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Dose-response relationships and extrapolation in toxicology - Mechanistic and statistical considerations
Citation:
Lutz, W., R. Lutz, D. Gaylor, AND R. Conolly. Dose-response relationships and extrapolation in toxicology - Mechanistic and statistical considerations. Edition 1, Chapter 52, Franz-Xaver Reichl and Michael K. Schwenk (ed.), Regulatory Toxicology. Springer, Heidelberg, Germany, 1:547-568, (2014).
Impact/Purpose:
The chapter will be part of a book to be published in English in Germany, with the European regulatory and academic communities expected to be the main audience. However, in todays’ world, science and regulatory approaches informed by science are increasingly globalized. The book will thus be globally relevant - since EPA attempts to use the best possible science in support of its regulatory activities, approaches to this challenge in other parts of the world are of both academic and practical interest to EPA scientists and regulators.
Description:
Controversy on toxicological dose-response relationships and low-dose extrapolation of respective risks is often the consequence of misleading data presentation, lack of differentiation between types of response variables, and diverging mechanistic interpretation. In this chapter, we address respective issues and illustrate them with appropriate examples taken from genotoxicity, mutagenicity, and carcinogenicity. At the low-dose end of the dose response, the rate of any interaction of a toxicant with a biological target molecule is proportional to its concentration. Linearity is therefore a reasonable default for extrapolation. In toxicity testing, however, we do not measure rates but concentrations of biomarkers, and extend the dose range to overt toxicity. Deviation from linearity is observed when factors that modulate the first-line rates come into play. Examples are saturation of receptor-ligand binding or of enzymatic reaction, as well as processes of induction and inhibition of downstream effects. As a special case of nonlinearity, there can also be a nonmonotonic shape of the dose-response curve, if background is affected by low-dose treatment in a direction opposite to what happens at high dose. We use computational modeling to characterize how competing influences that are dominant over different ranges of doses combine to generate nonmonotonicity. A mathematical threshold, where slope zero changes abruptly to slope >0 at some breakpoint of the dose-response "curve", cannot be supported by mechanistic considerations. However, a threshold can appear from superposition of two curves moving in opposite directions, a situation that can be explained and modeled on a mechanistic basis. Molecular biomarkers of toxicity as discussed above are continuous measures. This type of response variable has to be interpreted differently from an "incidence" of a toxic effect in a population, which is the result of a binary situation for individuals. An individual contributes either a 0 (no effect) or a I (effect) to the incidence, expressed as the fraction of affected individuals in the population. Regarding dose response, each individual has its own "threshold dose" to switch from 0 to I, which means that the dose-response "curve" is a staircase of individual threshold doses and reflects the tolerance distribution in the examined population. Extrapolation to low dose follows differences in individual susceptibility and cannot be predicted on the basis of the mode of first-line interaction alone. In the absence of knowledge on the distribution of factors that determine individual susceptibility, biologically motivated modeling by statistical sampling of distributions may as a first approach fill the gap. For complex endpoints of toxicity such as cancer, individual susceptibility is determined by multiplicative combination of numerous factors. The central limit theorem of statistics suggests that the dose response could be approximated by a cumulative normal dose-incidence curve against log (dose). For low-dose extrapolation of a cancer risk, the linear default becomes too conservative, the closer we approach dose zero. Finally, by combining continuous and binary responses, we investigate differences in individual susceptibility for situations that result in a nonmonotonic dose response for a biomarker. Monte Carlo simulations show that some individuals might indeed show a nonmonotonic or threshold-like shape, while others follow a monotonic course.