Abstract
For mixtures of many chemicals, a ray design based on a relevant, fixed mixing ratio is useful for detecting departure from additivity. Methods for detecting departure involve modeling the response as a function of total dose along the ray. For mixtures with many components, the interaction may be dose dependent. Therefore, we have developed the use of a three-segment model containing both a dose threshold and an interaction threshold. Prior to the dose threshold, the response is that of background; between the dose threshold and the interaction threshold, an additive relationship exists; the model allows for departure from additivity beyond the interaction threshold. With such a model, we can conduct a hypothesis test of additivity, as well as a test for a region of additivity. The methods are illustrated with cytotoxicity data that arise when Chinese hamster ovary cells are exposed to a mixture of nine haloacetic acids.
Original language | English (US) |
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Pages (from-to) | 510-522 |
Number of pages | 13 |
Journal | Journal of Agricultural, Biological, and Environmental Statistics |
Volume | 15 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2010 |
Keywords
- Dose threshold
- Dose-dependent interaction
- Synergy
ASJC Scopus subject areas
- General Environmental Science
- Applied Mathematics
- Agricultural and Biological Sciences (miscellaneous)
- General Agricultural and Biological Sciences
- Statistics and Probability
- Statistics, Probability and Uncertainty