Collaborative Research: Optimal Design of Experiments for Categorical Data

研究人员开发的方法，确定最佳和有效的设计实验分类数据。该项目包括三个主要部分。(i)广义线性回归模型下二元数据最优设计的识别。本部分包括考虑斜率和截距参数可能因不同受试者组而异的模型以及具有随机受试者效应的模型。(ii)确定处理的最佳分配到块的比较研究与二进制数据。逻辑模型是此类研究的热门选择。(iii)对数线性回归模型下计数资料最优设计之辨识。在这种情况下，研究人员还关注可以解释受试者异质性的模型的最佳设计。这个项目是创新的，因为它使用了一种新的技术，具有巨大的优势，比常用的几何方法。在许多科学研究中，如药物发现、临床试验、社会科学、市场营销等，分类反应在设计的实验中非常常见。广义线性模型（GLM）被广泛用于对此类数据进行建模。在这样的实验中使用有效的设计来收集数据是至关重要的。它可以减少达到指定精度所需的样本量，从而降低成本，或提高指定样本量的估计精度。虽然线性模型的最优设计的研究已经系统地发展了30多年，但很少有关于GLM最优设计的研究出版物。这个项目是重要的新的理论工具的引入及其对应用的影响。例如，该项目的结果显着减少了临床试验以及其他科学研究所需的时间，金钱和患者数量。这些结果可以帮助美国食品和药物管理局改进其临床试验指南。

The investigators develop methods for identifying optimal and efficient designs for experiments with categorical data. The project consists of three main parts. (i) Identification of optimal designs for binary data under generalized linear regression models. This part includes consideration of models in which slope and intercept parameters can vary for different groups of subjects and models with a random subject effect. (ii) Identification of optimal allocations of treatments to blocks for comparative studies with binary data. A logistic model is a popular choice for such studies. (iii) Identification of optimal designs for count data under loglinear regression models. In this setting, the investigators focus also on optimal designs for models that can account for subject heterogeneity. This project is innovative in that it uses a new technique that has vast advantages over the commonly used geometric approach. Categorical responses are very common in designed experiments in many scientific studies, such as drug discovery, clinical trials, social sciences, marketing, etc. Generalized Linear Models (GLMs) are widely used for modeling such data. Using efficient designs for collecting data in such experiments is critically important. It can reduce the sample size needed for achieving a specified precision, thereby reducing the cost, or improve the precision of estimates for a specified sample size. While research on optimal designs for linear models has been systematically developed over more than 30 years, there are very few research publications on optimal designs for GLMs. This project is important both for the introduction of novel theoretical tools and for its impact on applications. For example, the results of the project significantly reduce the time, money, and the number of patients needed in clinical trials, as well as other scientific studies. The results can help the U.S. Food and Drug Administration to improve its guidelines for clinical trials.