Crossover Designs for Comparing Test Treatments with a Control Treatment: Optimality, Efficiency, and Robustness

这个项目的目标是找到最优、有效或稳健的交叉设计，以比较几个测试处理和一个对照处理。A-最优性和MV-最优性被认为是最优性准则。将应用正交矩阵理论对相应的信息矩阵进行简化。在最优准则下，将使用置换技术来确定相应的可实现下界。为实现这一目标，我们设计了五个目标。(1)识别并构建传统模型下的最优/有效设计；(2)识别并构建自我和混合结转效应模型下的最优/有效设计；(3)识别并构建在各种模型下表现良好的稳健设计；(4)针对目标(1)至(3)提出相应的算法，并开发软件包以便于研究结果的传播和广泛应用；(5)开发内布拉斯加-林肯大学高级实验设计课程的课程。交叉设计已被广泛应用于各种领域，尤其是临床试验中。尽管在所有处理同等重要的情况下，已有大量关于识别和构建最优/有效或稳健的交叉设计的研究，但在将几个试验处理与对照处理进行比较时，关于此类设计的知识是极其有限和迫切需要的。目前，关于如何进行这样的实验，几乎没有适用的指导意见。这项研究的结果，如果应用，预计将显著减少临床试验所需的时间、金钱和患者数量。此外，预计这项研究将有助于FDA改进其交叉设计指南。此外，使用方便的软件包可以帮助统计学家和非统计学家利用该项目的研究成果，从而降低成本和加快新药开发。

The goal of this project is to find optimal, efficient, or robust crossover designs for comparing several test treatments with a control treatment. A-optimality and MV-optimality are considered as optimality criteria. Orthogonal matrix theory will be applied to simplify the corresponding information matrix. Permutation techniques will be employed to determine the corresponding achievable lower bounds under the optimality criteria. Five objectives are designed to accomplish this goal. (1) Identify and construct optimal/efficient designs under the traditional model; (2) Identify and construct optimal/efficient designs under the self and mixed carryover effects model; (3) Identify and construct robust designs that perform well under various models; (4) Propose corresponding algorithms for Objectives (1) through (3) and develop a software package to facilitate the dissemination and wide application of the research results; and(5) Develop curriculum in the University of Nebraska-Lincoln's advanced experimental design courses.Crossover designs have been widely used in a variety of fields, especially in clinical trials. Although there exists a great deal of research on identifying and constructing optimal/efficient or robust crossover designs when all treatments are equally important, knowledge on such designs when comparing several test treatments with a control treatment is extremely limited and urgently needed. At present, there is little applicable guidance on how to conduct such experiments. The results of this study, when applied, are expected to significantly reduce the time, money, and the number of patients needed in clinical trials. In addition, it is expected that this research will help the FDA improve its guidelines to crossover designs. Furthermore, the user-friendly software package can help both statisticians and non-statisticians to utilize research results from the project, thus reduce costs and speed up new drug development.