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INTRODUCTION:

The Public Health England technical briefings are technical documents indicating specific statistics and their breakdowns regarding COVID.

https://www.gov.uk/government/publications/investigation-of-novel-sars-cov-2-variant-variant-of-concern-20201201

In briefings 20, 21 and 22, the numbers seem to suggest that there is a greater number of people (> 50 years old) dying from COVID despite being double-vaccinated.

QUESTION:

Why are the numbers indicating this? Is there some kind of bias (e.g. survivor's bias) by looking at just the face-values?

Briefing 20

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Briefing 21 enter image description here

Briefing 22 enter image description here

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    Not sure this is on topic here as you're not skeptical of their numbers. "Why" questions are generally more suitable to medicalsciences.stackexchange.com Aside, I remember Chinese state-run press "noticing" this... although they stopped short of putting some spin on it, they did cover it along their line of "bad news from the West".
    – Fizz
    Sep 16 at 5:16
  • Twas at newseu.cgtn.com/news/2021-09-11/… The number of deaths per 100,000 was actually not greater for vaccinated, only the number of infections was in some age groups. I think you're looking at the raw count numbers, which is much more expected as the UK now has vaccinated 80% or something like that.
    – Fizz
    Sep 16 at 6:04
  • For the numbers you ask about, it's probably even more complicate because they are cumulative for February-August. The UK vaccinated the elderly first, as did many other countries. And the deaths recorded in that table seem to be after the vaccine, but not death necessarily from Covid, at least based on the table heading.
    – Fizz
    Sep 16 at 6:30
  • As that UK data (unlike say that from Israel) doesn't track/report too well how longer after the vaccine death happened (except relative to the 28-day cutoff), it's even harder to say if vaccine waning (faster in the elderly) might have contributed... or not.
    – Fizz
    Sep 16 at 6:37
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The official (high-level) explanation is

In the context of very high vaccine coverage in the population, even with a highly effective vaccine, it is expected that a large proportion of cases, hospitalisations and deaths would occur in vaccinated individuals, simply because a larger proportion of the population are vaccinated than unvaccinated and no vaccine is 100% effective. This is especially true because vaccination has been prioritised in individuals who are more susceptible or more at risk of severe disease. Individuals in risk groups may also be more at risk of hospitalisation or death due to non-COVID-19 causes, and thus may be hospitalised or die with COVID-19 rather than because of COVID-19.

This is from the surveillance report which is more verbose than the variants report, where you found that table.

I suspect this answer is not exactly satisfactory (to you) as it doesn't say (or even easily enable some calculation) how many deaths one could have expected given some X% vaccine effectiveness (and Y% percent vaccine coverage).

The surveillance report does calculate death rate in vaccinated vs unvaccinated per 100,000 persons. However, this is for a narrower interval "Rates (per 100,000) by vaccination status from week 32 to week 35 2021", not Feb-Aug as in the variants document/table.

enter image description here

When taking into account the vaccination curve(s) for a larger time interval, such per person data makes less sense and you'd/they'd have to consider something like person-exposure days.

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Bad estimates of the number of unvaccinated people can also explain these weird statistics.

Public Health England might have overestimated the unvaccinated population, which means that their estimation of the infection rate for unvaccinated persons is too low.


In addition to potential base rate fallacies pointed out in the other answers above, there might be an even more fundamental measurement error. The estimated infection rate of the unvaccinated population might be off because of bad estimates for the overall population of England. The More or Less podcast hosted by Time Hartford explains: (manual transcription from the audio source starting around 2:40)

We don't actually know how many unvaccinated people there are in England. Not even close. And that matters a lot because to talk about the infection rate in a group of people, we have to know how many people are in that group. Overestimate the number of people of unvaccinated people and you underestimate their infection rate. And we think that's what Public Health England have done.

To figure out the number of unvaccinated people, we know the number of vaccinated people, which is easy -- we know that from NHS records -- and then subtract that number from the total population. But we don't know the total population of England for sure, and even small changes in the estimate of population lead to big changes in changes in our estimates of the unvaccinated remainder.

More or Less goes on to explain that they believe that Public Health England chose a poor proxy for estimating the total population of England. Instead of using the Office of National Statistics (ONS) estimate, Public Health England used the number of people registered with doctors (NIMS). More or Less argues that this registration number is likely an overestimate of England's population, and that necessarily means that their unvaccinated population is also too large. This leads to the estimated infection rate of the unvaccinated population to be diluted and appear artificially lower than expected.

The reported difference between the two data sources for estimating the number of unvaccinated people age 40-79:

  • Based on NIMS data (doctor registrations): 3.5 Million
  • Based on ONS population estimate: 1.5 Million

Podcast Guest James Warm (a COVID modeler) explains that using these different estimates for the unvaccinated population changes the report rather dramatically:

... if you use the ONS data [instead of NIMS] to work out that [COVID] case rate, you get a case rate in the unvaccinated which is about double the rate of those who have two doses of vaccine.

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    This may actually explain the one in the graph (from my answer), which uses some base population(s), but not the ones in the OP's table, which are merely counts of events. Unless the vaccination records were bad/fake...
    – Fizz
    Sep 18 at 5:24
  • There's also a written piece theconversation.com/… on this issue, for those who prefer that to a podcast.
    – Fizz
    Sep 21 at 8:20
  • It would be helpful to explain how this affects the overall vaccination rate. Does it go from 50%->60%? 80%->90%?
    – Rob Watts
    Sep 21 at 19:28
  • For the vaccination rate, because the number of unvaccinated people changes both the numerator and denominator, it depends on the relative size of both populations. In the UK, the number of unvaccinated people is significantly smaller than the number of vaccinated people. This means that halving the estimate of unvaccinated people will make the vaccination rate get closer to 100% by about half the distance. So it could change a vaccination rate of 90% to something more like 95%. Obviously, you'd probably want to actually carry out the calculation, but this is a decent mental estimate.
    – ryanyuyu
    Sep 21 at 19:44
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If we picked 50% of people randomly and vaccinated them, then we would expect fewer Covid infections and fewer Covid deaths among the vaccinated (if the vaccination works). And we would expect the same number of other health problems (unless a Covid vaccination is unhealthy).

But that's not what happens. First, over 80% of adults in the UK are double vaccinated, so all the numbers for the vaccinated can be expected to be four times higher. Second, the unvaccinated tend to be more in groups that have naturally less risk, like young people. High risk + vaccinated will still be at higher risk of death than low risk + not vaccinated.

And consider what happens with more vaccination. If 100% are vaccinated, there will be ZERO deaths among unvaccinated.

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