Optimal designs for the individual and joint exposure general logistic regression models

Interest in administering compounds in combination lies both in enhancing efficacious effects and in limiting adverse effects. Although much statistical work has focused on developing mathematical functions to model the joint dose-response curves, relatively little work exists in regard to designing experiments for assessing joint action. A variety of parametric dose-response models based on either the normal or logistic probability distribution have been proposed in the literature. These models are typically nonlinear in the parameters, and as such, a nonlinear weighted least squares approach can be employed for the purpose of designing experiments. The approach is applicable across a wide variety of settings commonly associated with joint action data, including continuous and discrete responses, alternative error structures, and nonzero background response. Further, designs can be expressed in terms of proportionate responses associated with the individual compounds rather than dose levels, thereby providing for results that are applicable across compounds. As a precursor to this effort, optimal and minimal experimental designs for the case in which a single compound is administered have also been developed. Although the proposed methodology for deriving experimental designs can be applied to any nonlinear regression model, primary focus is given to the additive and nonadditive independent joint action (IJA) models for individual and combined exposures proposed by Barton, Braunberg, and Friedman (1).