Non-parametric conjunction null?

[lrq3000]

Hello,

I would like to use PALM to implement a non-parametric conjunction as defined in this paper. More precisely, this is to be applied on an fmri experiment, with the same dataset and subjects and data but on 2 different contrasts (eg, conjunction of [0.5 0.5 -0.5 -0.5] and [0 0 0.5 0.5]). I already have first-level BETA maps for all subjects and conditions, I just need to do the 2nd-level model, hopefully with a non-parametric conjunction and corrected with TFCE.

I have read the documentation and the various switches, but I cannot figure out how to do a non-parametric conjunction using PALM. According to the paper's Figure B1, the combination function needs to be the "maximum of p‐values for the partial tests, but with the p‐value computed as T [Nichols et al., 2005]", but I cannot find such a combination function under the -npcmethod switch nor under any other switch.

Thank you in advance to anyone who can enlighten me, I would be very glad to be able to use this method :-D

[nicholst]

@lrq3000,

I don't think it's a PALM option because it is a trivial manipulation: The minimum of p-values over each partial test. There is no new permutation or other calculation required.

I should note that the "min P" calculation is well defined for uncorrected voxel-wise P-values (which you could then submit to FDR thresholding, e.g. with FSL's fdr program) or voxel-wise FWE P-values. For TFCE, where each voxel is giving information over a variable and possible large expanse of space, I won't do the min P computation.

[lrq3000]

Dear @nicholst,

Thank you very much for your detailed reply and your explanation about TFCE, this is very helpful.

For my study design, I really need to ensure cluster-level correction, as the conjunction of voxels might produce a too high rate of false positive and hardly understandable results (with FDR thresholding, FWE being too conservative for my case). If I understand correctly, conjunction null is currently ill-defined for the calculation of cluster-level P-values (or is it only for TFCE?).

I thought cluster-level correction was possible after non-parametric combinations, even between modalities etc. Did I misunderstood? If correct, do you think a cluster-size or cluster-mass correction could be possible using an approach similar to non-parametric combinations but for conjunction null? If not, what do you think are the theoretical limits, or is it just that noone worked on this yet?

I think non-parametric combinations are a wonderful generic tool, and it would be equally wonderful and useful to have the same possibilities with conjunctions, since they are also very common in neuroimaging :-)

[lrq3000]

Addendum: from my understanding of the paper, the combination function was independent from correction, so that theoretically any set operation could work: here combinations = union, but potentially conjunction = intersection as hinted, and also exclusion, mutual exclusion etc.

[andersonwinkler]

Hi Stephen (@lrq3000),

The problem with trying to do a conjunction through a combining function is that it would not consider the correct null (IUT, as opposed to an UIT; see also Nichols et al 2005). In fact, that is available in PALM, though not generally recommended since, even for an UIT, the function using minT (or maxP) is also inconsistent: see Appendix B of Winkler et al 2016.

Your best approach is to do a voxelwise test, then take the minimum statistic (min T) or the largest p-value (max P, i.e., if the least significant is significant, then all others are).

Spatial statistics are precluded because of lack of spatial overlap over which a common null can be established, as indeed Tom explained above.

All the best,

Anderson