How to do Topological FDR

Many ask “how to do Topological FDR” in SPM ML. Below are the posts I found useful.

Originally Guillaume Flandin showed how to do that.;44838216.0904

The height threshold you define during the Results procedure is the feature-inducing threshold (used to define local maxima and clusters).
For topological FDR, I would typically choose “none” and a small T-value, for example 3.
The MIP will display all voxels whose T-value is above 3 and the Results table will display all local maxima whose T-value is above 3 (actually, at most 3 local maxima per cluster, more than 8mm apart) and the corresponding FWE p-values and FDR q-values for peaks and clusters.

If you want to threshold the MIP to a particular significance level, go through the Results procedure again and enter the corresponding height and extent thresholds (the 0.05 critical thresholds are indicated at the bottom left of the Results table):
(height) FWEp and FDRp for peak-FWE and -FDR.
(extent) FWEc amd FDRc for cluster-FWE and -FDR.

Jonathan Peele also gave a detail instruction of how to do that. This time he focused more on cluster-thresholded FDR.;6f4e0139.1110

> How can I see images with a threshold at the cluster-level instead of the peak level with the graphical user interface?

I’m not aware of a way to set a cluster-level threshold when running results the first time (i.e., “show everything that is cluster-level corrected p < .05").  What I would do is this: 1) Run results using some voxelwise threshold.  This threshold defines your clusters, and it's fine to use an uncorrected threshold (e.g., p< .001, uncorrected). 2) In the results table, for each cluster you will see the cluster extent (i.e. how many voxels) and the cluster-corrected p value.  In SPM8 you will see 2 cluster-corrected p values, one for topological FDR (Chumbley & Friston, 2009), one for random field theory (labeled FWE).  You can then look at the size of those clusters, and figure out the cluster extent  that divides p < .05 from the others.  For example, if a cluster of 300 voxels is p = .10, and a cluster of 400 voxels is p = .04, then you know that any cluster 400 voxels or larger would be p < .05. 3) Re-run the results, selecting the same voxelwise threshold. But now, in the minimum cluster extent, specify the cluster size you just figured out—in the above example, you could specify 400.

4) Now all of the displayed results should be cluster-level corrected.

5) If you want to save this thresholded image for displaying with another program, just click the “save” button, and you can write out a thresholded t map as a nifti file.

In practice this is actually fairly quick to do once you’ve done it a couple of times.

Note the difference between these two. Two-step approach is the same, but Guillaume’s way deals with peak and cluster threshold and Jonathan’s way deals with cluster threshold.

Voxel-wise FDR and Topological FDR

In SPM8, voxel-wise FDR was hidden and Topological FDR was introduced. What is Topological FDR? I find some useful notes from SPM8 Release Notes and a post by Tom Nichols to SPM-ML. I quote these two.

SPM8 Release Notes

Topological False Discovery Rate (FDR)

FDR control is an alternative to the more conservative “family-wise error” control for multiple comparisons. Historically, SPM has aimed to control FDR on voxels (the
expected fraction of false-positive/total-positive decisions made about individual voxels in an image). This is now superseded by FDR control of topological properties of the signal (i.e. control of properties that pertain to the spatial organization of activations – e.g. height and extent – and are not reducible to individual voxels). SPM is now able to identify significantly voluminous blobs according to a decision procedure that controls spatial-extent FDR. Thus, on average, the fraction of blobs falsely deemed to have significant spatial extent is controlled beneath say 5/100 = .05 or 1/100 = .01. More recent work is examining FDR control over local maxima.

A post to SPM-ML by Tom Nichols

In SPM8 FDR topological inference was introduced, and voxel-wise FDR inference hidden. Topological inference means inference on peaks and clusters; voxel-wise inference is based on every individual voxel in the image (instead of spatial features of the image). Thus “Topological FDR” means inference on clusters based on cluster size (or local peaks based on peak height), controlling the fraction of false positive clusters among all clusters (or false positive peaks among all peaks) on average, over many experiments.

While topological FDR results may be easier to interpret, in my experience it is is generally not very sensitivity and yields similar results to FWE-corrected inferences.

If you would like to use voxel-wise FDR in SPM8, edit spm_defaults, changing “topoFDR” line to read
defaults.stats.topoFDR = 0;
(quit and re-start SPM to take effect).

Chumbley, J., Worsley, K., Flandin, G., & Friston, K. (2010). Topological FDR for neuroimaging. NeuroImage, 49(4), 3057-64. doi: 10.1016/j.neuroimage.2009.10.090.

Chumbley, J. R., & Friston, K. J. (2009). False discovery rate revisited: FDR and topological inference using Gaussian random fields. Neuroimage, 44(1), 62–70. doi: 10.1016/j.neuroimage.2008.05.021.