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2015 ; 10
(7
): e0130494
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Data-Driven Method to Estimate Nonlinear Chemical Equivalence
#MMPMID26158701
Mayo M
; Collier ZA
; Winton C
; Chappell MA
PLoS One
2015[]; 10
(7
): e0130494
PMID26158701
show ga
There is great need to express the impacts of chemicals found in the environment
in terms of effects from alternative chemicals of interest. Methods currently
employed in fields such as life-cycle assessment, risk assessment, mixtures
toxicology, and pharmacology rely mostly on heuristic arguments to justify the
use of linear relationships in the construction of "equivalency factors," which
aim to model these concentration-concentration correlations. However, the use of
linear models, even at low concentrations, oversimplifies the nonlinear nature of
the concentration-response curve, therefore introducing error into calculations
involving these factors. We address this problem by reporting a method to
determine a concentration-concentration relationship between two chemicals based
on the full extent of experimentally derived concentration-response curves.
Although this method can be easily generalized, we develop and illustrate it from
the perspective of toxicology, in which we provide equations relating the sigmoid
and non-monotone, or "biphasic," responses typical of the field. The resulting
concentration-concentration relationships are manifestly nonlinear for nearly any
chemical level, even at the very low concentrations common to environmental
measurements. We demonstrate the method using real-world examples of
toxicological data which may exhibit sigmoid and biphasic mortality curves.
Finally, we use our models to calculate equivalency factors, and show that
traditional results are recovered only when the concentration-response curves are
"parallel," which has been noted before, but we make formal here by providing
mathematical conditions on the validity of this approach.
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