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A Four Step Approach to Evaluate Mixtures for Consistency with Dose Addition
Citation:
Hertzberg, R., Y. Pan, R. Li, L. Haber, R. Lyles, D. Herr, V. C. Moser, AND J. Simmons. A Four Step Approach to Evaluate Mixtures for Consistency with Dose Addition. TOXICOLOGY. Elsevier Science Ltd, New York, NY, 313(2):134-44, (2013).
Impact/Purpose:
The principal impact of the procedure described in this paper is that it describes the initial deveoplement and application of a novel methodology to evaluate mixtures for consistencyt with does addition a) that is useful for toxicology experimentation to examine the health effects of chemical mixtures, b) allows a risk assessor to understand if an assumption of dose addition is supported for their particular situation when both data on the components and the mixture are available and c) provides a useful risk assessment tool to predict the effect of a mixture when mixture data are lacking but data on the component chemicals are available.
Description:
We developed a four step approach for evaluating chemical mixture data for consistency with dose addition for use in environmental health risk assessment. Following the concepts in the U.S. EPA mixture risk guidance (EPA 2000a,b), toxicological interaction for a defined mixture (all components known) is departure from a clearly articulated definition of component additivity. In addition to similar toxicity across the component chemicals, the EPA guidance specifies two key theoretical characteristics of dose additivity: the mixture components have toxic potencies that are fixed proportions of each other (irrespective of dose), and the mixture dose term in the dose additive prediction formula, which we term the combined prediction model (CPM), can be represented by a linear combination of the component doses. A consequent property of the proportional toxic potencies is that the component chemicals must share a common dose response model, where only the dose coefficients depend on the chemical components. A further consequence is that the mixture data must be described by the same mathematical function ("mixture model") as the components, but with a distinct coefficient for the total mixture dose. The mixture response can then be predicted from the component dose response curves by using the CPM, with dose as the linear combination of component doses. The four steps are to evaluate: 1) toxic proportionality by determining how well the CPM matches the single chemical models regarding mean and variance; 2) fit of the mixture model to the mixture data; 3) agreement between the mixture data and the CPM; and 4) consistency between the CPM and the mixture model. Because there are four evaluations instead of one, some involving many parameters or dose groups, there are more opportunities to reject statistical hypotheses about dose addition, thus statistical adjustment for multiple comparisons is necessary. These four steps contribute different pieces of information about the consistency of the component and mixture data with the two characteristics of dose additivity. We examine this four step approach in how it can show the empirical support for dose addition as a predictor for an untested mixture in a screening level risk assessment. The decision whether to apply dose addition should be based on all four of those evidentiary pieces as well as toxicological understanding of these chemicals and should include interpretations of the numerical and toxicological issues that arise during the evaluation. This approach is demonstrated with neurotoxicity data on carbamate mixtures