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pTFCE: probabilistic Treshold-free Cluster Enhancement

Contents

1. Overview
2. Relation to TFCE
3. R package 3.1 Installation 3.2 Usage
4. SPM Toolbox 4.1 Installation 4.2 Usage
5. FSL extension 5.1 Installation 5.2 Usage
6. Nipype interface

Overview

The widely used threshold-free cluster enhancement (TFCE) [1] 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) generalization 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. We provide an estimation of these distributions based on Gaussian Random Field (GRF) theory. The conditional probabilities are then aggregated across cluster-forming thresholds by a novel incremental aggregation method. Our approach is validated on simulated and real fMRI data.

Simulation results strongly suggest that pTFCE is more robust to various ground truth shapes and provides a stricter control over cluster "leaking" than TFCE and, in the most realistic cases, further improves 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.

Relation to TFCE

Both TFCE and pTFCE are based on the integration of cluster-forming height threshold (h1, h2, …, hn) and the supporting section or cluster size (c₁, c2, …, cn) at that given height. The difference is that, while TFCE combines raw measures of height and cluster size to an arbitrary unit, pTFCE realises the integration by constructing the conditional probability p(h|c) based on Bayes’ rule, thereby providing a natural adjustment for various signal topologies. Aggregating this probability across height thresholds provides enhanced P-values directly, without the need of permutation testing. Since a p(h_i|c_i) value correspond to the actual threshold hi and not the actual voxel value v_x, a special equidistant incremental logarithmic probability aggregation method is needed to construct the enhanced probability.