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Simpson's paradox strikes again: Refuting reports vaxxed have 5x case fatality rate than unvaxxed

Updated: Sep 15, 2021

I have seen a lot of people obsessing with Table 5 of the August report put out the UK Public Health England focusing on the Delta variant


In Table 5 on page 17 of this report, you can see that:

  • There were 402 Covid deaths among 47,008 fully vaccinated for case fatality rate (CFR) of 0.86%, meaning 0.86% of confirmed Delta COVID-19 cases resulted in death.

  • There were 253 Covid deaths among 151,054 unvaccinated for CFR=0.17%

In these data, we see that the CFR for vaccinated was >5-fold higher than for unvaccinated (0.86/0.17=5.02). Is the case fatality rate really 5x higher for vaccinated than unvaccinated? I've heard some people say this, claiming it is evidence of Antibody Dependent Enhancement (ADE), in which an immune response in fact leads to worse outcomes if the person gets infected.

Fortunately, in this report they also split data out by age (<50/>50).

For the older group, the CFR for vaccinated (1.81%) is 3.3-fold LOWER than CFR for unvaccinated (5.96%). This suggests, for the group at real risk of death from COVID-19, with Delta the risk of death was more than 3-fold lower in vaccinated breakthrough infections than unvaccinated infections. For younger group, CFR for vaccinated (0.05%) is 1.57-fold higher than CFR for unvaccinated (0.03%). This may raise some concerns and is worth looking into. However, note how low the death numbers are -- only 13 in the entire vaccinated cohort of >25,000 infections, and there are no details on the characteristics of these individuals in the report. This is an extra 5 deaths over what we would expect if the CFR was no higher than in unvaccinated. Here we see another clear illustration of Simpson's paradox, given we have:

  • A confounding factor (age) that is strongly associated with both:

  • the outcome (death), since older people are MUCH higher risk to die of COVID-19, and

  • the exposure (vaccination), since older people had MUCH higher vaccination rates.

This phenomenon can produce a wildly distorted view if analysis is done without stratifying or otherwise adjusting for the confounding factor (here, age).


This phenomenon pops up ALL THE TIME right now, given how age is strongly associated with both vaccination status and severe disease outcomes in most places.


Now, to illustrate how strong this Simpson's effect is here, suppose instead of 13 deaths in the <50yr vaccinated group, there were 2 deaths. See the following table.

In this case, we would have that for both age groups, the CFR was much lower for vaccinated than unvaccinated by a factor of 4.2x for <50yr and 3.3x for >50yr, but if you compute it without stratification, you find the CFR for vaccinated is 5x HIGHER in vaccinated than unvaccinated. This shows how extreme this effect can be when you have a confounder (age) so strongly associated with both the outcome (death) and exposure (vaccination). Thus, I hope people realize soon that any estimate of vaccine effectiveness must adjust for age by stratification or some other approach or it will give very confusing and misleading results.

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eliphaslv
eliphaslv
Sep 25, 2021

'climbing on mirrors' it's getting quite boring, to be honest. Vaccinating very young people, under 20 let's say, was a nasty, irrational, silly idea. We will discover how much in near future.

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eliphaslv
eliphaslv
Sep 25, 2021

Mr morris, in Italy we say 'climbing on mirrors' to define the style of your effort. For under 50 it's not worthed at all being vaccinated, mainly cause we have a remarkable number of side effects. Not just in statistics, that exit anyway if you really look for them, cause they've been hided, but in everyday life. I'm an extrovert man, plenty of friends, so I've listened to and personally observed more damages - sometimes quite serious, ever heard about impotence? - then benefits. I'm not vaccinated at all, I go around and I've never had particular care, I'm under 50 and I'll be the evidence, in next months, that it would have been ok for almost everybody in that…

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Katiana Cordoba
Katiana Cordoba
Sep 21, 2021

We can clearly see here that vaccines might reduce deaths for people older than 50 however, (they don't talk comorbities and weight) but it doesn't do the same for those younger than 50. Why would they impose this vaccine as mandatory? Why instead of being really neutral, this website seems to be one to protect vaccine efficacy? If it was neutral there were a variety of information. The way they speak is protective of the narrative. Be careful with this kind of websites and stay very critical of what they inform.

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Replying to

would need to redo this analysis since the latest surveillance reports show vaccinated have higher rates of infection (on a per 100k basis). Much higher in fact in all groups over 30. Yes the data still bears out that deaths are 1/3rd or lower for vaccinated (although for under 50 the difference is so small on an absolute basis). Which is an interesting conundrum, because if vaccinated are spreading at twice the rate of the unvaccinated, and the deaths are 1/3rd, then the infection fatality rate is 1/6th. However, one has to ask, are the vaccinated, through higher infection rates, creating vaccine resistant mutations in the virus...

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Jack Reacher
Jack Reacher
Sep 18, 2021

Jeffrey, the numbers show that the CFR for < 50 yo is very low, and there is probably no statistical difference between vax and unvax. This only reinforces the idea that:

1. mandatory vaccination for all age group is absurd.

2. emergency pandemic measures are unwarranted. CFR is below or similar to influenza (depending on which season).


For older than 50 yo, data shows an ARR of 4.15% and RRR of 69%.

Also missing from your table are the 1 dose vaccination which gives about similar results for two doses. And you can check the latest Technical briefing 22.

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Jeffrey Morris
Jeffrey Morris
Sep 24, 2021
Replying to

This post does not push mandates. And with ARR you have to be careful with interpretation because they vary wildly depending on time frame (this one is short) and conditions in terms of number of community infections.

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Tom Moench
Tom Moench
Sep 16, 2021

Kathy, Dr. Campbell, reputable medical guy and good at explaining data, addressed your concern months ago here…

https://youtu.be/SHH1vWD19Fw

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Replying to

I disagree with you on Dr Campbell. I listened to quite a few of his early presentations but found his framing and analysis to be unsatisfactory. In fairness he would admit that the numbers/statistics are not his strong point, but what I took most issue to was his frequent conclusion: "this rate is about the same as that found in the general population, so it is acceptable ".


No! No! No! This is entirely the wrong conclusion. The correct question would be "Would this adverse event/death/incapacitation have occurred without the vaccination?"


This foundational question is not being answered by scientists, it is instead simply ignored. Therefore no conclusions can be drawn; a tragedy, in my view.

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