CAREER: Next Generation Functional Methods for the Analysis of Emerging Repeated Measurements

职业：用于分析新兴重复测量的下一代函数方法

• 批准号: 1454942
• 负责人: Ana-Maria Staicu
• 金额: $ 40万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-01 至 2021-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1454942&HistoricalAwards=false
• 关键词: CAREER; Next; Generation; Functional; Methods

This project will develop new statistical methods for the analysis of data structures that are correlated. A motivating example is a longitudinal neuroimaging clinical study of Multiple Sclerosis, where the focus is to study the natural evolution/dynamics of the disease over time. Patients are observed at multiple hospital visits, and the disease status is measured through a brain measurement, such as a one-dimensional brain summary or a three-dimensional brain scan. This work will be used: (i) to predict specific brain measurement at a future time; (ii) to assess the dependence between the brain measurement and age, and (iii) to quantify the association between a cognitive assessment and the specific brain measurement. The new statistical methods will be relevant to many other applications, including medicine, economics, environmetrics, and agriculture; they will allow scientists to analyze such data structures using methods that are theoretically sound, interpretable, and easily accessible. The proposed methods make major contributions to the area of functional data analysis and will impact other areas of statistical applications, such as brain imaging and dynamic treatment regimes. The integration of the research with education will impact society at various levels. The investigator will implement an educational initiative to increase exposure of middle-school and high-school students to exciting statistical methods, through hands-on project-related activities, and will increase exposure of undergraduate students to cutting-edge research in statistics. The investigator's outreach initiative to developing countries through teaching of functional data techniques is valuable for the advancement of all societies through the sharing and dissemination of knowledge.The development of the next generation statistical methods for the analysis of correlated data structures is necessary because of a longitudinal-based design: each subject is observed at repeated time visits and for each visit we record a functional variable, in addition to other scalar or vector variables. The project meets the growing demand for pragmatic and data efficient statistical methods for such complex data. Two situations are studied: a) the functional variables are the response of interest and b) the functional variables are predictors and another scalar variable is the response. In both cases, accounting for the dependence within the subject as well as for the longitudinal design is crucial for modeling and inference. However, current methods either ignore the dependence or are too complicated and computationally intensive. The specific research goals of this project are: 1) to introduce novel parsimonious modeling framework for the repeatedly observed functional variables, which allows to extract low dimensional features and use them to study the process dynamics; 2) to develop significance tests to formally assess the effect of covariates; and 3) to develop association models and inferential procedures when the functional variables are predictors and another scalar variable is the response observed in a longitudinal design.

这个项目将开发新的统计方法来分析相关的数据结构。一个鼓舞人心的例子是多发性硬化症的纵向神经影像学临床研究，其重点是研究疾病随时间的自然演变/动态。在多次医院访问中观察患者，并通过脑测量来测量疾病状态，例如一维脑总结或三维脑扫描。这项工作将用于：(i)预测未来特定的大脑测量；（ii）评估大脑测量与年龄之间的依赖关系，以及（iii）量化认知评估与特定大脑测量之间的关联。新的统计方法将与许多其他应用相关，包括医学、经济学、环境计量学和农业；它们将允许科学家使用理论上合理、可解释且易于获取的方法来分析这些数据结构。所提出的方法对功能数据分析领域做出了重大贡献，并将影响其他统计应用领域，如脑成像和动态治疗方案。研究与教育的结合将在各个层面对社会产生影响。研究者将实施一项教育倡议，通过与项目相关的实践活动，增加初中生和高中生接触令人兴奋的统计方法的机会，并将增加本科生接触统计前沿研究的机会。研究者通过传授功能数据技术向发展中国家开展的外联活动，通过分享和传播知识，对所有社会的进步都是有价值的。由于基于纵向的设计，开发用于分析相关数据结构的下一代统计方法是必要的：每个受试者在重复的时间访问中进行观察，对于每次访问，除了其他标量或向量变量外，我们还记录了一个功能变量。该项目满足了日益增长的对此类复杂数据的实用和数据高效统计方法的需求。研究了两种情况：a)函数变量是感兴趣的响应；b)函数变量是预测变量，另一个标量变量是响应。在这两种情况下，考虑主题内部的依赖性以及纵向设计对于建模和推理至关重要。然而，目前的方法要么忽略了相关性，要么过于复杂和计算量大。本课题的具体研究目标是：1)为反复观测的功能变量引入新的精简建模框架，提取低维特征并利用其研究过程动力学；2)制定显著性检验，正式评估协变量的影响；3)当功能变量为预测变量，而另一个标量变量为纵向设计中观察到的响应时，建立关联模型和推理程序。