Optimization Problems in Factorial and Response Adaptive Designs

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*Experimental design is a process of planning a study or investigating efficient methods for collecting data for scientific inquiry. It is a commonly used tool in scientific investigations with applications in industrial, agricultural, biological, pharmaceutical, and manufacturing sciences, etc. Due to the increasing cost of experiments, there is an urgent need for good designs that increase the efficiency of parameter estimation and the statistical power of the resulting tests. An optimal experimental design provides interpretable and accurate inference at minimal cost. Problems in optimal design include the selection of an appropriate optimality criterion or a mixture of several criteria and the determination of actual design, either analytically or numerically. The challenges in optimal design are characterized by methodological and computational issues, which provide opportunities for developing new optimality criteria, optimal design theory, methodology, and algorithms for searching for optimal designs. ****Fractional factorial designs are cost-efficient experimental plans for identifying and estimating important effects of multiple variables on a response. Due to budget limitations, multistage designs are widely used in advanced manufacturing processes, such as nanomanufacturing and pharmaceutical manufacturing. Response adaptive design (RAD) of clinical trials is becoming increasingly important and popular. In many clinical trials, covariate information is available and has a strong influence on the responses of patients. The proposed research is concerned with optimality problems in fractional factorial designs, multistage experiments, and response adaptive designs in the presence of covariates at both a theoretical and practical level. I will introduce new theory and methodology, extend and improve existing methods, and develop computational algorithms. Catalogues of optimal designs will be tabulated for practical use. The proposed research will provide theoretical developments and economical experimental plans for experimenters. The proposed research program will involve extensive training of highly qualified personnel (HQP) in preparing them for future positions in both academia and industry. **