Probabilistic TFCE: A generalized combination of cluster size and voxel intensity to increase statistical power.

The threshold-free cluster enhancement (TFCE) approach integrates cluster information into voxel-wise statistical inference to enhance detectability of neuroimaging signal. Despite the significantly increased sensitivity, the application of TFCE is limited by several factors: (i) generalisation to data structures, like brain network connectivity data is not trivial, (ii) TFCE values are in an arbitrary unit, therefore, P-values can only be obtained by a computationally demanding permutation-test. Here, we introduce a probabilistic approach for TFCE (pTFCE), that gives a simple general framework for topology-based belief boosting. The core of pTFCE is a conditional probability, calculated based on Bayes' rule, from the probability of voxel intensity and the threshold-wise likelihood function of the measured cluster size. In this paper, we provide an estimation of these distributions based on Gaussian Random Field theory. The conditional probabilities are then aggregated across cluster-forming thresholds by a novel incremental aggregation method. pTFCE is validated on simulated and real fMRI data. The results suggest that pTFCE is more robust to various ground truth shapes and provides a stricter control over cluster "leaking" than TFCE and, in many realistic cases, further improves its sensitivity. Correction for multiple comparisons can be trivially performed on the enhanced P-values, without the need for permutation testing, thus pTFCE is well-suitable for the improvement of statistical inference in any neuroimaging workflow. Implementation of pTFCE is available at https://spisakt.github.io/pTFCE.