Detecting departure from additivity along a fixed-ratio mixture ray with a piecewise model for dose and interaction thresholds

Sharon D. Yeatts, Chris Gennings, Elizabeth D. Wagner, Jane Ellen Simmons, Michael J. Plewa

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)510-522
Number of pages13
JournalJournal of Agricultural, Biological, and Environmental Statistics
Volume15
Issue number4
DOIs
StatePublished - Dec 2010

Keywords

  • Dose threshold
  • Dose-dependent interaction
  • Synergy

ASJC Scopus subject areas

  • Statistics and Probability
  • Agricultural and Biological Sciences (miscellaneous)
  • Environmental Science(all)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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