COVID Data Follies: Vaccination Rates, Relative Risk, and Simpson’s Paradox





On Monday, December 6, 2021, I gave a talk with the title “COVID Data Follies: Vaccination Rates, Relative Risk, and Simpson’s Paradox”, to the Actuarial Science program at Illinois State University (thanks for the t-shirt, y’all!):

You may have heard statistics in the news that most of the people testing positive for COVID, currently, in a particular location, or most of the people hospitalized for COVID, or even most of the people dying of COVID were vaccinated! How can that be? Does that prove that the vaccines are ineffective? Using real-world data, the speaker, Mary Pat Campbell, will show how these statistics can both be true and misleading. Simpson’s Paradox is involved, which has to do with comparing differences between subgroups with very different sizes and average results. Simpson’s Paradox actually appears quite often in the insurance world.

I will embed a recording of the event, copies of the slides, the spreadsheets, and the links from the talk.

Author(s): Mary Pat Campbell

Publication Date: 8 Dec 2021

Publication Site: STUMP at substack

Simpson’s Paradox and Vaccines




So what the chart in the tweet linked above is really showing is that, within the 10-59 age band, the average unvaccinated person is much younger than the average vaccinated person, and therefore has a lower death rate. Any benefit from the vaccines is swamped by the increase in all-cause mortality rates with age.

I have mocked up some illustrative numbers in the table below to hopefully show Simpson’s Paradox in action here. I’ve split the 10-59 age band into 10-29 and 30-59. Within each group the death rate for unvaccinated people is twice as high as for vaccinated people. However, within the combined group this reverses – the vaccinated group have higher death rates on average!

I and others have written to ONS, altering them to the concerns that this data is causing. It appears from a new blog they have released that they are aware of the issue and will use narrower age bands in the next release.

Author(s): Stuart Macdonald

Publication Date: 22 Nov 2021

Publication Site: COVID-19 Actuaries Response Group