A minimum Bayes Factor based threshold for activation likelihood estimation

Abstract

Activation likelihood estimation (ALE) is among the most used algorithms to perform neuroimaging meta-analysis. Since its first implementation, several thresholding procedures had been proposed, all referred to the frequentist framework, returning a rejection criterion for the null hypothesis according to the critical p-value selected. However, this is not informative in terms of probabilities of the validity of the hypotheses. Here, we describe an innovative thresholding procedure based on the concept of minimum Bayes factor (mBF). The use of the Bayesian framework allows to consider different levels of probability, each of these being equally significant. In order to simplify the translation between the common ALE practice and the proposed approach, we analised six task-fMRI/VBM datasets and determined the mBF values equivalent to the currently recommended frequentist thresholds based on Family Wise Error (FWE). Sensitivity and robustness toward spurious findings were also analyzed. Results showed that the cutoff log10(mBF)=5 is equivalent to the FWE threshold, often referred as voxel-level threshold, while the cutoff log10(mBF)=2 is equivalent to the cluster-level FWE (c-FWE) threshold. However, only in the latter case voxels spatially far from the blobs of effect in the c-FWE ALE map survived. Therefore, when using the Bayesian thresholding the cutoff log10(mBF)=5 should be preferred. However, being in the Bayesian framework, lower values are all equally significant, while suggesting weaker level of force for that hypothesis. Hence, results obtained through less conservative thresholds can be legitimately discussed without losing statistical rigor. The proposed technique adds therefore a powerful tool to the human-brain-mapping field.