Optimal Design for Non-Linear Models, With an Emphasis on Categorical Data

研究人员为非线性模型确定最优和有效的设计。重点是(1)二进制数据或计数数据的广义线性模型(GLM)；(2)事件相关功能磁共振成像(ER-fMRI)实验的非线性模型。对于其中的第一个，最近的结果大多局限于只有一个协变量的模型。研究人员研究了常见的具有多个协变量和高阶项的GLMS，如Logistic模型、Probit模型和对数线性模型。他开发了新的理论和计算工具，用于在各种最优标准下确定局部最优设计，以及确定稳健设计。对于第二个问题，研究人员在更现实的非线性模型下为估计血流动力学响应函数(HRF)和检测大脑活动的组合目标确定了最优和有效的设计。传统上，对于这些不同的目标，使用了两个单独的线性模型。使用单个非线性模型来模拟血流动力学响应有助于同时追求这两个目标。这种方法不仅提供了更自然的设计优化准则，而且为ER-fMRI实验带来了更好的设计。二元数据和计数数据在许多科学领域非常常见，如药物发现、临床试验、社会科学、市场营销等。尽管这些数据的分析模型和方法已经建立得很好，但关于有效利用现有资源的最优设计的研究却相当滞后。例如，在计划剂量反应研究时，重要的是要知道研究中应该使用哪种药物的剂量水平，以及应该将多少受试者分配到这些水平，以便为具有科学意义的问题获得最多的信息。研究人员和他的合作者开发的最新进展和新工具使人们有可能为各种常用模型得出最佳设计。在项目的第二部分，研究人员为ER-fMRI实验找到了有效的设计。这些实验是研究某些简单任务引起的大脑活动的尖端方法的一部分。核磁共振扫描仪中的受试者被呈现一系列任务，每个任务重复多次，并测量血流动力学响应。研究人员确定向受试者呈现任务的最佳且有效的顺序，以便为实验的科学目标获得尽可能多的信息。

The investigator identifies optimal and efficient designs for non-linear models. The focus is on (1) generalized linear models (GLMs) for binary data or count data; and (2) non-linear models for Event Related functional Magnetic Resonance Imaging (ER-fMRI) experiments. For the first of these, recent results are mostly restricted to models with a single covariate. The investigator studies common GLMs, such as logistic, probit and loglinear models, with multiple covariates and higher order terms. He develops novel theory and computational tools for identifying locally optimal designs under various optimality criteria as well as for identifying robust designs. For the second problem, the investigator identifies optimal and efficient designs under more realistic non-linear models for the combined objectives of estimation of the hemodynamic response function (HRF) and detection of brain activity. Traditionally, two separate linear models have been used for these disparate objectives. The use of a single non-linear model for modeling the hemodynamic response facilitates the simultaneous pursuit of both objectives. This approach provides not only a more natural formulation of design optimality criteria, but also results in better designs for ER-fMRI experiments.Binary data and count data are very common in many scientific fields, such as drug discovery, clinical trials, social sciences, marketing, etc. While models and methods of analysis for such data are well established, the study of optimal design for the efficient use of available resources lags considerably. For example, when planning a dose-response study, it is important to know which dose levels of a drug should be used in the study, and how many subjects should be assigned to these levels in order to get the most information for questions that are of scientific interest. Recent advances and new tools developed by the investigator and his collaborators make it possible to derive optimal designs for a variety of commonly used models. For a second part of the project, the investigator finds efficient designs for ER-fMRI experiments. These experiments are part of a cutting edge approach for studying brain activity caused by certain simple tasks. A subject in an MRI scanner is presented with a series of tasks, each of them repeated multiple times, and the hemodynamic response is measured. The investigator identifies optimal and efficient orders for presenting the tasks to a subject in order to gain as much information as possible for the scientific goals of the experiment.