Clustersize inference is more informative than TFCE

1871 

Abstract Submission 

Samuel Davenport¹, Wouter Weeda², Jelle Goeman³

¹University of Calfornia San Diego, LA Jolla, San Diego, CA, ²Leiden University, Leiden, South Holland, ³Leiden University Medical Center, Leiden, South Holland

Samuel Davenport  
University of Calfornia San Diego
LA Jolla, San Diego, CA

Wouter Weeda  
Leiden University
Leiden, South Holland

Jelle Goeman  
Leiden University Medical Center
Leiden, South Holland

Cluster-size inference is one of the most popular approaches in neuroimaging analysis but has been criticized for its dependence on an arbitrary (but important) cluster-forming threshold. Threshold-Free Cluster Enhancement (TFCE) was proposed in Smith (2009) with the aim of 1) decreasing the arbitrariness of the cluster-forming threshold and 2) being more sensitive to brain activation. Here we will show that TFCE does not achieve these aims. First, TFCE introduces more free parameters into the model than cluster-size inference, making it more dependent on researchers' choices. Second, the large clusters of TFCE, often mistakenly interpreted voxel-wise, actually hamper interpretation as the spatial specificity paradox increases. We will show, using recent advances in multiple testing, that cluster-size inference is a more robust way of doing neuroimaging analyses.

Traditional cluster-size inference makes the weak claim that one voxel within an observed significant cluster above the cluster-defining threshold (CDT) is active. Goeman (2023) showed that cluster-size inference can be embedded into a closed testing procedure. This embedding allows more informative statements to be made. In particular, it provides a 95%-confidence lower bound on the True Discovery proportion (TDP), the proportion of truly active voxels in every cluster. TFCE is often interpreted as making a stronger claim that all voxels in the TFCE-cluster are active. We explicitly refute this claim and prove that TFCE does not even, in general, allow inference that a single voxel is active in the TFCE cluster, but only that such a voxel exists in its surroundings.

TFCE aims to reduce the number of free parameters available for the user to select. However it in fact relies on 3 free parameters, E – the power of the cluster extent, H – the power applied to the height and h_0, which we call the TFCE cluster forming threshold. Thus TFCE introduces more parameters for the researcher not less. While users typically use the default parameter configuration when performing inference using TFCE the same is true for cluster size inference.

In order to compare the performance of TFCE and cluster-size inference in practice we compare the results of applying TFCE and cluster-size inference to two different brain imaging datasets, with their default parameter configurations. The first consists of the 80 subjects from the Human Connectome Project (Essen, 2013) who have performed a working memory task. The second consists of 124 subjects from who have undergone an auditory task. The results are shown in Figure 1. They illustrate that clustersize inference is substantially more informative than TFCE. Due to the large size of the TFCE clusters, TFCE is only able to make the weak statement that some voxel is active somewhere in the brain. Instead clustersize inference provides meaningful lower bounds on the proportion of active voxels within each cluster.

In Figure 2 we present the results from performing a simulation, adding smooth noise to a signal with two blocks. The results demonstrate the cluster leakage that can occur with TFCE, showing that interpreting TFCE voxelwise can lead to false positives.

The information provided by inference using TFCE is quite limited. TFCE clusters can span a large proportion of the brain making it very difficult to localize activation. Instead cluster-size inference is more informative, enabling increased localisation and TDP lower bounds for each cluster. Lower bounds could in principle be derived for TFCE from the embedded closed testing procedure but this seems a priori very difficult. Moreover TFCE is substantially slower than cluster-size inference because it requires that the TFCE statistic be calculated for each permutation. For these reasons we recommend that researchers use cluster-size inference, with lower-bound estimates of the number of active voxels within each cluster, over TFCE when performing brain-imaging analyses.

Activation (eg. BOLD task-fMRI) ²

Methods Development ¹

FUNCTIONAL MRI

Modeling

Statistical Methods

Other - TFCE, clustersize inference