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个实验中同时研究十几种或更多种药物，以确定具有高疗效和低毒性的新型药物组合。这给实验者和统计学家提出了新的挑战，因为随着药物数量的增加，药物组合的数量也呈指数级增长。 研究人员比以往任何时候都更加依赖于大型有效的实验设计，以便在数百万或数十亿种可能的药物组合中成功有效地识别一些重要的药物和药物相互作用。然而，在文献中，很少有好的设计和结果。为了满足这种大规模药物组合实验日益增长的需求，本项目旨在开发新的方法并构建有效的析因和复合设计。 该项目将有助于缩短各种科学研究的时间，大大降低实验成本。在药物组合实验中的应用将对发现各种常见疾病的新疗法产生直接影响，从而有助于促进国民健康。部分析因设计在从大量潜在变量中筛选重要因子方面具有成本效益;复合设计对于序贯试验以及构建响应面模型是必不可少的。本文提出了一种利用线性和二次函数构造多水平非正则部分因子设计的系统方法。 一个通用的理论，以获得重要的设计性能，如分辨率和像差。 介绍了研究定量因子水平排列下设计结构的新工具。 介绍了两类复合设计，并对其进行了深入的研究。 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性筛选设计。 这些复合设计具有许多理想的功能，比现有的复合设计更有效的因素筛选和响应面建模，特别是大规模的实验。

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.