Detecting interaction(s) and assessing the impact of component subsets in a chemical mixture using fixed-ratio mixture ray designs

Michelle Casey, Chris Gennings, W. Hans Carter, Virginia C. Moser, Jane Ellen Simmons

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


An important environmental and regulatory issue is the protection of human health from potential adverse effects of cumulative exposure to multiple chemicals. Earlier literature suggested restricting inference to specific fixed-ratio rays of interest. Based on appropriate definitions of additivity, single chemical data are used to predict the relationship among the chemicals under the zero-interaction case. Parametric comparisons between the additivity model and the model fit along the fixed-ratio ray(s) are used to detect departure from additivity. Collection of data along reduced fixed-ratio rays, where subsets of chemicals of interest are removed from the mixture and the remaining compounds are at the same relative ratios as considered in the full ray, allow researchers to make inference about the effect of the removed chemicals. Methods for fitting simultaneous confidence bands about the difference between the best fitting model and the model predicted under additivity are developed to identify regions along the rays where significant interactions occur. This general approach is termed the "single chemicals required" (SCR) method of analysis. A second approach, termed "single chemicals not required" (SCNR) method of analysis, is based on underlying assumptions about the parameterization of the response surface. Under general assumptions, polynomial terms for models fit along fixed-ratio rays are associated with interaction terms. Consideration is given to the case where only data along the mixture rays are available. Tests of hypotheses, which consider interactions due to subsets of chemicals, are also developed.

Original languageEnglish
Pages (from-to)339-361
Number of pages23
JournalJournal of Agricultural, Biological, and Environmental Statistics
Issue number3
StatePublished - 1 Sep 2004
Externally publishedYes


  • Departure from additivity
  • Dose-response data
  • Ray designs
  • Threshold models


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