CAREER: Optimal Design of Experiments for Generalized Linear Models

在这项工作中，PI是开发一种新的方法来确定最佳和有效的设计下的广义线性模型（GLM），包括基本的逻辑，概率单位和对数线性模型和一些其他的非线性模型。具体而言，本项目旨在实现以下三个目标：（i）确定非同质主题下的GLM的最佳设计。在这项研究中，最优设计的模型中，受试者被分为两个或多个组使用一个或多个因素，允许截距或斜率从一个组到另一个不同。随机受试者效应也可以用于组内受试者之间的差异。(ii)识别具有多个协变量的GLM的最优设计。对于具有多个协变量的GLM，很少有最优性结果。当存在多个协变量时，PI将研究GLM的最佳设计。这些模型也可以解释受试者的异质性。(iii)确定其他一些非线性模型的最优设计。在非线性模型中，大多数最优结果都是在所有参数的D-最优性下得到的。PI将研究一种通用方法，以确定在常用的最优性标准下，当所有或部分参数都感兴趣时，具有三个或更多参数的非线性模型的最优设计。拟议的研究将产生巨大的影响，因为它将填补文献中的几个空白：拟议的研究中的模型适应受试者和多个协变量之间的异质性;将提供具有三个参数的非线性模型的最优设计的一般解决方案。在拟议的研究中的技术是创新的，因为它产生了非常普遍的结果，超越了解决问题的个案的基础上。它有助于确定许多常用模型的局部最优设计的支持，并可应用于所有常见的基于信息矩阵的最优性准则。它既适用于受约束的设计区域，也适用于无约束的设计区域。此外，它可以应用于多阶段实验，其中初始实验可以用于提供未知参数的更好的想法。GLM和其他非线性模型已经广泛应用于社会科学和自然科学领域，如生物科学、药物研究、农业科学、经济学、市场营销等。本文的研究结果将对GLM在这些领域的应用产生深远的影响。例如，当这些发现应用于新药发现和开发期间的临床试验设计时，它们将显著减少这些试验所需的时间，金钱和患者数量。事实上，这项研究可以帮助美国食品和药物管理局改进其临床试验指南。为了有效地传播这项研究的结果，研究所将开发一个针对非专家用户的用户友好的软件包。为了成功地整合研究和教育，PI将在密苏里大学哥伦比亚分校开发先进的实验设计课程，并将该项目的研究结果纳入其中。研究生将接受培训，学习最佳设计的新领域，根据PI？的指导。最后，拟议的研究有可能刺激新的研究，并提供工具，用于确定最佳设计下的GLM或非线性模型在其他领域，如纵向数据分析和生存分析。

In this work, the PI is to develop a novel approach for identifying optimal and efficient designs under Generalized Linear Models (GLMs) including the fundamental logistic, probit and loglinear models and some other nonlinear models. Specifically, this project intends to achieve the following three objectives: (i) Identify optimal designs for GLMs under non-homogeneous subjects. In this study, optimal designs are derived for models in which the subjects are divided into two or more groups using one or more factors, allowing the intercept or slope to vary from one group to another. Random subject effects can also be allowed for differences among subjects within groups. (ii) Identify optimal designs for GLMs with multiple covariates. There are very few optimality results for GLMs with more than one covariate. The PI will study optimal designs for GLMs when multiple covariates exist. These models can also account for subject heterogeneity. (iii) Identify optimal designs for some other nonlinear models. In nonlinear models, most optimal results were derived under D-optimality for all parameters. The PI will investigate a general approach to identify optimal designs for nonlinear models with three or more parameters under commonly used optimality criteria when all or some of the parameters are of interest. The proposed research will have a tremendous impact because it will fill several gaps in the literature: the models in the proposed research accommodate heterogeneity among subjects and multiple covariates; general solutions for optimal designs of nonlinear models with three parameters will be provided. The technique in the proposed research is innovative in that it yields very general results that go beyond solving problems on a case-by-case basis. It helps to identify the support of locally optimal designs for many of the commonly studied models and can be applied for all the common optimality criteria based on information matrices. It works both with a constrained and unconstrained design region. Furthermore, it can be applied to multistage experiments, where an initial experiment may be used to provide a better idea of the unknown parameters. GLMs and other nonlinear models have been used in a wide range of social and natural science fields, such as biological sciences, pharmaceutical research, agricultural science, economics, marketing, etc. The results of this study will have a deep impact on the application of GLMs in these fields. For example, when the findings are applied to the design of clinical trials during new drug discovery and development, they will significantly reduce the time, money, and number of patients needed in these trials. In fact, this research can help the U.S. Food and Drug Administration to improve its guidelines for clinical trials. To effectively disseminate the results of this research, the PI will develop a user-friendly software package targeting non-expert users. To successfully integrate research and education, the PI will develop advanced experimental design courses at the University of Missouri-Columbia incorporating findings of this project. Graduate students will be trained to study optimal designs in the new fields, under the PI?s guidance. Finally, the proposed research has the potential to stimulate new research and to provide tools for identifying optimal designs under GLMs or nonlinear models used in other areas, such as longitudinal data analysis and survival analysis.