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expert reaction to latest R number and growth rate estimates published by the government

The government have released the latest estimates for the COVID-19 growth rate and R value.


Prof Kevin McConway, Emeritus Professor of Applied Statistics, The Open University, said:

“The latest estimates of the UK R number and the growth rate of new SARS-CoV-2 infections, from SAGE and the Government Office for Science (GOS), have been published. As always, they give ranges rather than a single figure. (It doesn’t make good sense to give single number estimates of R or the growth rate, because there’s too much unavoidable uncertainty in estimating them.) The range for the R number is not much different from last week’s – from 1.3 to 1.5, whereas last week it was 1.2 to 1.5 (and the week before, 1.3 to 1.6). This week’s range indicates that, on average, every 10 people infected now will infect somewhere between 13 and 15 others. That means that the pandemic will continue to grow – but R does not, on its own, tell us how fast it will grow. Also, the fact that the lower end of the range is slightly higher than last week’s lower end does not mean that R has certainly increased. For example it could have been 1.4 both this week and last, because that’s within both ranges.

“The growth rate does directly say how fast GOS and SAGE believe the pandemic will grow. This week’s range is from +4% to +7% per day. Last week’s range was +4% to +9%, so the upper end is smaller. So GOS and SAGE now don’t believe that the higher rates of growth, between 7% and 9% per day, are likely. But again, that doesn’t mean that the actual growth rate has changed. For instance, it could have been 5% per day in both this week and last.

“A 4% daily growth rate would mean that the number of cases doubles in about 18 days, while a 7% growth rate means the number would double in about 10 days. Even an 18 day doubling indicates reasonably rapid growth, though even a 10-day doubling is considerably slower growth than at the peak stage of growth in the first wave, back in March.

“GOS/SAGE also provide ranges for R and the growth rate for England on its own, and for English regions. All of these indicate that infections are continuing to grow. The growth rate ranges for the regions do not differ hugely from one region to another. There’s some indication that perhaps infections are growing rather more slowly in London than elsewhere, though they are definitely still growing. There’s also some indication that the growth rate may be slightly faster in the South West than in other regions – though the actual level of infection there is relatively low, so that the infection level there is unlikely to reach the current levels in the North of England any time soon, even if the growth rate really is slightly faster in the South West.

“How do these figures fit in with the estimates of infection rates from the ONS infection survey, also published today? The most accurately estimated figures from the ONS survey are for England. The SAGE/GOS range for R for England is slightly lower than for the whole UK, 1.2 to 1.4, and the growth rate range is the same as for the UK, +4% to +7% per day (corresponding to a doubling time between about 10 days and 18 days). ONS do not publish growth rates for their estimates. My fairly crude calculations, based on the ONS estimates of new infections, indicate a doubling time for infections of somewhere between one and two weeks. So they are in the same ballpark as the SAGE/GOS numbers. I wouldn’t necessarily expect them to match really closely anyway. The latest ONS figures are not for the current week, but for the week ending 8 October. They also do not include infections in people living in communal establishments such are care homes, prisons or some university halls of residence. The SAGE/GOS figures are intended to cover the whole population, and they have a more complicated timescale and use a wider range of data. Because they are based on numbers of hospital admissions, ICU admissions, and deaths, as well as new cases, and because it takes time for an infected person to become ill enough to require hospital treatment or, if it sadly happens, to die, there is an element of delay in the SAGE/GOS R and growth rate figures.

“Both sets of figures are clearly indicating that the pandemic is continuing to grow, and at a reasonably rapid rate, though it’s substantially slower than in the first wave in March. That’s concerning. I hope that current measures to contain the virus do turn out to be effective in slowing and, before long, reversing these increases.”


All our previous output on this subject can be seen at this weblink:


Declared interests

Prof Kevin McConway: “I am a Trustee of the SMC and a member of the Advisory Committee, but my quote above is in my capacity as a professional statistician.”

None others received.

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