Optimal Designs for Dose–Response Models With Restricted Design Spaces

Abstract

In dose–response studies, the dose range is often restricted because of concerns over drug toxicity and/or efficacy. We derive optimal designs for estimating the underlying dose–response curve for a restricted or unrestricted dose range with respect to a broad class of optimality criteria. The underlying curve belongs to a diversified set of link functions suitable for the dose–response studies and having a common canonical form. These include the fundamental binary response models—the logit and the probit, as well as the skewed versions of these models. Our methodology is based on a new geometric interpretation of optimal designs with respect to Kiefer's Φp criteria in regression models with two parameters, which is of independent interest. It provides an intuitive illustration of the number and locations of the support points of Φp-optimal designs. Moreover, the geometric results generalize the classical characterization of D-optimal designs by the minimum covering ellipsoid to the class of Kiefer's Φp criteria. The results are illustrated through the redesign of a dose ranging trial.