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Toxicol Sci. 2012 Oct;129(2):447-55. doi: 10.1093/toxsci/kfs209. Epub 2012 Jun 14.

Parameterizing dose-response models to estimate relative potency functions directly.

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Biostatistics Branch, National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709, USA.


Many comparative analyses of toxicity assume that the potency of a test chemical relative to a reference chemical is constant, but employing such a restrictive assumption uncritically may generate misleading conclusions. Recent efforts to characterize non-constant relative potency rely on relative potency functions and estimate them secondarily after fitting dose-response models for the test and reference chemicals. We study an alternative approach of specifying a relative potency model a priori and estimating it directly using the dose-response data from both chemicals. We consider a power function in dose as a relative potency model and find that it keeps the two chemicals' dose-response functions within the same family of models for families typically used in toxicology. When differences in the response limits for the test and reference chemicals are attributable to the chemicals themselves, the older two-stage approach is the more convenient. When differences in response limits are attributable to other features of the experimental protocol or when response limits do not differ, the direct approach is straightforward to apply with nonlinear regression methods and simplifies calculation of simultaneous confidence bands. We illustrate the proposed approach using Hill models with dose-response data from U.S. National Toxicology Program bioassays. Though not universally applicable, this method of estimating relative potency functions directly can be profitably applied to a broad family of dose-response models commonly used in toxicology.

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