A semi-parametric approach to estimate the family-wise error rate in fMRI using resting-state data

One of the most important considerations in any hypothesis based fMRI data analysis is to choose the appropriate threshold to construct the activation maps, which is usually based on p-values. However, in fMRI data, there are three factors which necessitate severe corrections in the process of estimating the p-values. First, the fMRI time series at an individual voxel has strong temporal autocorrelation which needs to be estimated to obtain the corrected parametric p-value. The second factor is the multiple comparisons problem arising from simultaneously testing tens of thousands of voxels for activation. A common way in the statistical literature to account for multiple testing is to consider the family-wise error rate (FWE) which is related to the distribution of the maximum observed value over all voxels. The third problem, which is not mentioned frequently in the context of adjusting the p-value, is the effect of inherent low frequency processes present even in resting-state data that may introduce a large number of false positives without proper adjustment. In this article, a novel and efficient semi-parametric method, using resampling of normalized spacings of order statistics, is introduced to address all the three problems mentioned above. The new method makes very few assumptions and demands minimal computational effort, unlike other existing resampling methods in fMRI. Furthermore, it will be demonstrated that the correction for temporal autocorrelation is not critical in implementing the proposed method. Results using the proposed method are compared with SPM2.