October 30, 2020

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 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 1.1 to 1.3, whereas last week it was 1.2 to 1.4 (and the week before, 1.3 to 1.5). This week’s range indicates that, on average, every 10 people infected now will infect somewhere between 11 and 13 others. That does still mean 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 1.2 both this week and last, because that’s within both ranges. But the lowering of both ends is at least a much more encouraging sign than if they had both gone up, and the chances are that R has indeed decreased.

“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 +2% to +4% per day. Last week’s range was +3% to +6%, so both ends are lower. That’s encouraging. 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. But a real fall does seem likely. A 2% daily growth rate would mean that the number of infections doubles in about 35 days, that’s 5 weeks, if the growth rate doesn’t change. A 4% growth rate means the number would double in about 18 days. Both of these do indicate that the number of infections is still growing, which isn’t good, but it is considerably slower growth than at the peak stage of growth in the first wave, back in the Spring.

“SAGE and GOS do also give ranges for R and the growth rate for the whole of England, and for the English regions. The range for R for England is the same as for the whole of the UK 1.1 to 1.3, and the growth rate range for England is set a little higher than that for the UK, at +3% to +5% per day, which is the same as the range for England last week. The ranges for R and the growth rate for the English regions do vary to a certain extent, but not much, and they all indicate continued growth in infections. That’s not good, but it could be worse.

“At least two other sets of estimates of R and the growth rate, for England, were published yesterday, as part of the interim report¹ on round 6 of the REACT-1 study, and as findings² from the MRC Biostatistics Unit (MRC-BSU) at Cambridge University.

“In broad terms, the MRC-BSU results are fairly similar to those from SAGE and GOS, on R for the English regions (MRC-BSU don’t publish a national R estimate) and on growth rates, though some of the ranges given by MRC-BSU are wider than those from SAGE. However, that’s perhaps not very surprising, as the estimates from MRC-BSU are among those that feed in to SAGE to give the official Government figures.

“However, the R and growth rate figures given by REACT-1, and based just on the partial results from their latest round (round 6), are very different from those in the Government release today. REACT-1 gave the R figure for England as about 1.6, with a range from about 1.3 to 1.9, so barely even overlapping with the SAGE/GOS R range. REACT-1’s growth rate range for England is from +4% to +11% per day, again barely overlapping with the SAGE/GOS range. The REACT-1 figures for the regions are slightly difficult to compare with the SAGE/GOS ones, because the two sources use a slightly different set of regions, but generally the REACT-1 ranges for R and the regional growth rates are considerably higher than the SAGE/GOS figures. (REACT-1 estimated that R was probably below 1 in the North East, but this can’t be compared with the SAGE/GOS estimates because they include the North East with Yorkshire.)

“On these national and regional R and growth rate figures, I am inclined to trust the SAGE/GOS figures more than those particular REACT-1 figures. The reason is that those specific REACT-1 figures are based on only the first part of the data from round 6 – the rest of the round hasn’t been analysed yet, and indeed some of the swabs haven’t even been taken yet, I believe. So they are essentially based on changes in the infection rates over just 8 days. That might well not be very reliable even for the whole of the country – but over those 8 days, in the smaller regions, there might only have been about 400 swabs tested each day, of which maybe only 5 or 6 would have tested positive. That’s unlikely to give a very reliable result (and that’s reflected in the very wide ranges that REACT-1 give for some of their regional results). We’ll have more reliable figures from REACT-1 when the whole of the round 6 results are published. The REACT-1 report yesterday also published estimates of R and the growth rate based, not just on these 8 days of round 6, but on the whole of round 5 in addition, and those figures are much more in line with the SAGE/GOS results.

“A limitation of the SAGE/GOS results is that they are based on a range of data including data on hospital admissions and deaths. Since it takes some time, after a person is infected, for them to require hospital admission , or, sadly, to die, this means that effectively the estimates of R and the growth rate are based on average changes over, roughly, the past three weeks. This would only be important if the pattern of growth changed a lot over that period (and I mean the pattern of growth rates, not the level of infections, which is bound to change if the pandemic is growing (or reducing)).”

1 https://www.imperial.ac.uk/news/207534/coronavirus-infections-rising-rapidly-england-react/

2 https://www.mrc-bsu.cam.ac.uk/nowcasting-and-forecasting-29th-october-2020/

https://www.gov.uk/guidance/the-r-number-in-the-uk

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

www.sciencemediacentre.org/tag/covid-19

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.”