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expert reaction to latest ONS Infection Survey data

The Office for National Statistics (ONS) have released their latest Infection Survey results. 


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

“The weekly updates from ONS on their infection survey continue to provide valuable information, but some care is needed in interpreting the results.  There are two particular new points this week.  First, though previous updates from the survey have continued to show a decreasing trend over time in the estimated number of people currently infected in England, this latest one reports that this trend has levelled off.  The report says, for instance, that the ONS statisticians cannot be sure whether the actual number of people testing positive for the virus in the latest two weeks for which data is available, 8-21 June, is higher or lower than the previous two time periods.  They can’t be sure partly because these results are based on a survey.  Not everyone in England has been tested.  The results come from swab tests on around 24,000 people in those two weeks, of which just 14 tested positive for COVID-19.  So the results have a statistical margin of error, and any changes between this two-week period and the recent past periods is within the margin of error of the survey.  I agree with the conclusions of the ONS statisticians that there is no evidence that the current trend is anything other than level.  The conclusions from a different, experimental, analysis of the data, developed by ONS’s partners in this study at the Universities of Oxford and Manchester, lead to the same conclusion on this.  Assuming that the levelling off is genuine, nothing in these data can tell us why that might be.  A temptation would be to link it to recent loosenings in lockdown, some at least of which happened about the same time as the levelling off – but just because two things happened at the same time, that doesn’t necessarily mean that one of them caused the other.

“It is inevitably slightly concerning that the previous downward trend seems to have stopped, though we cannot conclude that numbers of infections are actually rising again.  But the Government’s most recent estimates of the R number (reproduction number), and of the rate of growth or decrease in the number of infections, still show that numbers of infections are declining, at a rate currently estimated as being between 2% and 4%.  How can this be compatible with the ONS conclusion that the current trend could be flat?  One important reason is that all these estimates are based on data that is incomplete in some way – for example, the ONS results are based on a survey, not on testing everyone in the land, and the R number estimates use data on numbers of new cases, deaths, and other events, all of which are uncertain to differing extents.  The apparent difference between the ONS results and the Government R and growth rate figures is generally within the margin of error of the analyses.  Another reason is that the scope is different.  The ONS infection survey gives estimates for the so-called community population, so does not cover people in institutions such as hospitals or care homes.  The Government R and growth rate figures include the whole population.  Other reports indicate, for instance, that infection rates in care homes have been falling considerably, which might make estimates for the whole population show a decline even if the rate in the community (private households) is not changing.  And the ONS results are just for England, whereas the other Government estimates are for the whole of the UK.  Maybe there is a difference between the current track of the epidemic in England and in the rest of the UK.  (The results do not provide any clear evidence of a marked difference of this kind, but all the results are subject to some statistical uncertainty.)

“The other new feature this week in the ONS survey results is the provision of regional estimates of the percentage of the population that would test positive.  On the face of it, these results appear to show some quite marked differences between regions.  But, because the numbers of people tested in a single region is inevitably a lot smaller than the number tested in the whole country, the statistical margins of error (confidence intervals or credible intervals) around these regional estimates are quite wide.  The ONS statisticians say that, on the basis of their data, it is not possible to be confident that there are differences in the percentage of people infected in different regions, and I agree with them on that.  Another analysis does indicate that the downward trend in infections does appear to be levelling off in some regions, though again there is quite a lot of statistical uncertainty about that.  That uncertainty will reduce as time passes and more swab tests are done within this survey.”


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

On estimates of R and growth rate:

“The link to Scotland explains that SAGE’s uncertainty interval for R in Scotland, namely 0.6 to 0.8, is a 90% uncertainty range.  Should I assume that SAGE’s  uncertainty range for England (0.7 to 0.9) is likewise a 90% uncertainty range, not a 95% uncertainty range.  The latter could be expected to be wider.  For transparency in future reports, please clarify the intended uncertainty range of R and for change in growth rate as 90% or 95%.”

On the ONS Infection Survey data:

“By contrast, the ONS Infection Survey clearly reports 95% confidence intervals and, for the first time, includes regional estimates.  More importantly, perhaps, is the warning that the steady decrease in new infection incidence has stalled.  Interesting, too, is the additional finding that, over the course of a week, we may expect 4 new infections per 10,000 persons or 7.5 newly infected households per 10,000 households.

“Good design pays enormous dividends as the ONS Infection Survey reminds us weekly.”


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

“The latest ONS population surveillance data has shown a slight increase in infections (but not statistically significant) this week but the previous week’s figure was particularly low; overall the trend remains down.  This upturn needs to be considered with the number of people being found positive and hospital admissions as part an overall picture as to where we are heading with COVID-19.  It is something that needs to be kept an eye on.

“As the numbers of people with COVID-19 decline the accuracy of this data declines at the same time.

“There is marked regional variation but the numbers are small in each region and the confidence intervals overlap so therefore we cannot really know how much local variation there is.  The national and regional R figures are calculated using a number of additional data sources.

“This study estimates 22,000 people developed COVID-19 in a week but only just over 9,000 people tested positive.  Allowing for people without symptoms many people who have symptoms are not being tested.  We need to find ways to reduce this shortfall.

“No new antibody results were reported and hopefully more regionally specific data will be available soon.”


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


Declared interests

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

None others received.

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