Studies in Factorial and Composite Designs with Applications to Drug Combination Experiments

技术的进步使研究人员能够在一次实验中同时研究十几种或更多的药物，以确定高效低毒的新型药物组合。这给实验者和统计学家带来了巨大的新挑战，因为药物组合的数量随着药物数量的增加而呈指数级增长。研究人员比以往任何时候都更加依赖大型有效的实验设计，以成功和有效地确定几种重要的药物以及数百万或数十亿种可能的药物组合中的药物相互作用。然而，在文献中很少有好的设计和结果可用。为了满足这种大规模药物联合实验日益增长的需求，该项目旨在开发新的方法学并构建有效的析因设计和组合设计。该项目将有助于缩短研究时间，极大地降低各种科学研究的实验成本。药物联合实验的应用将对发现各种常见疾病的新疗法产生立竿见影的影响，从而有助于促进国民健康。部分析因设计对于从大量潜在变量中筛选重要因素具有成本效益；复合设计对于序贯实验以及建立响应面模型是必不可少的。提出了一种利用线性函数和二次函数构造多水平非正则部分析因设计的系统方法。提出了获得诸如分辨率和像差等重要设计特性的一般理论。介绍了研究定量因素水平排列下的设计结构的新工具。对两类组合设计进行了深入的介绍和研究。第一类包括两水平和三水平析因设计，第二类包括两水平析因设计和三水平确定型筛选设计。这些组合设计具有许多理想的特征，在因素筛选和响应面建模方面比现有的组合设计更有效，特别是在大规模实验中。

The advance in technology enables researchers to investigate a dozen or more drugs simultaneously in a single experiment in order to identify novel drug combinations with high efficacy and low toxicity. This raises substantial new challenges to experimenters and statisticians, because the number of drug combinations grows exponentially as the number of drugs increases. Researchers rely more than ever on large efficient experimental designs in order to successfully and efficiently identify a few important drugs and drug interactions among millions or billions possible drug combinations. However, few good designs and results are available in the literature. To address the growing needs from such large-scale drug combination experiments, this project aims at developing new methodology and constructing efficient factorial and composite designs. This project will help shorten investigation time and reduce experimental cost tremendously in a wide variety of scientific researches. The applications to drug combination experiments will have an immediate impact on discovering novel treatments for various common diseases and hence help advance the national health. Fractional factorial designs are cost-effective for screening important factors from a large pool of potential variables; composite designs are indispensable for sequential experimentation, as well as for building response surface models. A systematic method is proposed for constructing multi-level nonregular fractional factorial designs using linear and quadratic functions. A general theory is developed for obtaining important design properties such as resolution and aberration. New tools are introduced for studying design structure under level permutations for quantitative factors. Two classes of composite designs are introduced and studied thoroughly. The first class consists of a two-level and a three-level factorial design; the second consists of a two-level factorial and a three-level definitive screening design. These composite designs have many desirable features and are more effective than existing composite designs for factor screening and response surface modeling, especially for large-scale experiments.