Contributions in Design of Experiments: Methods and Applications
Advisor: Hongquan Xu and Weng Kee Wong
Progresses in science and technology continuously raise new challenges to experimenters and statisticians, calling for innovation in methodological and theoretical development of experimental design. Factorial designs are popular experimental plans for identifying important factors. Motivated by real world applications, we construct efficient and optimal factorial designs with applications in the fields of, but not limited to, biomedical sciences, for drug combination determination, and marketing survey research. First, we provide a novel application of fractional factorial designs to investigate a biological system with Herpes simplex virus type 1 and six antiviral drugs. We show how the sequential use of two- and three-level fractional factorial designs can screen for important drugs and drug interactions, as well as determine potential optimal drug dosages. Second, we construct a new class of composite designs based on a two-level factorial design and a three-level orthogonal array. These new composite designs have many desirable features and are effective for factor screening and response surface modeling. Finally, motivated by the need for smaller optimal discrete choice experiments, we propose a novel application of blocked factorial designs for designing discrete choice experiments for estimating main effects, and main effects plus some two-factor interactions, with 100% efficiency. These observations have major implications in the understanding of factorial designs, ultimately leading to a better design practice and theory.