Simpson's Paradox, Vaccine Effectiveness, and the Delta Variant // Math Minute [#38] [STATISTICS]

Описание: Have you heard? New data came out of Israel in August of 2021, and vaccine effectiveness is in the tank. Must be the Delta Variant, right? Not necessarily.

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There's a statistical phenomenon called Simpson's Paradox that I think better explains what's going on with the data in Israel. Simpson's Paradox occurs when looking at a data set as a whole tells a very different story than when you chunk it according to certain variables. In the case of the vaccine data here (taken from https://www.covid-datascience.com/pos..., if you break the data into smaller chunks based on age, what's happening becomes more clear.

Vaccine effectiveness remains high within an under-50 bracket and an over-50 bracket. But because the over-50 bracket is both the most likely group to be vaccinated and the most at-risk group, the cases among the vaccinated, over-50 population end up overwhelming the cases among every other group, dragging down full population effectiveness.

Even understanding something like that was going on in the background, I had trouble piecing together why the numbers were working the way they were. So I modeled out the data in Desmos so I could play around with it more easily. You can see my work here: https://bit.ly/SimpsParadox. That graph charts total population vaccine effectiveness as the percentage of the population under 50 rises. You can see how changing underlying variables, like case rates and percentage of the given populations vaccinated will change the shape of the effectiveness curve.

Ultimately, one of the things I love about mathematics is that it allows us to explore and investigate phenomena like this and come to a better understanding of the world as a result.

There are, of course, other correlations you could also explore. You could imagine splitting up the population by what type of vaccine they had: moderna vs. pfizer. You could look at how the vaccine rollout affected different populations at different times. You could look at the difference between variants over time, comparing delta to omicron for example. But ultimately, Simpson's paradox tells us that there may be confounding factors as we split up the data into more and more groups.

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