Optimal designs for the emax, log-linear and exponential models

Abstract

We derive locally D- and ED p -optimal designs for the exponential, log-linear and three-parameter emax models. For each model the locally D- and ED p -optimal designs are supported at the same set of points, while the corresponding weights are different. This indicates that for a given model, D-optimal designs are efficient for estimating the smallest dose that achieves 100 p % of the maximum effect in the observed dose range. Conversely, ED p -optimal designs also yield good D-efficiencies. We illustrate the results using several examples and demonstrate that locally D- and ED p -optimal designs for the emax, log-linear and exponential models are relatively robust with respect to misspecification of the model parameters.