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Testing for additivity in chemical mixtures using a fixed-ratio ray design and statistical equivalence testing methods
- Source :
- Journal of Agricultural, Biological, and Environmental Statistics. 12:514-533
- Publication Year :
- 2007
- Publisher :
- Springer Science and Business Media LLC, 2007.
-
Abstract
- 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 using 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.
- Subjects :
- Statistics and Probability
Applied Mathematics
Mixture model
Agricultural and Biological Sciences (miscellaneous)
Confidence interval
Statistical power
Additive function
Statistics
Applied mathematics
Statistics, Probability and Uncertainty
General Agricultural and Biological Sciences
Null hypothesis
Equivalence (measure theory)
General Environmental Science
Statistical hypothesis testing
Mathematics
Confidence region
Subjects
Details
- ISSN :
- 15372693 and 10857117
- Volume :
- 12
- Database :
- OpenAIRE
- Journal :
- Journal of Agricultural, Biological, and Environmental Statistics
- Accession number :
- edsair.doi...........a59541b5eb19a89ad549f7d72c8cbb17