Linear No-threshold (LNT) vs. Hormesis: Paradigms, Assumptions, and Mathematical Conventions that Bias the Conclusions in Favor of LNT and Against hormesis.

The linear no-threshold assumption misunderstands the complex multiphasic biological response to ionizing radiation, focusing solely on the initial physical radiogenic damage. This misunderstanding is enabled (masked and amplified) by a number of mathematical approaches that bias results in favor of linear no-threshold and away from alternatives, like hormesis, that take biological response into account. Here we explore a number of these mathematical approaches in some detail, including the use of frequentist rather than Bayesian statistical rules and methods. We argue that a Bayesian approach cuts through an epidemiological stalemate, in part because it enables a better understanding of the concept of plausibility, which in turn properly rests on empirical evidence of actual physical and biological mechanisms. Misuse of the concept of plausibility has sometimes been used to justify the mathematically simple and convenient linearity-without-a-threshold assumption, in particular with the everywhere-positive slope that is central to linear no-threshold and its variants. Linear no-threshold's dominance in the area of dose regulation further rests on a misapplication of the precautionary principle, which only holds when a putative caution has positive effects that outweigh the negative unintended consequences. In this case the negative consequences far outweigh the presumed hazards.