LEAPS-MPS: Functional Data Analysis for Conditional Quantiles with Applications in Medical Studies

University Of North Carolina At Charlotte, Charlotte NC

Investigators

Abstract

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). Functional Data Analysis (FDA) investigates data containing information that varies over a continuum such as the temporal and spatial domains, with tremendous implications for many real-world applications, including finance, natural language processing, electric grid stabilization, and especially the medical field. For example, data types such as functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG) provide multiple observations for different locations of the brain and scalp, and are prime contenders of FDA. However, both fMRI and EEG data are often highly skewed and may contain outliers; currently, traditional FDA methods are not able to analyze them fully and accurately. Despite the many recent advancements in the FDA literature, this area is still in its infancy with much potential yet to be uncovered. The project addresses this gap by developing a novel approach for analyzing functional data that is better able to account for heavy skewness and outlying observations. This approach will be used to examine both fMRI and EEG data with the goal of investigating two important neurological disorders: (1) attention deficit hyperactivity disorder (ADHD) and (2) alcoholism. Neurological disorders exhibit brain activity characterized by drastically different biochemical and electrical behavior where the output is either atypically high or atypically low, and hence more effectively analyzed using this new method. The results will be incorporated into open-source software for reproducibility and further research, and for encouraging possible future collaborations in the medical community. A new summer research program will support students from underrepresented backgrounds who will analyze the fMRI and EEG data sets and will provide recommendations and suggestions to the medical community through public dissemination. This experience will improve students’ attitudes towards STEM careers, help them develop skills necessary for the 21st-century workforce, and encourage them to seek advanced degree opportunities. The project will provide research training opportunities at the graduate level as well. The infinite dimensional nature of functional data motivates the use of dimension reduction techniques, whereas the skewness and outlying observations often encountered in medical data require the use of quantile regression (QR). Despite recent advancements in FDA, there is no current work on the intersection of both dimension reduction and QR for FDA. Therefore, the project addresses this gap by (1) developing a dimension reduction technique for QR with infinite dimensional functional predictors, (2) extending the method to incorporate additional categorical predictors that are common in medical studies, and (3) integrating the methods into students’ training through investigation of the medical disorders of ADHD and alcoholism. This work will develop computationally efficient algorithms that will be disseminated through the PI’s existing software. Finally, this research will lead to new critically needed statistical methods for medical researchers working with rare diseases and will help clinicians to garner more actionable insight. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.