Optimal designs for semi-parametric dose-response models under random contamination

With the increasing popularity of personalized medicine, it is more and more crucial to capture not only the dose-effect but also the effects of the prognostic factors due to individual differences in a dose-response experiment. This paper considers the design issue for predicting semi-parametric dose-response curves in the presence of linear effects of covariates. Inspired by the Neyman-Pearson paradigm, a novel design criterion, namely bias constraint optimality, is introduced to minimize the overall prediction error. The corresponding equivalence theorems are established, the characteristics of the optimal designs are shown, and an equivalent bias compound optimality criterion is proposed for practical implementation. Based on the obtained theoretical results, efficient algorithms for searching for optimal designs are developed. Numerical simulations are given to illustrate the superior performance of the obtained optimal designs.