Extended Youden Design in Biological Assays and Optimal Design for Nonlinear Models

This dissertation includes two topics in optimal design. Chapter 1 discusses the optimal design of biological assay experiments, of which the challenges lie in the multiple nuisance assay factors and the control required in each block. To solve this problem, we focus on a 2-way elimination of heterogeneity problem with non-equireplicated setup and propose and Extended Youden Design (EYD) that is optimal in this scenario. We also provide the construction of EYD based on Set of Distinct Representatives and demonstration with 3 example setups. The EYD provides an efficient solution in the biological assay applications and establishes discussion of optimality for 2-way elimination of non-replicated block designs. Chapter 2 discusses optimal designs for nonlinear models without canonical forms. The current complete class strategy succeeded in providing a unified framework to identify optimal designs for nonlinear models, but couldn't support application to many models due to the assumptions. In this chapter, we propose a tool called Ancillary Functions for these models so that the previously violated assumptions are validated. We also provide results on minimally supported designs with proper condition. This tool is demonstrated with three two-parameter dose-response models. The results of this paper add to the previous complete class framework and make the minimally supported design available for more nonlinear models that were previously not feasible.