Optimal designs for dose–response models with linear effects of covariates

Personalized medicine is becoming more and more important nowadays since the efficacy of a certain medicine vary among different patients. This requires to combine the effects of the prognostic factors or covariates along with different dosages when planning a dose–response experiment. Statistically, this corresponds to the construction of optimal designs for estimating dose–response curves in the presence of covariates. Some characteristics of the optimal designs are derived in order to search such optimal designs efficiently, and an equivalence theorem of the locally ϕ_s-optimal designs is established accordingly. Computational issues are also studied and presented with theoretical backups. As applications of the above theories, the locally optimal designs are searched out in several situations. Some simulations reveal that the searched locally optimal designs are robust to the moderate misspecification of the prespecified parameters.