A Unifying Concept for Assessing Toxicological Interactions: Changes in Slope

Abstract

Robust statistical methods are important to the evaluation of toxicological interactions (i.e., departures from additivity) among chemicals in a mixture. However, different concepts of joint toxic action as applied to the statistical analysis of chemical mixture toxicology data or as used in environmental risk assessment often appear to conflict with one another. A unifying approach for application of statistical methodology in chemical mixture toxicology research is based on consideration of change(s) in slope. If the slope of the dose-response curve of one chemical does not change in the presence of other chemicals, then there is no interaction between the first chemical and the others. Conversely, if the rate of change in the response with respect to dose of the first chemical changes in the presence of the other chemicals, then an interaction is said to exist. This concept of zero interaction is equivalent to the usual approach taken in additivity models in the statistical literature. In these additivity models, the rate of change in the response as a function of the i(th) chemical does not change in the presence of other chemicals in a mixture. It is important to note that Berenbaum's (1985, J. Theor. Biol. 114, 413-431) general and fundamental definition of additivity does not require the chemicals in the mixture to have a common toxic mode of action nor to have similarly shaped dose response curves. We show an algebraic equivalence between these statistical additivity models and the definition of additivity given by Berenbaum.

Additive effects of levonorgestrel and ethinylestradiol on brain aromatase ( cyp19a1b ) in zebrafish specific in vitro and in vivo bioassays

“…Then, common maximum responses were estimated. At present, there is still a discussion on the validity of the CA model when single compounds produce different slopes because this would suggest that the mode of action is different (Backhaus et al 2004, Gennings et al 2005: the concept of Toxic Equivalent Factor is a more restrictive version of CA (Webster 2013).. For that reason, when this was not detrimental to the model fit, a common slope was also estimated for single compounds. The only free remaining parameter was then the EC50.…”

Impact of co-exposure with lead and decabromodiphenyl ether (BDE-209) on thyroid function in zebrafish larvae

“…To test possible effects between Pb and BDE-209, we employed the concept of interaction as a change in slope proposed by Gennings et al (2005). In their model, the slope of a dose-response curve of a certain chemical can be altered in the presence of another chemical.…”

“…For evaluation of the interaction between the two compounds, we used the method proposed by Gennings et al (2005). Fig.…”

Basic principles of toxicological evaluation of mixtures

“…Obrnuto, ako se nagib krive doza odgovor ne menja u prisustvu druge supstance onda hemikalije ne intereaguju tj. kombinuju se aditivno (13,14). Grafički prikaz ovog koncepta dat je na Slici 1.…”