forgiven for thinking this might be a way of keeping us scared. So might the process – now fortunately stopped – of counting people as Covid-19 deaths if they had had a positive test in the distant past, even if they had clearly died of something else. 

In reality, counting cases has only limited use anyway, because the numbers depend heavily on how many tests are available and who is allowed to have them. As testing is concentrated on those most likely to be infected, it produces a higher positive rate than is likely to exist in the rest of the population.

But even that higher rate is currently only between one and three per cent, which is worryingly close to the  possible false positive rate of 0.8-4.0% and raises the possibility of these numbers containing a high proportion of false positives. Which set of numbers is the Government using? 

Making predictions on what’s going to happen is always tricky, and one thing we’ve learned during the pandemic is that experts don’t always agree. But it definitely helps to start with the right information and that means counting cases for the day of the test and deaths for the day people die.

Using the information on the day it is reported is much less accurate because it brings in too many other variables about how the information is collected. 

Unfortunately, it appears that Professor Chris Witty and Sir Patrick Vallance used the reported cases in their amazing graph. They then took one number – the 3,105 cases reported on September 15 – and showed what would happen if that number doubled every seven days, despite the fact that the preceding numbers gave no indication that this would actually happen. 

If this is an example of the mathematical reasoning behind the current increase in restrictions, we should be seriously worried. 

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Diana Kimpton
Diana Kimpton is a maths graduate and an author. She specialises in writing about horses and numbers, but not usually at the same time.

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