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

A typical fMRI data analysis proceeds via the generalized linear model (GLM) with Gaussian noise using a model based on the experimental paradigm. This analysis ultimately results in the production of z-statistic images corresponding to the contrasts of interest. Thresholding such z-statistic images at uncorrected thresholds suitable for testing activation at a single voxel results in the problem of multiple comparisons. A number of methods which account for the problem of multiple comparisons have been proposed including Gaussian random field theory, mixture modeling and false discovery rate (FDR). The focus of this paper is on the development of a generalized version of FDR (GFDR) in an empirical Bayesian framework, specially adapted for fMRI thresholding, that is more robust to modeling violations as compared to traditional FDR. We show theoretically as well as by simulation that for real fMRI data various factors lead to a mixture of Gaussians (MOG) density for the "null" distribution. Artificial data was used to systematically study the bias of FDR and GFDR under varying intensity of modeling violations, signal to noise ratios and activation fractions for a range of q values. GFDR was able to handle modeling violations and produce good results when FDR failed. Real fMRI data was also used to confirm GFDR capabilities. Our results indicate that it is very important to account for the form and fraction of the "null" hypothesis adaptively from the data in order to obtain valid inference.