2024 Theses Doctoral

Innovations in Functional Data Analysis with Applications in Neuroscience and Women's Health

Stoms, Madison Emily

Functional data analysis (FDA) offers a robust statistical framework for handling complex data arising from a variety of fields. The presented dissertation focuses on the development and application of innovative FDA methods to analyze scientific data. We introduce three novel approaches tailored to distinct health-related topics: the mechanisms of neural activation during skilled movement and the role of the menstrual cycle in clinical studies performed on women.

In the realm of neuroscience, we propose a functional clustering method designed to analyze high-dimensional, temporal data collected across multiple trials of varying conditions. Leveraging two datasets involving motor neuron behavior in mice, our method identifies latent neuron subgroups and conducts group-specific dimensionality reduction. Through simulations and real-data analyses, we demonstrate the method's efficacy in capturing subtle differences between groups, offering insights into the underlying mechanisms of voluntary movement.

Turning to women's health, we address the often-overlooked effects of the menstrual cycle in clinical research. We develop a method to estimate menstrual cycle day using hormone values derived from a single spot urine sample. We leverage patterns of hormonal variation obtained from two sources of data, which follow a collection of women across a full cycle. Through simulations and real data applications, we demonstrate our ability to obtain accurate estimations of cycle day within three days of the truth in optimal settings. This work paves the way for improved model accuracy and statistical power in clinical studies performed on women. Furthermore, we propose an innovative analysis strategy to model menstrual cycle day as an effect modifier on the relationship between hormone levels and breast cancer risk, providing insights into the cyclic variations of hormone levels and their implications on breast cancer etiology.

This dissertation aims to advance our understanding of complex health-related processes and empower clinicians and researchers to develop more personalized interventions. The dissertation structure comprises detailed chapters discussing the development, application, and results of each method, highlighting the pivotal role of functional data analysis in advancing scientific research and discovery.