There has been a lot of talk about a UK Health Security Agency (UKHSA) technical report. It includes information on COVID-19 case rates in England for vaccinated and unvaccinated groups (Table 5). For some the immediate reaction to these data has been outright disbelief, others have used the data to support pre-existing, and incorrect, views that vaccines are not effective. Neither of these reactions is right.

**Understanding the issues properly is extremely complex, but what we do know with some certainty, is that while the vaccine will not stop the spread of the virus completely, it has been shown to help improve outcomes.**
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Are the two groups in question comparable? It is easy to see that there may be different behaviours in people who have had two vaccinations compared to those who have had none.

**One hypothesis is that those with two vaccinations are more likely to get tested, meaning the case rates will look relatively higher for this group compared to the unvaccinated group. There will also be different risks associated with each group, the vaccination programme prioritised vulnerable groups and frontline health and social care workers, so includes those who are more at risk of infection. **We haven't seen evidence to quantify the impact of these risks and behaviours, but it's likely there will be an impact.

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**In the calculation of COVID-19 case rates the most significant choice is the decision on what population estimates to use to calculate the rates ("the denominator").** There are two obvious choices: the National Immunisation Management Service (NIMS) or the ONS mid-year population estimates. Each source has its strengths and limitations and

**we don't yet know the true** figure for the denominator. [..]

There are many advantages to using NIMS, not least because it is consistent with international approaches to considering immunisations and allows for analysis which would not be possible using aggregate population estimates. However, we also know that

**NIMS overestimates the population**. Similarly, there are strengths in using ONS mid-year estimates, but we know these can have particular difficulties for small geographic breakdowns. We also know that the time lag created by using mid-year 2020 estimates has a disproportionate impact in older age groups – for example, it means that in more granular age bands some older age groups show more people having been vaccinated than the ONS population suggests exist. [..]

Looking just at the adult population,

**Figure 1 shows the different results which come from using the two different denominator options** for the population who have never had a COVID-19 vaccine.

[..] While we don't yet know the true figure for the unvaccinated population, this seemingly simple choice has a huge impact. It is particularly problematic in this circumstance because

**any error in the total population estimate is applied in its entirety to the unvaccinated population.**
As an example, for the 70 to 79 population, the NIMS figure is just 4% higher than the ONS mid-year estimates (5.02 million and 4.82 million respectively). These figures can then be used in combination with the data on total people vaccinated from NIMS to estimate the total number of people not vaccinated. In doing this, the difference of nearly 200,000 in the total population estimates is applied entirely to the relatively small number of 70 to 79 year olds who are not vaccinated. It means the NIMS estimate for the unvaccinated population in the 70 to 79 age band is 363% higher than the estimate of those not vaccinated based on the ONS mid-year estimates.

**So, an estimate 4% higher at the 70 to 79 age band has led to an estimate 363% higher in the estimate of the unvaccinated population at that age band.** This has a huge impact on the case rates for this group, and the conclusions drawn from the data.