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Testing for Additivity in Chemical Mixtures Using a Fixed-Ratio Ray Design and Statistical Equivalence Testing Methods
Citation:
Stork, L. G., C. Gennings, W. H. Carter, R. E. Johnson, D. P. Mays, J. E. SIMMONS, E. D. Wagner, AND M. J. PLEWA. Testing for Additivity in Chemical Mixtures Using a Fixed-Ratio Ray Design and Statistical Equivalence Testing Methods. JOURNAL OF AGRICULTURAL, BIOLOGICAL, AND ENVIRONMENTAL STATISTICS. American Statistical Association, Alexandria, VA, 12(4):514-533, (2007).
Impact/Purpose:
The study was done to develop a method for evaluation of additivity using the principle of confidence interval inclusion. The authors make sure of a very rich data set developed by several of the authors (Plewa, Wagner, Simmons)
Description:
Fixed-ratio ray designs have been used for detecting and characterizing interactions of large numbers of chemicals in combination. Single chemical dose-response data are used to predict an “additivity curve” along an environmentally relevant ray. A “mixture curve” is estimated from the mixture dose-response data along the ray. A test of additivity is equivalent to a test of coincidence of these two curves, which is based on the traditional hypothesis testing framework that assumes additivity in the null hypothesis and rejects with evidence of interaction. However, failure to reject may be due to lack of statistical power, making the claim of additivity problematic. As a solution we have developed rigorous methodology to test for additivity based on statistical equivalence testing logic in which additivity is claimed based on pre-specified biologically important additivity margins, if the data support such a claim. Using the principle of confidence interval inclusion, a confidence region about the difference of meaningful functions of model parameters from the mixture model and that predicted under additivity is computed. When the confidence region is completely contained within the additivity margins then additivity is claimed with a Type I error rate chosen a priori to be some acceptably small value. The method is illustrated using an environmentally relevant fixed-ratio mixture of nine haloacetic acids where cytotoxic response is measured.
