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expert reaction to latest ONS Infection Survey data

The Office for National Statistics (ONS) have released the latest data from their COVID-19 Infection Survey for England and Wales.


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

“As they do every week, the latest provisional results from the ONS Infection Survey provide some interesting new insights. The most useful feature of these findings is that they come from a carefully designed survey of the whole community population of England (the population living in private households, excluding people living in communal establishments like care homes, hospitals or prisons), so they won’t be adversely affected by things like differences between different towns in the amount of testing being done. Because the survey does not cover people in communal establishments, its results can’t be used to measure infection rates there – but the great majority of people in England live in private households, so the results do apply to most of us. (At the last Census in 2011, more than 98 people out of every 100 inhabitants of England lived in a private household.) But, like every week, we must remember that these results are provisional – not all the results of the latest swab tests have been received, and so the numbers for the most recent period might eventually be revised a little.

“As in last week’s report, the ONS statisticians conclude that the previous decline in the number of people who would test positive for a current COVID-19 infection has levelled off. The levelling off did not happen as a sudden change, so it’s difficult to say exactly when it started – perhaps since early or middle June. All the results are subject to some degree of statistical uncertainty, mainly because they are based on a sample of the population. That sample is quite large as survey samples go – over 23,000 swabs tested in this study in the latest fortnight (14-21 June) – but just 12 of those swabs were positive for the infection, so there’s uncertainty about the exact infection rate. So the data are consistent with a small fall in the number of people infected in the most recent two weeks, compared to the previous period, or a small rise, or no change in either direction, and that’s why the ONS statisticians are right to say “we do not have evidence that the current trend is anything other than flat.”

“The ONS report also presents estimates of the trends over time in infection rates in the various English regions. Again they comment that the trend appears to have levelled off in some regions. I’d agree with that – though the patterns are not particularly clear, because the statistical uncertainty is greater in relation to a region than to the whole of the country, because the number of swabs taken in a regions is a lot less than the number in the whole country. This also means that, although there are apparently quite big differences in infection rates between regions, we can’t even be really confident on the basis of this survey that there are really regional differences in infection rates at all. And it is not possible to use these results to identify local ‘hot spots’, because the survey does not take enough samples in local areas to provide useable estimates of the infection rate for a town or a city (other than the very largest cities – results are available for London).

“As well as estimating the number of people in the English community population who would test positive for COVID-19, the ONS report also provides evidence of the so-called ‘incidence rate’, which is the rate of new infections in a given time period. That’s different from the overall proportion of people infected at any one time. The overall number of people infected in the most recent 14 days will change, compared to the previous 14 day period, because some people who were previously infected will have recovered from the infection, and some other people will be newly infected. The incidence rate measures just the new infections. The incidence can be more challenging to estimate than the total number of people infected, because there are fewer new infections that the total number of infected people – but a strength of this survey approach, with regular sampling taking place all the time, is that it is possible to estimate the incidence rate and track how it changes over time. A survey that just collected data over a brief period could not do that. The main conclusion drawn by the ONS statisticians from the incidence rate estimation is that the incidence rate may have increased very slightly in the most recent weeks, but because there is even more statistical uncertainty in the incidence rate estimates than in the overall estimates, they cannot be at all certain that this increasing trend in the survey results truly represents the trend in the country. The data are consistent with a small real increase, but they are also consistent with a small decrease, or with no change. The estimated number of new infections per week, based on the period from 14 to 27 June, is 25,000, but the statistical uncertainty around that figure means that it could plausibly be as small as 13,000 or as large as 46,000. But even if the true figure were only 13,000 new infections a week, that’s a pretty substantial number.

“In principle, it would be the incidence figures of new infections that might tell us something about the immediate effects of changes in policy, such as various loosenings of lockdown, but the changes in incidence rate are not really estimated accurately enough to make that link clear – and in any case, if the incidence rate does change, it’s difficult to be sure that any change would be a consequence of the change in policy, as opposed to something that just coincidentally happened at about the same time, for a quite different reason.

“This new report includes some new data from antibody testing – the tests that look for evidence in blood samples that a person was infected with the new coronavirus at some previous time. These estimates are also based on survey data, and indeed on fewer samples than is the case for the swab tests used to check for current infection, so there is quite a lot of statistical uncertainty. Scaled up to the whole community population of England, the ONS statisticians estimate that somewhere between 2,120,000 and 3,660,000 of us would test positive for antibodies. Those estimates have increased a bit since the previous results of antibody tests were announced, but it’s not possible to tell whether the increase is because more people have been infected, or simply because of the considerable statistical uncertainty in the results.”


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.”

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