Hello Gang,

thanks for your comment.

Gang Chen wrote:

> FDR may be generally more conservative than FWE, but not
> always. In occasions when you don't want to smooth the original
> signal as much as usual (e.g., maintaining the signal strength
> in a small region in the brain), FDR may be more favorable. In
> other words, a few voxels with high statistic values in such
> scenario will be easier to survive FDR than FWE.

If I understand correctly, the reason would be that with typical FWE (thinking of alphasim) the uncorrected p value is set *a priori*, and then surviving voxels are considered irrespective of how significant they were. So with p=1e-3 uncorrected, we could have three voxels A, B, C with p_A=1.1e-3 (survived almost), p_B=9e-4 (survived only just) and p_C=1e-9 (survived easily) yet alphasim treats B and C the same and A differently. With FDR, A and B are treated almost the same but C differently. And if C was a single voxel it might still survive the FDR threshold, while it would never survive the alpahsim one.

To follow up on this, recently there was this nice paper by Smith and Nichols describing a technique they called "threshold free cluster enhancement" (TFCE) (http://www.ncbi.nlm.nih.gov/pubmed/18501637). The idea is similar to alphasim, but the great feature of this approach is that it does not require an uncorrected p value a priori. Instead, for TCFE one takes many different p values, each resulting in different activation maps, and then computes a weighted sum over all these maps (that are clustered first) to assign a cluster-size corrected p value for each voxel. (A while ago I wrote a simple implementation for surface analysis and this seems to work quite nicely). With such an approach, also small clusters of highly active voxels would get a very significant p-value. Importantly it still takes into account the spatial neighbourhood of such voxels, so it seems that such a cluster will be even more significant using TFCE than with FDR. Does this makes sense? Do you see any drawbacks of TFCE?

> > If we have a statistical brain map that is not very smooth,
> we may find many
> > very 'active' voxels (i.e. very low p values). If we smooth
> the data first
> > before doing the stats, however, the distribution of these p
> values will
> > change (and typically voxels will become less significantly
> active, but in
> > larger clusters). Importantly, the procedure for computing
> FDR q values
> > remains the same.
>
> Well, the procedure for FDR correction is the same, but the
> smoothing will change the p-value distribution as well to the
> extent dependent upon the smoothing size, leading to a slightly
> different q-value from the original one without smoothing.

That's what I meant. Generally after smoothing we will have fewer voxels that survive a given <q FDR threshold, as the extreme low FDR q-values will 'average out' spatially with neighbouring voxels that have higher q-values. So with FDR, we will generally find less voxels 'active' after smoothing, right?

> One problem with FDR is its high sensitivity to the statistic
> landscape. If there are huge number of isolated individual
> voxels with low p-values either outside, along the boundary, or
> inside the brain (CSF or white matter, for example), FDR will
> definitely please you!

Unfortunately I don't follow your logic here. You're not talking about grey matter masking right?
For the FDR case, if we have many 'irrelevant' (outside grey matter) voxels that show low p-values, then that would mean that 'relevant' voxels have a lower chance of being significant. For the alphasim case, if relevant voxels tend to cluster together but irrelevant ones are scattered randomly (as we would expect if some brain regions shows an experimental effect), it seems to me that relevant voxels in clusters would be favored. Is that intuition correct?

Thanks again, and I look forward to your reaction. I've always felt a need for a little more clarification on these whole brain correction for multiple comparison issues, and it would be great if you could answer my questions.

cheers,
Nick