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

Abstract

The threshold-free cluster enhancement (TFCE) approach integrates cluster information into voxelwise 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 comparison 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.

Impulsive prepotent actions and tics in Tourette disorder underpinned by a common neural network

“…We performed whole-brain multivariate voxel-based regression analyses using the Permutation Analysis of Linear Models implemented in Matlab [25], on gray matter signal and the DTI metrics (FA and MD) including the total intracranial volume as covariable of noninterest and the zscore of premature response as covariable of interest. The threshold for significance was set at p ≤ 0.05 following familywise error correction corrected within modality and within contrast, following probabilistic threshold-free cluster enhancement [26] and 5000 permutations.…”

Mesocorticolimbic Interactions Mediate fMRI-Guided Regulation of Self-Generated Affective States

“…The second-level random effects group analysis was performed by entering single subject contrast images into one sample t-tests. Whole brain statistical maps were thresholded at p < 0.001 corrected at the cluster level for multiple comparison using a probabilistic threshold-free cluster enhancement (pTFCE) [52,53], an approach that integrates cluster information into voxel-wise statistical inference so as to enhance detectability of the neuroimaging signal and to control for the Type I error. In order to increase the statistical power of fMRI analysis, considering the relatively limited sample size, hypothesis-driven regions-of-interest (ROIs) statistical analysis was first performed [54,55].…”

“…Temporal correlations were analyzed separately for up and down emotion regulation runs. Significant correlations were assessed considering a threshold of p < 0.001 cluster level corrected for multiple comparison using pTFCE [52,53].…”

Deciphering the scopolamine challenge rat model by preclinical functional MRI

“…This thresholding method was used to enhance the detection of large activation clusters unlikely to be random false positives originating from multiple comparisons [24]. Furthermore, we applied the probabilistic threshold-free cluster enhancement (pTFCE) [25] with corrected significance threshold of P=0.05. pTFCE provides a natural adjustment for various signal topologies (thereby enhanced P-values directly, without permutation testing).…”