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expert reaction to latest R number and growth rates published by the government and latest data from the ONS Infection Survey

The government have published the latest estimates for the COVID-19 R value in England and Wales, and the Office for National Statistics (ONS) have published the latest data from their COVID-19 infection survey. 


Dr Jason Oke, Senior Statistician at the Nuffield Department of Primary Care Health Sciences, University of Oxford, said:

“I think week to week changes should be interpreted carefully as they are less reliable than looking at longer term trends.  According to their exploratory modelling of the longer term trend (see figure 4 and sheet 3c in the infection survey data sheet) the number of new infections have been increasing by approx. 150 per day in the last week of July.  The ONS modelling suggests that the number of new infections has been increasing, slowly, but there is uncertainty as to the exact trend.  A steady rise in infections would correspond with the estimates of R close to 1 but not over 1.”


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

“Because of all the uncertainty, because the R estimates and infection survey results are measuring rather different things based on different data sources, and because the latest infection survey trends and the latest R estimates do not relate to exactly the same time periods, I don’t think there’s any inconsistency between the results, and I don’t think any further reconciliation between them is needed.  These aren’t things you can just read off a meter, as it were.

“On the ONS data, there are 2 different sets of things that might be considered as numbers of ‘cases’ – the number of people who would test positive in the community in England (and they’ve just added data on Wales) if they were tested, and the number of new cases per day that are estimated to be happening.  (In the jargon, these are the prevalence and incidence figures.)  These aren’t the same (because, once someone has been infected, they will remain infected for a time, so they’ll contribute to the first set of numbers for some time until the infection is no longer detectable, but they count as a new case only the first time they would test positive.  Both are important but in somewhat different ways.  For both of these sets of numbers, the ONS report says that the numbers “have risen since the lowest recorded estimate, which was at the end of June, but there is evidence that this trend may be levelling off when compared with last week’s headline estimate.”  That seems reasonable to me, but the increase from the lowest point until the latest date covered in the ONS data (2 August) is relatively a bit bigger for the new cases than for the number of positive tests.  I don’t think that’s alarming in any sense, given that there’s quite a lot of uncertainty in these estimates, but possibly the new cases rate (the incidence rate) is more relevant to R.

“ONS aren’t in a position to say something as simple as ‘the number of infections went up last week but didn’t rise this week’.  They say things that are inevitably rather vaguer than that, about “some evidence” and about general directions of change.  They do that on purpose, because that data that they have would not support any stronger statements.  “Evidence that the trend may be levelling off” is a long way from saying ‘cases didn’t rise’.  ONS are saying something more like ‘We can’t be sure of the exact direction that the figures are moving in, because there’s too much uncertainty, because these results are based on a sample of the population (albeit a pretty big sample), not the whole population.  But the data are consistent with the rise in the latest numbers this week being less than the rise we reported last week, and indeed with there being no increase from last week to this – but there’s a lot of uncertainty and we really can’t be sure that this is what has already happened.’  But those are my words, not theirs!

“The R numbers (and growth rate estimates) are based on a considerably wider range of data than just the infection survey results (and indeed, wider than data that are just about testing for current COVID-19 infections).  They also use data, for instance, on “hospital admissions, ICU admissions and deaths”, as the Government report says, and as it points out, there’s a delay of 2 or 3 weeks between a new infections happening and infections showing up in data on hospital and ICU admissions and deaths.  Thus changes in the R number now might reflect increases in new cases a couple of weeks ago – when ONS data were at least suggesting there might well be some increase.

“The R number report also says, “Models that use COVID-19 testing data tend to have less of a time delay and have recently suggested higher values for R in England.”  But this is referring to recent testing data, not this week’s ONS figures specifically (and both last week and this, ONS was saying that their infection survey results were consistent with an increase in new cases since the lowest numbers in late June).  The R number report says that, because of this, they might expect further changes in the R and growth rates in the next few weeks.  They also state that “For this reason [i.e. recent testing data], SAGE is no longer confident that R is currently below 1 in England.”

“But the report also puts 1 at the top range of their estimate of possible R values in England.  The range goes from 0.8 to 1.0, and they say “The most likely true values are somewhere towards the middle of these ranges [for R and for the growth rate].”  They are saying that their best guess is that R is still less than 1 in England, but they are expressing their uncertainty that it is definitely less than 1.”


Commenting only on the ONS Infection Survey data:

Prof Sheila Bird, Formerly Programme Leader, MRC Biostatistics Unit, University of Cambridge, said:

Response-rates by invited households: Two changes have been made to the ONS Infection Survey.

“First, Wales has been included from 29th June.  Welsh data are reported separately.  Judging by the width of corresponding confidence intervals for 30 July, sample size for Wales is about 40% of that for England.  The participation rate by invited households in Wales was 22% (770 of 3472 invited households).

“Second, from 13 July 2020, additional households in England are being randomly selected from the so-called Address Base.  These household are not known to include a member who has given prior consent to be re-contacted by ONS.  Thus far, only 10% of Address Base households have agreed to participate.  The Address Base household-participation rate may increase once the initial full 4-weeks have been completed but would have to increase considerably to match the 30% participation-rate by contact-me-again households from 31st May, let alone the ONS Infection Survey’s initial 50% participation-rate by contact-me-again households in its pilot phase from 26th April 2020.

“Not only has the participation rate by households in England decreased but also the swab-rate by household members: down from 95% in the pilot phase through 78% from 31 May to 65% by members of participant Address Base households.

“In summary, individuals who provided first swabs were equal to the number of contact-me-again households approached in the pilot; reduced to 60% of the number of contact-me-again households approached from 31 May; and to 21% of the number of randomly selected Address Base households approached from 13 July 2020.  The average number of participants per participating household has remained around two throughout.  Hence, ONS has to approach 10 randomly-selected Address Base households to secure consent from at least one household member.

“Once a clinically effective test for SARS-CoV-2 antigen in saliva is available, ONS Infection Survey’s response rates may recover.

“Meanwhile, more than re-weighting may be necessary to cope with response-rates by invited households which are 30% or lower.  Representativeness is put in jeopardy because the 30% who consent from a random-sample are no longer assuredly constitute a random sample.

Bayesian weighted modelling estimation for England of daily number of new infections: Due to ONS Infection Survey’s evolving response-rate, I tend to focus on the ONS Infection Survey’s Bayesian estimates for England which were 3700 new infections daily (uncertainty: 2100 to 6400) during the week of 27 July to 2 August versus 2800 new infections daily (uncertainty 1500 to 5500) during the week of 13-19 July 2020.  Both have wide uncertainty as does the MRC Biostatistics Unit’s most recently released estimate of 3200 new infections daily (credible interval: 1700 to 5800).

“Unlike the latter estimate, the ONS Infection Survey can, and does from time to time, report what proportion of those who were swab-test positive had symptoms on the swab-day (or recently).  An update on this type of analysis would be particularly useful just now.”


Dr Yuliya Kyrychko, Reader in Mathematics, University of Sussex, said:

“While the headline figure for R number in the UK is estimated to be just below or around one, there is significant amount of variation among different UK regions that is masked by this single number.  For example, the overall R number for England has not changed since last week, it remains 0.8-1, but the data shows that this number has grown in London and the Midlands, which probably led SAGE to conclude that in all likelihood R in England is not below 1.

“The fact that the R number has remained unchanged and possibly greater than one in North West and South West, suggests that despite the recent ONS data indicating levelling off of new cases, the infection remains quite prevalent in the community, hence, recommendations on social distancing and other protective measures should continue to be followed to avoid a significant growth of infection in those regions.  This is particularly important in the context of expected large numbers of people going to beaches over the coming weekend due to continuing heatwave.”


Dr Konstantin Blyuss, Reader in Mathematics, University of Sussex, said:

“Compared to last week, all UK countries except England have seen an increase in R number, with particularly alarming trend in Northern Ireland, where the latest estimates give the value of R possibly as high as 1.8. ONS estimates 3,700 new daily cases of coronavirus infection in England alone, suggesting that despite some levelling off compared to the last week, the general level of infection remains high in the community, with some regions in the country having a high chance of substantial growth in cases in the near future.

“In this respect, all efforts should be made to ensure that the infection is closely monitored to avoid local outbreaks and the need of lockdowns that have happened recently.  Of course, this also relies on cooperation from everyone in terms of maintaining social distancing, using necessary protection where appropriate, as well as reporting and cooperating with the track-trace-isolate program.”


Dr Shaun Fitzgerald FREng, Royal Academy of Engineering Visiting Professor at the University of Cambridge, said:

“It doesn’t surprise me that the growth rate is slightly higher this week but still less than 0%.  The R number (average number of people an infected person subsequently infects) is a bit higher but still less than 1.  Hence we are not seeing positive exponential growth.”


Prof Steven Riley, Professor of Infectious Disease Dynamics, Imperial College London, said:

“Scientists are using a variety of data sources to track the R value.  On average, the data used for SAGE R estimates is a little slower than ONS data.  Therefore, the R rise from SAGE is better compared with previous ONS reports.”


Prof Keith Neal, Emeritus Professor of the Epidemiology of Infectious Diseases, University of Nottingham, said:

“Making estimates of R with small number of cases becomes increasingly difficult and inaccurate.  Hence the wide range of the estimates.

“A local cluster in one part of a region such as Leicester in the East Midlands can give a value over 1 overall for the region but the figure would be much lower in the rest of the region.

“These local clusters need to be identified and managed with locally targeted measures.

“For many parts of the country infection rates continue to fall but caution and avoidance of high risk mixing needs to continue.

“If R goes above 1 this is likely to be due a mixture of areas with some above and below 1.

“The best way the public can help control COVID-19 is to get tested if they have symptoms, and if positive isolate and identify their contacts.”



R and growth rates:


ONS Infection Survey:


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


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