select search filters
roundups & rapid reactions
before the headlines
Fiona fox's blog

expert reaction to ONS Infection Survey technical article: analysis of positivity after vaccination, June 2021

The Office for National Statistics (ONS) have released a technical article looking at COVID-19 infection after vaccination.


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

“It has been made very clear, in previous statements and reports about vaccination, that the protection provided by vaccines against infection with the virus that can cause Covid-19 is not perfect.  That’s true for every vaccine for every disease – some people can still become infected even after they have been vaccinated.  This new bulletin reports on an analysis of data from the Covid-19 Infection Survey (CIS) by ONS and their academic partners that throws some light on how likely it is to become infected after vaccination, and on how that chance changes with time since vaccination, with the vaccine that was administered, and with some characteristics of the people involved.

“Vaccines take some time to have their full effect on the immune system – it’s generally been said that vaccines against Covid-19 need two or three weeks to take full effect.  This report emphasises that.  Overall, across both vaccines that were studied (Pfizer/BioNTech and Oxford/AstraZeneca), about one person in every two hundred, who had a first dose, tested positive for the vaccine at some point afterwards.  The rate of infection was considerably less after the second dose, about one in a thousand.  That emphasises the importance of getting both doses, though we’ve got to remember that the overall infection rate in the country was falling during much of the time when these data were collected, and, on average, second doses would have occurred at a later time, when infection risk was less, even for unvaccinated people.  This difficulty of comparing infection rates, at times when the level of infection in the country were different, also may interfere with comparisons between the two vaccines.  The rate of infection after the first dose was smaller in people who had the Oxford/AZ vaccine than for those who had Pfizer – but, on average, the date when people had the AZ vaccine was about a month later that the date when people had the Pfizer vaccine, and general infection rates would have fallen a lot over one month in the period studied.

“The risk of being infected after vaccination is highest in the first 21 days after the first vaccine dose.  That’s not surprising, given that the vaccine might not have had its full effect on the immune system.  What’s perhaps more surprising is that there’s some evidence from these results that the infection rate increase for a time after the first vaccination, peaking at about 16 days after vaccination.  That feature isn’t so clear after adjustments have been made to allow for various differences in characteristics on the people studied, such as their age, gender, ethnicity, and the type of area where they live.  The peak infection rate after the adjustment appears to come earlier, around a week after the vaccination, but it’s still there.  However, as Figure 1* in the bulletin shows, there is a great deal of statistical uncertainty.  There also may be differences between the two vaccines, though the statistical uncertainty means that we can’t be entirely sure of that.

“By the time a month or more has passed since vaccination with the first dose, the infection rate had fallen to a very low level.  Exactly what that rate is would vary quite a bit from person to person depending on their characteristics and on when they were vaccinated.  The bulletin presents estimates for a 60 year old man, not working in health and care, in a household of size 3 that is not multigenerational, living in an area of average deprivation in a major urban area, with no long-term health conditions, who has had one vaccine dose in early February.  In a group of 100,000 men like that, six weeks after their vaccination, ONS would expect somewhere between 2 and 5 of them to become infected each day, allowing for the statistical uncertainties.  That would be the case six weeks after the assumed date of vaccination, so in mid-March – at other times when overall infections in the country were lower or higher, the chance would be different.

“This isn’t the first study** that has shown evidence of an increase in infection rates in vaccinated people during the first weeks after vaccination, compared to just before or at the time of vaccination.  This ONS bulletin suggests various reasons why it might happen.  One, that applies to the CIS data, is that some of the people who tested positive in the survey after vaccination may have initially been infected shortly before they were vaccinated, rather than after.  That can happen because, although people are repeatedly tested for the virus in this survey, that happens at intervals initially of a week and later of a month, so there is no way to tell exactly when someone was first infected.  Other reasons mentioned in the bulletin are that people might have been infected at the vaccination centre, that they may have decided to be vaccinated because people around them were infected (and those people might have passed on the infection to the vaccinated person shortly after vaccination), or that people changed their behaviour after vaccination, maybe mixing more with others before the vaccine had had time to take effect.  The data analysed here can’t tell us which, if any, of these explanations is true.

“Reassuringly, the research found that people who were infected after vaccination were less likely to have any symptoms of Covid-19 than unvaccinated people who became infected, and also had lower viral loads on average.  Lower viral load is associated with less severe disease, and also with a smaller chance of transmitting the infection to others.  So there’s evidence that, even if someone is still infected despite being vaccinated, they are likely to be less ill (and more likely not to be ill at all), and less likely to infect others.

“In the analysis of characteristics of people who tested positive after vaccination, the groups who were more likely to be infected after vaccination mostly correspond to the groups who would be more likely to be infected even if they weren’t vaccinated – people working in patient-facing health care and in care homes, those living in larger households, in areas of higher deprivation, and in rural villages rather than large urban areas.  None of that is very surprising, I think.  Generally, there’s quite a strong effect of age, with younger people showing a considerably higher risk of infection after vaccination than older people.

Further information

“This ONS article is labelled ‘technical’ because it involves some quite complicated statistical analysis.  The analysis approach is reasonably standard, but it is quite flexible, and may require some more ‘tuning’ to ensure that it is dealing appropriately with all features of the data.  Though overall the approach is good, in my view, the writers do point out that this is the first stage of their analysis, and some of the footnotes in the data tables indicate that it may be necessary to reconsider some aspects.  I don’t think that that invalidates any of the main conclusions that I have discussed above, but some of the details may change if and when they publish further similar analyses.”

* Annoyingly, Figure 1 seems not to say what the units are for the rate of new infections. I believe it is the rate of testing positive per 100,000 participants per day.

**Another study, also using CIS data, involving the same researchers, and mentioned in this ONS bulletin, is at Note that this is a preprint that hasn’t been through peer review yet. The page that I have linked to on the preprint server reports, rightly, that there is a newer version of the preprint available, but something seems to have gone wrong with the Figure numbering and the diagram that shows this effect of the time after vaccination is rather hard to find in the newer version. (The relevant diagram is identical in both versions.)



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.”

in this section

filter RoundUps by year

search by tag