Inference in functional mixed regression models with applications to Positron Emission Tomography imaging data

Area of Science:

• Neuroscience
• Biostatistics
• Functional Data Analysis

Background:

• Positron Emission Toming (PET) imaging is crucial for exploring protein density in the human brain.
• Current methods for analyzing impulse response functions (IRFs) in PET data are limited to single brain regions.
• Understanding regional protein density variations is key to studying neurological conditions.

Purpose of the Study:

• To develop advanced functional mixed models for analyzing PET data.
• To extend existing methods for impulse response function (IRF) estimation to simultaneously model multiple brain regions.
• To provide robust inference strategies for fixed effects in functional regression models.

Main Methods:

• Utilized a function-on-scalar regression framework for functional mixed models.
• Developed an extension of nonparametric IRF estimation for simultaneous multi-region analysis.
• Proposed two general approaches for permutation testing in functional regression models.
• Identified strategies for exchangeable units and constructed permutation tests.

Main Results:

• Successfully modeled multiple brain regions concurrently using functional data analysis principles.
• Demonstrated the application of the developed methods to real PET data.
• Illustrated the ability to explore the effects of depression and sex on brain protein density (IRFs).

Conclusions:

• The proposed functional mixed model approach enables simultaneous analysis of multiple brain regions from PET data.
• The developed methods offer enhanced capabilities for understanding protein density variations and their associations.
• This work provides a valuable tool for neuroscience research, particularly in studying conditions like depression.