Optimal designs for the EMAX, log-linear and exponential linear and exponential model

In this paper we derive locally D-and ED p -optimal designs for the exponential, log-linear and three parameter EMAX-model. We show that 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, Doptimal designs are efficient for estimating the smallest dose which achieves 100p% of the maximum effect in the observed dose range. Conversely, ED p -optimal designs also yield good D-eciencies. We illustrate the results using several examples and demonstrate that locally D-and ED p -optimal designs for the EMAX-, log-linear and exponential model are relatively robust with respect to misspecification of the model parameters