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Comment by souterrain | Hacker News Reader

> The results suggest that 277 cases of cardiovascular disease would arise each year in 100,000 heavy consumers of ultra-processed foods, versus 242 cases in the same number of low consumers.

So, one is 14% more likely. But at 0.242% and 0.277% chance the correlation seems unusual to even mention.

I’m not a statistician. Is this typical of such studies?

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Oh, and as for the model used, Cox multifactorial analysis is fine, except they forgot to add an unknown member to the parameter set. Without it, this cannot measure unknown unknowns and you cannot say if the analysis makes sense. If unknown covariate has higher hazard ratio than known covariate, something is off. Another way to validate is to calculate goodness of fit for each covariate.

The strong assumption in Cox model is that hazards are independent constant multiplicative which might not be true at all. (Such as limited detoxication capacities or hazards varying over time, or hazard clusters, or synergy between hazards. These are all examples of nonlinearities.)

In case anyone wants a primer: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2394368/

FAMD and MFA would show whether the simple nonparametric linear constant hazard model holds between paired variables.

This is correlation on a self selected group. A different statistical correction is needed for those. (These people are not being fed this diet despite their wishes, so there are lifestyle, metal health and other correlates.)

Thus causality can go either way with multiple factors interfering. The experiment is not powered enough to actually derive a conclusion. They'd need at least a 2 million sample sizes for each group to show anything other than noise, and that's with the ultra fancy multilinear math used in genetics to untangle multiple factors. (Advanced variants of FAMD.)

Welcome to land of observational studies.

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