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expert reaction to the latest fortnightly release on the Coronavirus Infection Survey looking at antibody and vaccination data for the UK, 9 June 2021

The Office for National Statistics (ONS) have released the latest report from the COVID-19 infection survey, looking at antibody and vaccination data for the UK.


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

“The latest fortnightly ONS release on antibodies and vaccinations in the UK community population shows a continuing increase in the numbers of people who test positive for antibodies to the virus that can cause Covid-19. The data now go up to the week ending 23 May. Two weeks before that, as reported in the last ONS bulletin, about 75% of adults aged 16 and over would have tested positive for antibodies (slightly fewer in Scotland than in the other UK countries). Now that figure is up to about 80%, four in five, in England, Wales and Northern Ireland, and slightly lower (just over 70% or seven in ten) in Scotland.

“The estimates are based on a survey, and any estimates based on a survey are subject to some statistical uncertainty. But the people tested for the survey form a reasonably representative sample of the population, and adjustments are made to allow for aspects that aren’t entirely representative, so I wouldn’t expect any major biases. The statistical margin of error means that the true percentage who would test positive for antibodies might be a bit less than 80%, or a bit more, but not too much (For England, the central estimate is about 80%, but the margin of error goes from about 77% to about 83%. The margins of error are wider in the other UK countries, because the numbers of people tested in the ONS survey are smaller.) This is generally good quality data.

“As these numbers increase, people always ask whether they are high enough for herd immunity. That’s not straightforward to answer, and to some extent goes beyond my own expertise. But I’ll make a few points.

“First, calculations of the herd immunity threshold involve the numbers who are immune from further infection, and having antibodies isn’t the same as being immune. There are other aspects of the immune system, particularly cell-based immunity, that antibodies don’t measure. And it’s possible that antibody levels that are too small to detected by these blood tests might still contribute to immunity. So testing for antibodies can’t give a precise measure of levels of immunity.

“It’s possible that the association between immunity and antibody positivity is different in people who were infected naturally, and people who have antibodies because of vaccination. The results in this bulletin can’t distinguish between these two possible sources for antibodies. ONS have said1 that they have been using a method of testing for antibodies that can make that distinction since March, but that is not yet reflected in this bulletin. Even if this makes no difference to immunity, it could be useful to know how many people got antibodies from infection and how many from vaccination.

“Second, figures that have been previously reported for the level of immunity needed for herd immunity might well no longer apply. The level depends on how infective the virus is. The Alpha (‘Kent’) variant is more infective than the original versions of the virus, and evidence has recently emerged that the Delta (‘India’) variant is more infective still – that will put up the required level compared to calculations from before one or both of these variants became dominant in the UK.

“Third, we’ve got to remember that the 80% figure from these data is only for the population aged 16 and over, and about a fifth of the population of the UK is aged under 16. People under 16 are extremely unlikely to get seriously ill if they are infected, but they can be infected and they can pass the infection on to others, even if that is rather less likely than for older people. Some of the under 16s will have antibodies because they have previously been infected, but the figure in under 16s will be considerably less than 80%, so the national figure for the whole population must still be considerably less than 80%.

“Finally, it’s worth pointing out that herd immunity wouldn’t mean no Covid-19, even if the immunity is very long-lasting. Some people will still be susceptible to infection, and there can still be outbreaks involving those people. Those outbreaks will be likely to peter out pretty quickly of their own accord, it’s true, but not without putting at risk people who are not immune.

“The figures in this bulletin for percentages of people vaccinated are, as the bulletin makes clear, not the same as those that come from other sources (for example, those reported daily on the dashboard at But that doesn’t mean they are definitely worse (or better), just different. There are possible issues with the percentages on the dashboard too. To work out what percentage of the population, or of an age group, that have been vaccinated, you need to know how many were vaccinated, but also how big the population is. The numbers vaccinated are probably known pretty accurately. The population sizes aren’t. Some of the dashboard figures use ONS population estimates, which won’t be exact because it’s a long time since the last Census. (The figures from this year’s Census aren’t yet available. ONS don’t just use the figures from the 2011 Census for current population estimates, they revise them on the basis of other data, but they can’t be perfect.) Other dashboard figures use NHS estimates of the numbers on various NHS records, but again they can’t be totally accurate.”





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 its Advisory Committee.  I am also a member of the Public Data Advisory Group, which provides expert advice to the Cabinet Office on aspects of public understanding of data during the pandemic.  My quote above is in my capacity as an independent professional statistician.”

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