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D-OPTIMAL EXPERIMENTAL DESIGNS TO TEST FOR DEPARTURE FROM ADDITIVITY IN A FIXED-RATIO RAY MIXTURE.
Coffey, T., L. Stork, C. Gennings, W. H. Carter, J E. Simmons, AND D W. Herr. D-OPTIMAL EXPERIMENTAL DESIGNS TO TEST FOR DEPARTURE FROM ADDITIVITY IN A FIXED-RATIO RAY MIXTURE. Presented at Society of Toxicology, Baltimore, MD, March 21-25, 2004.
Risk assessors are becoming increasingly aware of the importance of assessing interactions between chemicals in a mixture. Most traditional designs for evaluating interactions are prohibitive when the number of chemicals in the mixture is large. However, evaluation of interactions with many chemicals is becoming easier through recent advances in statistically-based experimental design. Using a fixed-ratio mixture ray with chemicals in relevant proportions results in an economical design that allows estimation of additivity and interaction for a mixture of interest. This methodology is easily extended to a mixture with a large number of chemicals. Using this methodology, optimal experimental conditions can be chosen that increase the power of detecting a departure from additivity. Although these designs are well known for linear models, optimal designs for nonlinear threshold models have had few applications in toxicology. A D-optimal criterion that minimizes the variances of the parameters of a nonlinear threshold model was used to create an optimal design for a fixed-ratio mixture ray. For a fixed sample size, this design selects the experimental doses and number of observations per dose level that result in minimum variance of the model parameters and increased power to detect departures from additivity. A related design that utilizes a D-optimality criterion is also presented that results in minimum variance when some mixture data are available but additional doses are desired. An optimal design for both scenarios is illustrated using data collected on a 2:1 ratio (chlorpyrifos:carbaryl) mixture experiment. For this example, the optimal designs for the nonlinear threshold model depend on prior specification of a dose threshold. Supported by T32 ES07334-01A1 (NIEHS, NIH) and CR-828-11401 (U.S. EPA). This is an abstract of a proposed presentation and does not necessarily reflect EPA policy or the official views of the NIEHS, NIH.