[gwillen]

I'm not a statistician, but I think there's a bit in your excerpt that is actually a concerning display of poor statistical literacy.

If you're fitting a function which grows asymptotically (i.e. is monotonically increasing at least past a certain point), the best (polynomial) fit absolutely cannot have a negative quadratic as the leading term. If your model gives one, it is 100% guaranteed to be an artifact. Treating it as "suggesting some downward curvature" is a pretty bad misunderstanding.

If you have doubts about this, consider what would happen if we added datapoints at higher doses. Every single datapoint we add to the right side of the graph will make the fit of a negative quadratic significantly worse. Ultimately, if you continue the graph indefinitely to the right, the fit of a negative quadratic is guaranteed to be infinitely bad. Any hint to the contrary is inherently an artifact of the limited dataset.

(It may well be the case that, under certain conditions with a range-restricted dataset like this, such a finding might indeed be more likely if the true function has some downward curvature. But that's not statistics, it's voodoo. All the associated statistical parameters, p-value, likelihood ratio, etc., are absolutely meaningless nonsense.)

[omgJustTest]

I think that in this case it is definitely a case of analytic-cotorsion.

There is _heated_ and mostly opinionated debate about the low-dose regime. Briefly some people believe low-doses of radiation have a threshold (that one could get a certain amount before having excess cancer risk), there is "no-threshold" meaning relative risk = 1 and dose = 0, and there are people who say that some radiation is good for us because it stimulates our repair mechanisms and kills weak cells.

All of this heated debate brings us to the currently misunderstood findings, and is why the author's say over-and-over that the linear model is a good fit.

People, specifically the regulators and the nuclear industry, make a _bunch_ of health decisions on excess risk based on Linear-No-Threshold (LNT) models because they believe it is conservative.

The main issue here is that in order to get good statistics, you have to irradiate people, and the two best datasets prior to today are Hiroshima survivors and the small number of low-dose exposures. People are torturing this analysis to resolve the debate, which in my opinion only feeds it.