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

该项目将开发新的统计方法，用于分析相关的数据结构。一个激励性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。患者在多个医院就诊时被观察，并且通过脑部测量来测量疾病状态，例如一维脑部汇总或三维脑部扫描。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依赖性;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，生物计量学和农业;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这些数据结构。所提出的方法作出重大贡献的功能数据分析领域，并将影响其他领域的统计应用，如脑成像和动态治疗制度。研究与教育的结合将在各个层面影响社会。调查员将实施一项教育倡议，通过与项目有关的实践活动，增加初中和高中学生接触令人兴奋的统计方法，并增加本科生接触统计学前沿研究的机会。 调查员通过教授实用数据技术向发展中国家推广的主动行动，对于通过分享和传播知识促进所有社会的进步是很有价值的，由于采用了以数据为基础的设计，有必要开发下一代统计方法，用于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，并且对于每次访问，除了其他标量或向量变量之外，我们还记录函数变量。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，以及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，考虑对象内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密集。本计画的具体研究目标为：1）针对可重复观测的函数变数，提出新颖的简约建模架构，以提取低维特征，并将其应用于过程动态的研究; 2）发展显著性检定，以正式评估协变数的影响;（3）在纵向设计中，当功能变量为预测变量，另一个标量变量为反应变量时，建立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.