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

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成像临床研究，重点是研究疾病随时间的自然演变/动力学。患者在多次医院就诊时被观察，疾病状态通过大脑测量来衡量，例如一维大脑摘要或三维大脑扫描。这项工作将用于：(I)预测未来时间的特定大脑测量；(Ii)评估大脑测量与年龄之间的相关性；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、可解释和易于访问的方法来分析此类数据结构。拟议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制度。研究与教育的结合将对社会产生不同层面的影响。调查员将实施一项教育倡议，通过实践项目相关活动，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学前沿研究的机会。调查员通过教授功能数据技术向发展中国家开展的外联活动对通过分享和传播知识促进所有社会的进步很有价值。由于基于纵向的设计，有必要开发下一代统计方法来分析相关的数据结构：在重复的时间访问中观察每个受试者，对于每次访问，我们除了记录其他标量或向量变量外，还记录一个函数变量。该项目满足了对这种复杂数据的实用和数据效率统计方法的日益增长的需求。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，考虑到对象内部的相关性以及纵向设计对于建模和推理都是至关重要的。然而，现有的方法要么忽略了这种依赖关系，要么过于复杂和计算量大。本项目的具体研究目标是：1)为重复观察的功能变量引入新的简约建模框架，允许提取低维特征并将其用于研究过程动力学；2)开发显著性检验以正式评估协变量的影响；以及3)当函数变量是预测变量且另一个标量变量是纵向设计中观察到的响应时，开发关联模型和推理程序。

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.