title: Detecting Departure From Additivity Along a Fixed-Ratio Mixture Ray With a Piecewise Model for Dose and Interaction Thresholds.
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.
authors.affiliation: Assistant Professor of Biostatistics, Department of Medicine, Medical University of South Carolina, 135 Cannon St., Suite 303, MSC 835, Charleston, SC 29425, USA ( yeatts@musc.edu ).
authors.forename: Sharon D
authors.initials: SD
authors.lastname: Yeatts
authors.forename: Chris
authors.initials: C
authors.lastname: Gennings
authors.forename: Elizabeth D
authors.initials: ED
authors.lastname: Wagner
authors.forename: Jane Ellen
authors.initials: JE
authors.lastname: Simmons
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Plewa