Ds-optimal designs for studying combinations of chemicals using multiple fixed-ratio ray experiments

Abstract

Detecting and characterizing interactions among chemicals is an important environmental issue. Traditional factorial designs become infeasible as the number of compounds under study increases. Ray designs, which reduce the amount of experimental effort, can be considered when interest is restricted to relevant mixing ratios. Simultaneous tests for departure from additivity across multiple fixed-ratio rays in the presence and absence of single chemical data have been developed. Tests for characterizing interactions among subsets of chemicals at relevant mixing ratios have also been developed. Of primary importance are precise estimates for the parameters associated with these hypotheses. Since the hypotheses of interest are stated in terms of subsets of parameters, we have developed a methodology for finding Ds-optimal designs, which are associated with the minimum generalized variance of subsets of the parameter vector, along fixed-ratio rays. We illustrate these methods by characterizing the interactions of five organophosphorus pesticides (full-ray) as well as a subset of pesticides (reduced-ray) on a measure of motor activity. Copyright © 2004 John Wiley & Sons, Ltd.