Bayes estimate of primary threshold in clusterwise functional magnetic resonance imaging inferences

Clusterwise statistical inference is the most widely used technique for functional magnetic resonance imaging (fMRI) data analyses. Clusterwise statistical inference consists of two steps: (i) primary thresholding that excludes less significant voxels by a prespecified cut-off (eg, $$ ); and (ii) clusterwise thresholding that controls the familywise error rate caused by clusters consisting of false positive suprathreshold voxels. The selection of the primary threshold is critical because it determines both statistical power and false discovery rate (FDR). However, in most existing statistical packages, the primary threshold is selected based on prior knowledge (eg, $$ ) without taking into account the information in the data. In this article, we propose a data-driven approach to algorithmically select the optimal primary threshold based on an empirical Bayes framework. We evaluate the proposed model using extensive simulation studies and real fMRI data. In the simulation, we show that our method can effectively increase statistical power by 20% to over 100% while effectively controlling the FDR. We then investigate the brain response to the dose-effect of chlorpromazine in patients with schizophrenia by analyzing fMRI scans and generate consistent results.