How to Lie with Statistics - What is the real percentage of Unvaccinated individuals in England?

Trying to figure out why there are so many numbers bandied around.

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What is the real percentage of unvaccinated individuals in England? It should be an easy equation. We take the total population, we minus the number of people vaccinated with at least one shot. We divide this number by the total population and we multiply that number by 100.

(Total population - Vaccinated population) / Total population * 100.

So if the total population was 1000 and 750 people were vaccinated the equation would be

1000-750 = 250

250/1000 = 0.25

0.25 * 100 = 25%

25% of the fictional population are unvaccinated. Simple. But apparently it’s not. As I wrote about a few days ago, the BBC, when promoting their new ‘documentary’ about the unvaccinated, claimed the number of unvaccinated adults in England was 8 percent.

However, the UK Health Security Agency (UKHSA), in their weekly COVID-19 surveillance report produce this chart, showing almost 30% of the population unvaccinated, or just under 20% of adults.

A comment on my previous article suggested they are just using government figures. Looking at the government data shows that only 6.7% of the population (12+) are unvaccinated.

Today, the BBC are again reporting that 3 million adults are still unvaccinated.

BBC News (UK) @BBCNews

Covid: 3m adults still unvaccinated in England

bbc.in3m adults in England still have no Covid vaccineSome are vulnerable people who could get extremely sick if they were to catch Covid, warn experts.

This BBC article is reporting on a National Health Service (NHS) England report which is where the 3 million number comes from. (The NHS report wants to redouble efforts to reach the unvaccinated and have set themselves the challenge to vaccinate 500,000 more people, as well as increase the (first) booster rate from 73% to 80% within four months).

In the report, I couldn’t see where they got the 3 million figure from but if true would represent 7% of the adult population. To get this percentage I used the latest census data (from 2021) which gives 43,432,100 over 20s in England. Unfortunately, the age categories are 15-19 and then 20-24 so it is impossible to separate out 18-20 year olds.

So 7% of adults? 8% of adults? 20% of adults? 30% of the whole population? What is the real percentage of unvaccinated adults in England. This is bugging me, I want to know the real number.

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The formula at the beginning says we need ‘total population’ and ‘vaccinated population’. That’s it, it can’t be that hard. So let’s start with vaccinated population.

Data from the government website is up to 12 July, whilst the UKHSA data is only weekly, so up to 3 July 2022. So I’ll look at the data up to 3 July for both so it is consistent.

Government data show 45,090,778 first doses have been give in England, whilst the UKHSA shows 43,971,294. A difference of 1,119,484. So firstly, why the difference?

A document explaining how the information is obtained says that “a small number of these vaccinations will have been administered to individuals aged under 12, therefore the uptake reported will be a slight overestimate. Some of the vaccinations included in calculating the overall vaccine uptake rate will have been administered to people who live outside of England, but similarly vaccinations of any English residents who were vaccinated outside of England will not be included.”

So under 12s have actually been included. If we add under 12s to the UKHSA data we get 44,480,115 which leaves a difference of 610,663. It seems there may be some vaccine tourism going on with potentially over 600,000 non-English people getting vaccinated in England.

The UKHSA data is extracted from the National Immunisation Management Service (NIMS). NIMS data includes individuals registered with the NHS who are currently alive in the resident population.

So, the difference in number of people having been vaccinated may either be explained by individuals not registered with the NHS or some kind of vaccine tourism, whereby non-English visitors get vaccinated whilst in the country and are added on to the government numbers. (As I’ll show later on, it is more likely to be vaccine tourism as NIMS data is more likely to be overestimating things)

It is unclear which number is the most reliable as it can’t be ascertained whether the additional numbers are unregistered English citizens or foreign ‘vaccine tourists’. I will therefore go with the government figure of 45,090,778 as it may include a lot of people who are not registered with the NHS.

Denominator

Next on to the denominator, population size.

Using the explanatory information, we are told “the overall uptake figures reported on the GOV.UK dashboard…are all calculated using Office for National Statistics (ONS) 2020 mid-year population estimates as the denominator.”

In a further explanatory paper the ONS 2020 mid-year population is estimated at 56,550,000. However, the latest census data from 2021, puts the English population at 56,489,800. Not a bad estimate to be fair!

I will use the entire population (instead of just adults) as the explanatory data on vaccinations says it includes under 12s.

So using the ONS denominator, we can complete the equation.

56,489,800-45,090778 = 11,399,022

11,399,022/56,489,800 = 0.2

0.2 * 100 = 20%

So using that data we can conclude that 20% of the entire population is unvaccinated.

However, the UKHSA use the NIMS data which includes all individuals registered with the NHS. This puts the total population at 63,391,306, a massive 6.9 million difference! NIMS data is likely to be an overestimate due to reporting lags with death registration data but not by 6.9 million! It seems like a lot of people didn’t fill in the census, tut tut.

Using the NIMS data gave the UKHSA result (previously mentioned) of almost 30% of the population unvaccinated.

However, as I am feeling generous, I will assume the NIMS data is overreporting and split the difference. This gives a population size of almost 60 million. Using this denominator gives the unvaccinated percentage as 25%.

So, to sum up, the only way to achieve an unvaccinated rate of around 7-8% is to use the government data on total number of first dose vaccinations for over 12 year olds and to use the ONS denominator for the population size.

However, there is a discrepancy between the stated number of vaccinations given in the government and UKHSA data. Exploring where this discrepancy is from leads us to conclude that the government data actually includes under 12s when it says it doesn’t. It also includes vaccinations given to people who don’t live in England.

Furthermore, there is a discrepancy in population size and it would be reasonable to conclude that people registered with a GP would be more accurate than census data. This is because almost everyone needs to see a GP at some point but many people can’t be bothered to fill in a census, don’t realise they have to, or don’t want to if they are in the country illegally.

Therefore, considering all the facts, it is much more reasonable to say the unvaccinated population is 25-30%.

And finally, even thought they don’t like to admit it, the government actually agree with me. Even though at the top of their website, the headline figure states a 93.3% uptake, at the bottom of the page they provide a heatmap which almost exactly matches the UKHSA data. Therefore, confirming the 25-30% unvaccinated rate.

So, any nonsense of only 3 million unvaccinated, or a 7-8% unvaccinated rate is completely false, or at best not presenting all the facts.