Baseline shenanigans

Vaccine denial and vaccine hesitancy have a very long history and as with many of these things, overt nonsense is mixed in with genuine concerns. Many socially and economically disadvantaged groups have reasons to be wary of the medical profession and many developing nations have reasons to be wary of initiatives from Western governments and/or companies for example.

However, what we’ve seen almost in real-time is vaccine misinformation shift from being a fringe belief only partly connected with ideology to something that is increasingly not just political but politically partisan.

As always, my canary in the coal mine for tracking this is Theodore Beale aka Vox “I’m not a neo-Nazi” Day. Now Day has a long history of pushing vaccine misinformation and fears, including hyping up concerns about mercury in vaccines and the false claims of vaccines being a cause of autism. Yet despite a history of raising fears about “vaccine safety” that date back to at least 2004, the volume of his posts about vaccines split approximately 50/50 from prior to 1/1/2021 to after 1/1/201*

His latest (false) claim is that “Vaccinated 5x More Likely to Die” He is wrong and demonstrably so but how he gets to this conclusion is instructive. If you guessed that he gets there via bad numeracy and poor reasoning you will be correct. If you also guessed “via second-hand sources” you would also be correct.

Now we will have to do some arithmetic but it’s only division.

There is usually a nugget of truth somewhere and in this case, the nugget is a UK government report on the prevalence of different variants of the SARS CoV-2 virus (alpha, delta, alligator etc). You can find the report here

Vox D then grabbed some other persons attempt to spin one table from that report and then did some basic arithmetic to jump to an erroneous conclusion.

“Do the math. An unvaccinated individual in the UK who contracts COVID has a 1 in 597 chance of dying. A fully-vaccinated individual has a 1 in 117 chance of dying, which is 5.1 times greater.”

Where is the error? Not in the division. He divided some numbers and got those values but simply doing a calculation correctly isn’t the same as doing the right calculation.

The data he worked with is from a table on pages 18 & 19 from the report above. In fact, he’s mainly using the last row of the table which spills over onto page 19. I’ve put together the rows and columns he used but I won’t include all the other columns to focus on the numbers he uses:

Total2 dosesUnvaccinated
All Deaths (delta)742402253
All delta cases30001047008151054
Per cent0.25%0.86%0.17%
1 chance in404.3261456116.9353234597.0513834
Data taken from Table 5. Attendance to emergency care and deaths of confirmed and provisional Delta cases in England by vaccination status
(1 February 2021 to 2 August 2021) with added calculations

Out of context, that looks alarming and confusing! Yeah but no. It’s horribly misleading and relies on two errors. The first is that you aren’t comparing like with like from the data in the table itself and the second is a baseline error. Day claims that a “fully-vaccinated individual has a 1 in 117 chance of dying” but that conclusion is demonstrably false.

So the first error can be seen directly in the table. The data split cases by age: <50 years old and ≥50 years old. That’s obviously important with mortality statistics (and even more so with COVID19) but also with vaccination status.

Do the same calculations again but this time use the data from the table that is specific to the age groups.

Total2 dosesUnvaccinated
Deaths <50711348
Cases <5026574925536147612
Per cent0.03%0.05%0.03%
1 chance in3742.9436621964.3076923075.25
Deaths ≥50670389205
Cases ≥5033736214723440
Per cent1.99%1.81%5.96%
1 chance in50.3522388155.1979434416.7804878

The first problem with Day’s calculation becomes apparent. The proportions of the two age groups is different between the 2 dose group and the unvaccinated group. A greater proportion of the unvaccinated over 50s died compared to the 2 doses over 50s.

So OK, Day screwed up that “5.1 times greater” figure and screwed up the probability by comparing two groups that were demographically dissimilar but don’t the data still point to their being an issue? After all for the under 50s that small percentage who died is still bigger than the percentage for the unvaccinated? Still no because it ignores a key fact about the UK for the time range the table applies to.

Britain started its vaccine program very early and by 2 August 2021, a majority of people had been vaccinated The vaccines aren’t foolproof, they do reduce the risk of catching COVID19 and do reduce the chance of hospitalisation and death substantially but there’s always some chance. So we also have to factor in the proportions of the population vaccinated.

By 2 August, 71% of the UK population over 16 had received two doses of a COVID19 vaccine. 86.2% had received at least one dose, which leaves 13.8% unvaccinated at all. We can’t directly apply those numbers to the numbers above because obviously, those proportions shifted over the several months worth of data shown in the table above. The number of cases from fully vaccinated people comes from a much bigger group of people than those from the unvaccinated. Not only that but you are unlikely to have the same patterns of hospital admission between vaccinated and unvaccinated people as well as other demographic differences between the two.

*[based on using date ranges in a site-specific Google search – your mileage may vary]

14 thoughts on “Baseline shenanigans

  1. Someone elsenet pointed out, last week, that these comparisons aren’t controlling for comorbidities (things like existing heart problems, cancer, and immune suppressant drugs). In a lot of places, people who are at higher risk have been prioritized for vaccination. So the comparison isn’t “cancer patient who has been vaccinated” vs “cancer patient who hasn’t been vaccinated”–it’s “cancer patient who has been vaccinated” vs “otherwise healthy person who hasn’t been vaccinated.

    Also, those comorbidities include people who are on immunosuppressant drugs, such as organ transplant recipients and people with lupus. It looks as though at least some of immune suppressants can interfere with the vaccine, which further complicates the comparisons. All fascinating and probably stress-inducing if you’re a clinician trying to decide which of your patients should be getting the booster shots first, or whether it’s worth risking an interruption in their ongoing treatment before giving the vaccine, but confusing at the statistical/epidemiological level.

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    1. Yes indeed. Part of the reason why I picked on this example is the data itself provided a quantifiable instance of it being not a like-for-like comparison. However, all those issues (particularly who was sensibly prioritised for vaccination) play a role also.

      Also, given how bad covid got in the UK “unvaccinated” doesn’t mean “no immunity” – many more of the unvaccinated in the UK will have had a covid infection compared with say Australia or NZ

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  2. The quick sanity check is that the case fatality rate in a more or less unvaccinated population at the start of the year was 2.0%. If vaccination made you more likely to die the current case fatality rate would be predicted to be higher. In reality, it’s 0.3%. (Though, in addition to not being happy about the governments’ willingness to accept a rate equivalent to 35,000 deaths per year, I’m not happy about the trajectory of COVID deaths.

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    1. You put a smiley, but I think “technically” is actually a very important word.

      It’s also shorter than saying “I’m not a neo-Nazi, but I believe in and promote the same things they do”.

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  3. Beale isn’t a neo-Nazi the same way Arnold Leese didn’t believe in the Holocaust. (Look it up, then shudder.)


      1. I’m actually not so sure. Like most of the on-air talent at Fox appears to have done, he may have gotten vaccinated while spitting out anti-vaccine nonsense. I mean, their audience will never know, right? (Tucker Carlson, I’m looking at you.)

        At the same time, you do see reports at the lower levels of the conservative noise machine where regional conservative talk radio hosts didn’t get vaccinated and died from COVID. This is very, very, very roughly the area where Teddy is in the conservative media hierarchy, and I think we’ve seen other examples where he’s believed his own bullshit. Teddy is not always as smart as he thinks he is.

        tl;dr I wouldn’t be surprised if he wasn’t vaccinated, either.

        Liked by 2 people

    1. Well it is not important if the math is correct, it looks correct. So fine win for rethoric, Aristotelle. (Pedestrian people call it lying, but the truth doesn’t matter to genius Beale)
      But this is actually a thing that is common ground for many of the pups and scrappys. We had a lot of mathfails or fails from other logic disciplines from them, so this is part of a pattern.

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