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.)
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.)