The Epidemiologist Fallacy marries the Ecological Fallacy with the P-value Fallacy. The Ecological Fallacy is when it is said X causes Y, but X is not measured, and instead a proxy is. The P-value fallacy is to suppose a wee p-value has confirmed X causes Y. The P-value Fallacy can also be done with Bayesian methods, as in the example given.
The paper shown does not use P-values, but does use parameter-based Bayesian measures which exaggerate evidence. The paper is “Particulate matter air pollution and national and county life expectancy loss in the USA: A spatiotemporal analysis” by Bennett et al. in PLOS Medicine.
The real heart of the P-value Fallacy is to suppose measures on parameters of probability models for W (the proxy for X), or even for X, apply to the certainty or uncertainty of Y, which is false.
What we want is this:
Pr(Y | X),
for example Pr(Dementia | PM2.5 exposure), but what we get is
Pr(t(parameter) | W),
i.e. the P-value relating to some parameter-based statistic, or
f(parameter | W),
i.e. some measure or statement about a parameter relating to the proxy. Neither of these are even close to being the same thing as Pr(Y | X). Not even close.
See the video for the Double Epidemiologist Fallacy! This is when X is said to cause Y, but when X is not measured, nor is Y measured. Proxies for both are used, and wee p-values or Bayes factors on parameters are used for “confirmation.”
More in-depth examples and explanations of the The Epidemiologist Fallacy: The Epidemiologist Fallacy Strikes Again — Pesticides & Autism, EPA, CARB, And Air Pollution, Premature Birth Rate Edition, Too Damn Sure: The Epidemiologist Fallacy, Autism Caused By Highways?, Road Rage: Paper Says Living Near Road Causes Dementia, and Uncertainty!
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