Optimization Problems in Factorial and Response Adaptive Designs

* 实验设计是一个规划研究或调查有效方法以收集科学探究数据的过程。它是一种常用的工具，在科学研究中的应用，在工业，农业，生物，制药和制造科学等由于实验成本的增加，有一个迫切需要良好的设计，提高效率的参数估计和统计功率的结果测试。 最佳实验设计以最小的成本提供可解释和准确的推断。优化设计中的问题包括选择适当的最优性准则或几个准则的混合，以及通过分析或数值方法确定实际设计。优化设计中的挑战的特点是方法和计算问题，这为开发新的优化准则，优化设计理论，方法和算法搜索最优设计提供了机会。* 部分因子设计是一种具有成本效益的实验计划，用于识别和估计多个变量对响应的重要影响。由于预算限制，多级设计广泛用于先进的制造工艺，如纳米制造和制药。 临床试验的反应自适应设计（RAD）正变得越来越重要和流行。在许多临床试验中，协变量信息是可用的，并对患者的反应有很大的影响。建议的研究关注的最优性问题，部分因子设计，多阶段实验，和响应自适应设计中存在的协变量在理论和实践层面。我将介绍新的理论和方法，扩展和改进现有的方法，并开发计算算法。最佳设计的目录将被制成表格以供实际使用。本研究将为实验者提供理论上的发展及经济的实验方案。拟议的研究计划将涉及对高素质人员（HQP）的广泛培训，为他们在学术界和工业界的未来职位做好准备。**

*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. **