Take care with claims about unvaccinated case charges | David Spiegelhalter and Anthony Masters

ITV’s political editor, Robert Peston, wrote a Twitter thread with the headline: “Infections larger amongst double vaxxed for these [aged] 40 to 79 than for non-vaxxed.” ITV modified that headline, however Peston was stunned that these figures “occasioned so little debate”. So let’s debate them.

A Public Well being England report on 9 September confirmed that over the earlier 4 weeks there had been, for instance, greater than 97,000 instances amongst folks aged between 40 and 49. The massive majority (greater than 82,000) had been vaccinated. That is anticipated when vaccine protection is excessive and safety not excellent: most automotive occupants who die in highway incidents are carrying seatbelts.

The shock got here from the reported case fee per 100,000 inhabitants being larger for absolutely vaccinated folks (1,116) aged 40 to 49 than for unvaccinated (880), which seems to query the effectiveness of the vaccines. However the issue is that we don’t understand how many individuals haven’t been vaccinated, as a result of we don’t understand how many individuals dwell in England, thus demonstrating the necessity for the latest census.

PHE makes use of Nationwide Immunisation Administration System (Nims) estimates of 8.1 million adults aged 40 to 49 in England. These numbers rely on GP information and have a tendency to overcount. The Workplace for Nationwide Statistics (ONS) additionally produces inhabitants estimates, primarily based on the 2011 census, migration and dying registrations and estimates 7.1 million adults in that age group, 1,000,000 fewer than Nims.

As much as 5 September, NHS England reported 6.4 million folks in that age group had obtained a Covid-19 vaccine dose. So the ONS inhabitants estimate leaves about 700,000 unvaccinated folks aged 40 to 49, whereas utilizing Nims means 1.7 million. It is a large distinction.

ONS figures won’t be excellent, however counsel about 2,000 confirmed instances per 100,000 unvaccinated folks aged 40 to 49, twice the speed as within the vaccinated group, and roughly what we’d count on. Equally, ONS estimates give decrease case charges in absolutely vaccinated folks than unvaccinated in all ages under 80. There may be different variations between vaccinated and unvaccinated teams, together with the propensity to get examined.

It’s unlucky Robert Peston’s tweets have been misinterpreted by these sceptical of vaccines.

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

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