Empirical null and false discovery rate analysis in neuroimaging

Area of Science:

• Neuroimaging
• Statistical Analysis
• Data Science

Background:

• Neuroimaging statistical analysis relies on thresholding methods like Family-Wise Error Rate (FWER) and False Discovery Rate (FDR) control.
• Accurate inference hinges on the correct specification of the null distribution for test statistics.
• Existing methods may fail when theoretical null distributions do not align with observed data, as seen in fMRI and DTI.

Purpose of the Study:

• To address the limitations of theoretical null distributions in neuroimaging statistical parametric mapping.
• To introduce and validate the use of an empirical null distribution estimated directly from the data.
• To explore the relationship between FDR control and posterior probability thresholding using an empirical null framework.

Main Methods:

• Development and application of an empirical null distribution estimation method.
• Comparison of empirical null with theoretical null distributions (normal, t, chi(2), F) using fMRI and DTI data.
• Utilizing a two-class mixture model to estimate the proportion of non-active voxels and derive FDR estimates.

Main Results:

• Demonstrated discrepancies between theoretical and observed null distributions in neuroimaging datasets.
• The empirical null provides a data-driven approach for global correction of null assumption biases.
• Established an equivalence between FDR control and posterior probability thresholding, with empirical null-derived FDR estimates acting as empirical Bayes estimates.

Conclusions:

• The empirical null distribution offers a robust solution for more accurate statistical inference in neuroimaging.
• This approach enhances the reliability of findings from functional MRI (fMRI) and Diffusion Tensor Imaging (DTI) studies.
• The empirical null framework provides a unified perspective on FDR control and posterior probability thresholding in neuroimaging.