A Two-Stage Response Surface Approach to Modeling Drug Interaction

Studies of drug combinations have become increasingly important, especially in treating malignant cancers. Researchers are interested in identifying compounds that act synergistically when combined. Such synergy is usually measured through an interaction index. The existing statistical methods, in general, estimate the interaction index using pooled data from compounds administered individually and in combination. In this article, we propose a two-stage response surface approach. Parameters of monotherapy dose–response curves are estimated and then incorporated in estimating the interaction index through a quadratic response surface model. Using multiple simulation studies, we demonstrate that the new method gives less biased estimates for both monotherapy dose–response curves and interaction index. Also developed is a bootstrapping method that allows constructing a confidence interval for interaction index at any combination dose levels. An example is provided to illustrate the method.