Optimal designs for dose-response models with restricted design spaces

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 Φ_p 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 Φ_p-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 Φ_p criteria. The results are illustrated through the redesign of a dose ranging trial.