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

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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.