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expert reaction to the ONS Infection Survey, UK: 23 October 2020

The Office for National Statistics, have released the latest data from their COVID-19 Infection Survey.


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

“This week’s report on the ONS Infection Survey extends the data up to mid-October (16th). There isn’t much in it in the way of good news. The estimate of the number of people in the whole English community population that would test positive for the virus has continued to increase, still with no clear sign that the rate of increase is slowing. ONS say the same about their estimates of the daily number of new infections. There are small hints in some of the ONS analyses that, just maybe, the rates of increase in both these quantities are slowing. But here I’m really grasping at straws for a bit of good news – the evidence for any slowing is statistically very weak, if it’s there at all, and in any case, we’re still talking about an increasing number of infections, that is doubling every two weeks or less.

“As always, results from the ONS survey should provide more reliable estimates of these numbers than, for example the figures that come from testing in the Test and Trace programme. That’s not because the tests used are any different – the swabs are analysed in the same labs using the same methods – but because the ONS survey uses data from a reasonably representative sample of the community population. They are tested only to provide these estimates, and not because they have asked for a test because they have symptoms, or have been advised to have a test by health professionals.

“Overall, ONS estimate that, in the week ending 16 October, 1 in 130 of the English community population (excluding people who live in communal establishments like care homes or some university halls of residence) would test positive for SARS-CoV-2. Like all estimates from surveys, there’s some uncertainty about it, and the data are consistent with a rate between 1 in 120 and 1 in 130. The central ONS estimate of the number of people who would test positive is 433,300, with a credible interval (plausible range) from 407,500 to 459,300. The central estimate is 96,800 higher than last week’s figure – that’s a lot more people who would test positive. These are all estimates of the numbers who would test positive. At this level of infection, it’s very likely the case that the number of false negatives (people who are actually infected but would test negative) considerably outnumber the number of false positives (people who are not infected but would test positive), so that the actual numbers of infected people are likely to be higher than those estimates. This week ONS have done some estimation of the percentage of people who are actually infected, allowing for testing errors, and they indicate that the percentage of people infected, on average over the fortnight from 3 to 16 October, might well be somewhere between 0.87% and 1.07%. corresponding to somewhere between 1 in 90 and 1 in 110 people being infected with the virus. (Indeed ONS also produced some other estimates, based on what they (and I) consider to be unlikely numbers for the false negative rate, which would put the proportion of infected people even higher.)

“ONS estimate that, in the week from 10 to 16 October, there were 646 new infections per million people each day, with a credible interval from 546 to 855. In numbers across the English community population, that’s 35,200 new infections each day (with a credible interval from 29,800 to 46,600). “Last week the central estimate was 27,900, so again a very considerable increase. These figures, as always, are much higher than the daily reported ‘new cases’ on the Government dashboard, for which the daily rate (as an average over 7 days) was about 14,000 for England for the week in question. The difference is partly because people without symptoms would be unlikely to be tested under the system that provides these daily dashboard figures, so they would not show up as a confirmed case. People with no symptoms are still tested if they are in the ONS survey sample, and some of them will actually be infected and test positive. That’s part of the reason why the results of the ONS survey can tell us more, and more accurately, than the information from general swab testing that goes into the dashboard.

“As has been the case for several weeks now, there are some big differences in the rates of positive tests between different English regions. Rates continue to be highest in the three regions of the North (North East, North West, Yorkshire & the Humber). In the North East region, as last week, there’s evidence that the rate of increase may be levelling off or perhaps even falling, though the rate remains high there with an estimated 1 in 80 people testing positive, and there’s a lot of statistical uncertainty. Last week, there was some indication that the increase might also be levelling off in Yorkshire & the Humber, but ONS were very cautious in their interpretation and suggest this may not continue. This week, it indeed seems that that trend hasn’t continued, though the actual rate at which infections are increasing may be slower than it was a few weeks ago. In the North West, there’s no clear sign of a slowing in the rate of increase, and the central estimate is that about 1 in 60 people in that region would test positive. Rates in other parts of the country are lower, though most regions are still showing clear increases on last week. The possible exceptions are the South West region and the East Midlands, where there are some signs that the infection rate might be falling.

“As in recent weeks, infection rates are highest in the younger age groups, particularly those aged about 17 (school year 12) to age 24, where ONS estimate that about 1 in 50 would test positive. The speed at which the infection rate is increasing in that age group appears to be slackening a bit compared to recent weeks, which is a good sign, but ONS are still estimating that the rate is increasing rather than falling. In fact the rate of infection is estimated to be increasing across all age groups, with the possible exception of school years 7 to 11 (age roughly 11 to 16) where there are some signs that the increase has slowed and the rate could even be falling. But there’s a lot of statistical uncertainty about the trend in that age group, and ONS (rightly) give strong warnings about over-interpreting it. This week, unlike previous recent weeks, there seems to be pretty clear evidence that the rate of infection is increasing in the 70 and over age group as well, though the rate there does remain much lower than most of the others. Roughly, the estimates are that somewhere between 1 in 190 and 1 in 260 of the 70+ would test positive, on average, if tested in the most recent two weeks (3 to 16 October).

“The survey is now running in all four UK countries. This is the first week in which ONS have had enough data to publish results for Scotland. The estimated rate of positive tests there, over the most recent two weeks (3 to 16 October), is 0.57%, or about 1 in 180 people, though there is a lot of statistical uncertainty about that figure. The central estimate is less than the current estimate of the rate in England, though because of the statistical uncertainty, we can’t conclude with certainty that the rate is lower in Scotland. Things may become clearer as more data is collected in Scotland. For Wales, there’s some evidence that the rate of infection has increased in recent weeks, though there is still uncertainty about that because not so many test results are available in Wales as in England. The estimate for the proportion of the Welsh community population who would test positive, in the most recent week (10 to 16 October), is 1 in 180, with a wide uncertainty interval going from 1 in 100 to 1 in 400. In Northern Ireland, trends are even less clear, because the survey has been running for a shorter time and the number of people tested is even smaller. There is some evidence that the infection rate is increasing there, and the estimate for the proportion testing positive is pretty high for the most recent fortnight (3 to 16 October) – a central estimate of 1 in 100 people, with an interval from 1 in 70 to 1 in 160.”


Prof James Naismith FRS FRSE FMedSci, Director of the Rosalind Franklin Institute, and University of Oxford, said:

“The ONS figures estimate an increase of 27, 900 to 35, 200 cases per day for the week ending 16th October. This is not as fast as before, it gives a doubling time of around 21 days. There is some unavoidable uncertainty in these measurements, so it is too early to draw firm conclusions as to whether the rate of increase has really decreased but it is hopeful.

“Feeding these numbers back in the yesterday’s track and trace numbers reveals the scale of the challenge facing the current PCR based test, track and trace system. Testing identified less than half the people who got infected in the week ending 14th October. This is a disease which is asymptomatic for the majority and rapidly spread. It is very hard to track and trace.

“For each person ONS identifies as infected, track and trace would estimate they have at least 1 non household contact.

  • For every 100 infected people then, we have 100 people to trace. This MAY be an underestimate.
  • Track and trace identifies around 7 of them within 24 hrs (ignoring delays in test results which might decrease this further).
  • Track and trace only ever reaches around 20 of them.
  • We have no idea whether they isolate effectively.”


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 received.

None others received.

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