Take care with claims about unvaccinated case rates

·2 min read

ITV’s political editor, Robert Peston, wrote a Twitter thread with the headline: “Infections higher among double vaxxed for those [aged] 40 to 79 than for non-vaxxed.” ITV changed that headline, but Peston was surprised that these figures “occasioned so little debate”. So let’s debate them.

A Public Health England report on 9 September showed that over the previous four weeks there had been, for example, more than 97,000 cases among people aged between 40 and 49. The huge majority (more than 82,000) had been vaccinated. This is expected when vaccine coverage is high and protection not perfect: most car occupants who die in road incidents are wearing seatbelts.

The surprise came from the reported case rate per 100,000 population being higher for fully vaccinated people (1,116) aged 40 to 49 than for unvaccinated (880), which appears to question the effectiveness of the vaccines. But the problem is that we don’t know how many people have not been vaccinated, because we don’t know how many people live in England, thus demonstrating the need for the recent census.

PHE uses National Immunisation Management System (Nims) estimates of 8.1 million adults aged 40 to 49 in England. These numbers depend on GP records and tend to overcount. The Office for National Statistics (ONS) also produces population estimates, based on the 2011 census, migration and death registrations and estimates 7.1 million adults in that age group, a million fewer than Nims.

Related: Covid levels rising among schoolchildren in England, data shows

Up to 5 September, NHS England reported 6.4 million people in that age group had received a Covid-19 vaccine dose. So the ONS population estimate leaves about 700,000 unvaccinated people aged 40 to 49, while using Nims means 1.7 million. This is a massive difference.

ONS figures will not be perfect, but suggest about 2,000 confirmed cases per 100,000 unvaccinated people aged 40 to 49, twice the rate as in the vaccinated group, and roughly what we might expect. Similarly, ONS estimates give lower case rates in fully vaccinated people than unvaccinated in all ages below 80. There may also be other differences between vaccinated and unvaccinated groups, including the propensity to get tested.

It is unfortunate Robert Peston’s tweets have been misinterpreted by those sceptical of vaccines.

• David Spiegelhalter is chair of the Winton Centre for Risk and Evidence Communication at Cambridge. Anthony Masters is statistical ambassador for the Royal Statistical Society

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