Enhanced false discovery rate using Gaussian mixture models for thresholding fMRI statistical maps.

Area of Science:

• Neuroimaging
• Statistical analysis
• Brain imaging analysis

Background:

• Functional magnetic resonance imaging (fMRI) analysis commonly uses the generalized linear model (GLM).
• Thresholding z-statistic images in fMRI presents a multiple comparisons problem.
• Existing methods like Gaussian random field theory, mixture modeling, and false discovery rate (FDR) address this issue.

Purpose of the Study:

• To develop a generalized false discovery rate (GFDR) method within an empirical Bayesian framework.
• To create an fMRI thresholding approach more robust to statistical modeling violations than traditional FDR.
• To adaptively account for the form and fraction of the null hypothesis from data for valid inference.

Main Methods:

• Developed a generalized false discovery rate (GFDR) method in an empirical Bayesian framework.
• Utilized theoretical analysis and simulations with artificial and real fMRI data.
• Systematically studied the bias of FDR and GFDR under varying modeling violations, signal-to-noise ratios, and activation fractions.

Main Results:

• Demonstrated that real fMRI data often exhibit a mixture of Gaussians (MOG) density for the null distribution.
• GFDR showed robustness to modeling violations, yielding good results where traditional FDR failed.
• Simulations confirmed GFDR's ability to handle violations effectively.

Conclusions:

• GFDR provides a more robust approach to multiple comparisons in fMRI thresholding compared to traditional FDR.
• Adaptive accounting for the null hypothesis's form and fraction is crucial for valid fMRI statistical inference.
• The developed GFDR method is essential for accurate brain imaging analysis.