Bayes Estimate of Primary Threshold in Cluster-wise fMRI Inferences

Cluster-wise statistical inference is the most widely used technique for functional magnetic resonance imaging (fMRI) data analyses. Cluster-wise statistical inference consists of two steps: i) primary thresholding that excludes less significant voxels by a pre-specified cut-off (e.g., p < 0.001); and ii) cluster-wise thresholding that controls the family-wise error rate (FWER) caused by clusters consisting of false positive suprathreshold voxels. It has been well known that the selection of the primary threshold is critical because it determines both statistical power and false discovery rate. However, in most existing statistical packages, the primary threshold is selected based on prior knowledge (e.g., p < 0.001) without taking into account the information in the data. In this manuscript, we propose a data-driven approach to objectively select the optimal primary threshold based on an empirical Bayes framework. We evaluate the proposed model using extensive simulation studies and an fMRI data example. The results show that our method can effectively increase statistical power while effectively controlling the false discovery rate.