Economical designs for detecting and characterizing departure from additivity in mixtures of many chemicals

A well-chosen experimental design can result in efficient estimation of model parameters and often savings of resources. When the interaction of components in a mixture is under study, a useful experimental layout is a factorial design - where all combinations of the levels of each component are observed together. However, as the number of components in the mixture becomes large, these types of designs become infeasible. Using the definition of additivity as proposed by Berenbaum, some authors have instead used an experimental design necessary to estimate coefficients in an additivity model where only dose-response (concentration-effect) information of single compounds is required. Two approaches for using an additivity model are described. Both compare what is observed with what is predicted under the assumption of additivity. One is based on a comparison of responses to a mixture of interest; the other is based on a comparison of locations of mixtures that yield the same predicted response when the components are at a fixed proportion. An example using a threshold model for the dose-response relationship is provided.