Post sponsored by

Source: United Kingdom – Executive Government & Departments

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

“The UK Government has published its weekly update to the estimates of the UK R number and the growth rate of new SARS-CoV-2 infections. 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 1.2 to 1.4, whereas last week it was 1.3 to 1.5 (and the week before, 1.2 to 1.5). This week’s range indicates that, on average, every 10 people infected now will infect somewhere between 12 and 14 others. That means that there will be more infections in the next ‘generation’ of infections, so the pandemic will continue to grow. The fact that both ends of the range are slightly lower than last week does not mean that R has certainly decreased. For example it could have been 1.3 both this week and last, because that’s within both ranges. But the lowering of both ends is at least a more encouraging sign than if they had both gone up.

“If R is bigger than 1, that tells us that the number of infections will continue to grow, but it doesn’t directly tell us how fast it will grow. The growth rate does directly say how fast SAGE (and Government Office of Science (GOS), who publish the figures) estimate that the pandemic will grow. This week’s range is from +3% to +6% per day. Last week’s range was +4% to +7%, so both ends are slightly lower. That’s slightly encouraging, but again, it doesn’t mean that the actual growth rate has definitely fallen. For instance, it could have been 5% per day in both this week and last.

“A 3% daily growth rate would mean that the number of cases doubles in about 23 days, while a 6% growth rate means the number would double in about 12 days. A 23-day doubling still certainly indicates growth that needs to be contained, though even a 12-day doubling is considerably slower growth than at the peak stage of growth in the first wave, back in the Spring.

“GOS/SAGE also provide ranges for R and the growth rate just for England, and for the English regions. (Estimates for the other UK countries are published by their devolved governments.) For England, the R range is the same as for the whole UK, R 1.2 to 1.4. The growth rate range for England is slightly different, +3% to +5% per day. The R and growth rate ranges for the separate English regions are mostly fairly similar to those for England as a whole, though they indicate slightly slower growth than the English average in the North, Midlands and London, and slightly faster growth in the other southern regions (South West, South East and East of England). Given the inevitable uncertainty in these estimates, these differences in ranges may not be important and indeed may not exactly correspond to true differences in the progress of the pandemic between regions. And they do all indicate that infections are continuing to grow across the whole country.

“How do these figures fit in with the estimates of infection rates from the ONS infection survey, published earlier today? The most accurately estimated figures from the ONS survey are for England. The SAGE/GOS range for growth rate in England, +3% to +5%, corresponds to a doubling time for infections of between two and three weeks. ONS do not publish growth rates for their estimates. My fairly crude calculations, based on the ONS estimates, 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, even if not identical. 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 16 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.

“There are also some differences between the SAGE/GOS estimates and the ONS infection survey estimates for the regions of England. One awkwardness in comparing them is that the ONS figures use a different set of regions – what are sometimes called Government Office regions – than those that the SAGE figures use, which are for NHS regions. Also, the Government R and growth rate estimates give figures only for how infection numbers are changing in different regions, and not what the percentages of infected people actually are in the regions. (ONS estimate the percentages of people who would test positive (with a swab test) in each region.) Very broadly, the two pictures do match – numbers of infections growing in all, or almost all, regions. On average, both indicate that the numbers are growing more slowly (in percentage terms) in the Northern regions, and indeed also in the Midlands and London, than in the more Southern regions, though the ONS data show that the actual level of infections in the North is considerably higher than in the South. There is a discrepancy in the Midlands, where the ONS survey indicated a reasonably rapid rise in infections in the West Midlands, but a slowing of increase or even possibly a fall in the East Midlands. This cannot show up in the GOS/SAGE numbers, which use a single Midlands region that covers both East and West. But both sources indicate that the rate of increase is higher in the Southern English regions (apart from London) than elsewhere. These increases are starting from lower numbers of infections than elsewhere, but it will be important to control the increases before infections get to high levels in the South. There’s a difference between the two sources of data in relation to the South West, where the SAGE/GOS figures indicate faster growth than in every other English region, but the ONS infection survey suggests that infections are not rising fast and may even be decreasing. However, current levels of infection are lower in the South West than in any other English region, and low numbers of infections make the growth of the pandemic more difficult to estimate accurately. So it’s impossible for me to judge which data source has got the direction of change correct in the South West. We’ll eventually find out.

“Both sets of figures are clearly indicating that the pandemic is continuing to grow, and at a fairly rapid rate, though it’s substantially slower than in the first wave in March. That’s concerning, and the indication of faster growth rates in the South do indicate that there’s no room for complacency about the pandemic anywhere in the country, even in places where infections rates are currently quite low. I hope that current measures to contain the virus do turn out to be effective in slowing and, before long, reversing these increases. There’s some evidence from some Northern regions that things can improve, but they haven’t improved nearly enough yet.”

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.”


MIL OSI United Kingdom