Collaborative research: A major leap forward: Optimal designs for correlated data, multiple objectives, and multiple covariates

在许多研究领域，如生物科学、健康科学、社会科学、工程学、营销学、教育学等，设计性实验是科学过程中不可或缺的一部分。精心选择的设计有助于收集数据，以固定成本最大化感兴趣的科学问题的信息，或最小化所需级别的信息的成本。许多实验涉及相关数据、多个目标或多个协变量，但对如何在这些环境中识别好的设计知之甚少。这个项目确定了如何为最常用的统计模型找到针对这些类型的问题的有效设计。在这个项目中开发的工具具有巨大的社会影响潜力，因为设计的实验经常被用来加深许多不同领域的知识。该项目的结果将通过易于使用的软件提供给其他领域的研究人员，这些软件实现了开发的算法。研究生将被培养成实验设计方面的研究人员。这一项目的成果是对实验优化设计的理解和知识的重大飞跃。最近主要研究人员和其他人的贡献对推进非线性和广义线性模型的最优实验设计产生了重大影响。然而，这些结果在很大程度上局限于(I)独立数据；(Ii)使用单一的最优化标准；以及(Iii)使用单一的协变量。虽然这些结果本身就很重要，但这个项目将把方法和工具扩展到相关数据、多目标和多协变量的问题。后者可以由实验者可以选择的协变量和在设计阶段已知或未知但实验者无法控制的协变量的混合组成。初步结果表明，现在是采取这些具有挑战性但至关重要的步骤的好时机。建立一个框架来为这些类型的问题派生和确定最佳设计，将为我们的集体设计工具箱提供一个非常必要的补充。目前的结果非常稀少，而且只针对非常专门的问题，这些问题主要是由数学可行性驱动的。该项目开发的工具可以为模型和条件选择有效的设计，这些模型和条件比目前考虑的要现实得多。

Designed experiments form an integral part of the scientific process in many areas of research, such as the biological sciences, the health sciences, the social sciences, engineering, marketing, education, and others. A well-chosen design facilitates the collection of data that maximizes the information for the scientific questions of interest at a fixed cost, or that minimizes the cost for a desired level of information. Many experiments deal with correlated data, multiple objectives, or multiple covariates, but little is known about the identification of good designs in such settings. This project establishes how to find efficient designs for these types of problems for the most commonly used statistical models. The tools developed in this project have a tremendous potential for impact on society because designed experiments are used so often to further knowledge in many different fields. Results from the project will be made available to researchers in other areas through easy-to-use software that implements algorithms that are developed. Graduate students will be trained to become researchers in design of experiments. The outcomes of this project constitute a major leap forward in understanding and knowledge of optimal design of experiments. Recent contributions by the principal investigators and others have had a significant impact on the advancement of optimal design of experiments for nonlinear and generalized linear models. However, these results have for the most part been limited to (i) independent data; (ii) use of a single optimality criterion; and (iii) use of a single covariate. While these results are arguably important in their own right, this project will extend methods and tools to problems with correlated data, multiple objectives, and multiple covariates. The latter could consist of a mix of covariates that can be chosen by the experimenter and covariates that, known or unknown at the design stage, cannot be controlled by the experimenter. Preliminary results indicate that this is an opportune time to make these challenging but critical steps. Building a framework for deriving and identifying optimal designs for these types of problems will provide a much needed addition to our collective design toolbox. Current results are very sparse and only for very specialized problems that are mostly motivated by mathematical feasibility. The project develops tools to select efficient designs for models and conditions that are far more realistic than those that have been considered so far.