Collaborative Research: Optimal Design of Experiments for Categorical Data

研究人员开发了利用分类数据确定最佳和有效的实验设计的方法。该项目由三个主要部分组成。(I)广义线性回归模型下二元数据最优设计的识别。这一部分包括考虑斜率和截距参数随不同受试者组而变化的模型以及具有随机受试者效应的模型。(2)确定分组处理的最佳分配，以便用二进制数据进行比较研究。逻辑模型是这类研究的流行选择。(3)确定对数线性回归模型下计数数据的最优设计。在这种情况下，研究人员还将重点放在能够解释受试者异质性的模型的最佳设计上。这个项目是创新的，因为它使用了一种新技术，与通常使用的几何方法相比具有巨大的优势。在药物发现、临床试验、社会科学、市场营销等许多科学研究的设计性实验中，范畴反应是非常常见的，广义线性模型被广泛用于对这些数据进行建模。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，或提高对指定样本量的估计精度。虽然线性模型的最优设计研究已有30多年的历史，但关于广义最小二乘模型最优设计的研究文献却很少。该项目对于引进新的理论工具及其对应用的影响都是重要的。例如，该项目的结果显著减少了临床试验和其他科学研究所需的时间、金钱和患者数量。这一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.