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

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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.