Parametric modeling and optimal experimental designs for estimating isobolograms for drug interactions in toxicology

ABSTRACTIn toxicology and related areas, interaction effects between two substances are commonly expressed through a combination index evaluated separately at different effect levels and mixture ratios. Often, these indices are combined into a graphical representation, the isobologram. Instead of estimating the combination indices at the experimental mixture ratios only, we propose a simple parametric model for estimating the underlying interaction function. We integrate this approach into a joint model where both the parameters of the dose-response functions of the singular substances and the interaction parameters can be estimated simultaneously. As an additional benefit, this concept allows to determine optimal statistical designs for combination studies optimizing the estimation of the interaction function as a whole. From an optimal design perspective, finding the interaction parameters generally corresponds to a -optimality resp. -optimality design problem, while estimation of all underlying dose re...