Spatially Varying Coefficient Model for Neuroimaging Data with Jump Discontinuities

Area of Science:

• Neuroimaging analysis
• Statistical modeling
• Biostatistics

Background:

• Massive neuroimaging datasets present challenges due to complex spatial correlations.
• Existing models may not adequately capture piecewise smooth regions with unknown edges and jumps common in neuroimaging data.

Purpose of the Study:

• To propose a novel Spatially Varying Coefficient Model (SVCM) for analyzing neuroimaging data.
• To account for multiple piecewise smooth regions, unknown edges, jumps, and spatial correlations in 3D imaging data.

Main Methods:

• Developed a SVCM incorporating a measurement model with multiple varying coefficient functions, a jumping surface model, and a functional principal component model.
• Implemented a three-stage estimation procedure for simultaneous estimation of varying coefficient functions and spatial correlations.
• Utilized a fast multiscale adaptive estimation and testing procedure to preserve edges in piecewise-smooth regions.

Main Results:

• Systematically investigated asymptotic properties, including consistency and asymptotic normality, of parameter estimates.
• Established uniform convergence rates for estimated spatial covariance functions, eigenvalues, and eigenfunctions.
• Demonstrated the excellent performance of SVCM through Monte Carlo simulations and real data analysis.

Conclusions:

• The proposed SVCM effectively models complex associations in neuroimaging data with spatial variations.
• The developed estimation procedure accurately estimates varying coefficients and spatial correlations while preserving data structures.
• SVCM offers a robust framework for analyzing large-scale neuroimaging studies.