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佳的，有效的，或强大的交叉设计比较几个测试处理与控制处理。A-最优性和MV-最优性被认为是最优性准则。应用正交矩阵理论简化相应的信息矩阵。置换技术将被用来确定相应的最优性准则下的可实现的下限。为实现这一目标，制定了五项目标。(1)识别并构造传统模型下的最优/有效设计;（2）识别并构造自身和混合携带效应模型下的最优/有效设计;（3）识别并构造在各种模型下表现良好的稳健设计;（4）针对目标（1）~（3）提出相应的算法并开发一套软件，方便研究成果的推广和广泛应用;（5）开发内布拉斯加大学林肯分校的高级实验设计课程。交叉设计已广泛应用于各种领域，尤其是在临床试验中。虽然存在大量的研究，确定和构建最佳/有效的或强大的交叉设计时，所有的治疗都同样重要，这样的设计比较几个测试治疗与控制治疗的知识是非常有限的，迫切需要。目前，关于如何进行这种实验的适用指导很少。这项研究的结果，当应用时，预计将显着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，方便用户的软件包可以帮助统计人员和非统计人员利用该项目的研究成果，从而降低成本，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.