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 This is now superseded by FDR control of topological properties of the signal (i.e. control of properties that pertain to the spatial organization of activations – e.g. height and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.

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