Dear Joaquim and SDM users,

While undertaking a coordinate meta-analysis (VBM gray matter - but potentially could apply to fMRI) I came across a unusual ring/circle rather than a blob on the final SDM map. I am unsure if this is an unusual error/artifact or there is some other reason for this. Please see attached image

I have simplified the SDM analysis to see if others can reproduce this - the blob is from a single coordinate at 22,-51,-48 with a t score of -4. Looking at the attached image on the left is the image MyMean_z_p_0.00500_1.000_10_neg.nii.gz on the right is the image pp_StudyA.nii.gz. The right image shows the preprocessed image of the single coordinate - one can see the gray matter mask affects the region but does not touch the maximum, however in the thresholded negative z score image (left) the effect is quite different and there is a ring around a z score of zero

To simplify the analysis I have only 3 studies and 2 of these have no coordinates and one study has the single coord - even if other studies are added the aftifact remains.
I will attempt to attach the input files in a follow-up email.

I am using SDM 4.31 on linux (virtual machine on a Mac) but one of my students reproduced this on SDM 4.31 on Windows

Many thanks,

Matthew

To follow-up all input files required are on the attachment to reproduce this issue

Using SDM 4.31 I did the following
Preprocessing - choose VBM gray matter, all other options are default
Mean - default options
Threshold - default options
Open MyMean_z_p_0.00500_1.000_10_neg.nii.gz to see the ring

I have tried increasing the t value and this can lead to a dot within the ring, if the coordinate is moved this can result in a normal single blob being produced. I'm wondering if it is therefore some interaction between the gray matter mask and the thesholding causing this

Thanks,

Matthew

Dear Matthew,

thank you very much for noting this issue, I must say I had not seen it before but I could easily replicate it with your data.

After some simulations, my view is that this is not a software bug but something similar to a small statistical artifact. Currently, SDM assigns a null effect size to voxels far from any peak, but this is indeed conservatively biased when other studies report a peak there, because the most likely effect size is not zero (see http://archpsyc.jamanetwork.com/article.aspx?articleid=2469108 for details). I think that these conservatively biased effect sizes inflate the estimated between-study heterogeneity, decreasing the z-values, up to the paradox that the higher the effect size of the voxels of another study reporting a peak there, the lower the statistical significance of the voxels in the meta-analysis. At least, this is what seems to happen in the toy simulation below...

Fortunately, the simulation also shows that the paradox is rather small, so that the strange rings would only appear when the threshold is in a small range of effect sizes (see the plot attached).

Also, I hope that new versions of SDM will address this issue.  ;-)


library(meta)
x = -100:100 / 2 # This is a line of voxels
a = exp(-4 * log(2) / 20^2 * x^2) # Peak at x = 0, FWHM = 20mm
b = rep(0, length(x)); # No close peaks
c = rep(0, length(x)); # No close peaks
vara = 1 / 28 + 1 / 30 + (1 - (gamma((58 - 3) / 2) / gamma((58 - 2) / 2))^2 * (58 - 4) / 2) * a^2
varb = 1 / 26 + 1 / 33 + (1 - (gamma((59 - 3) / 2) / gamma((59 - 2) / 2))^2 * (59 - 4) / 2) * b^2
varc = 1 / 30 + 1 / 20 + (1 - (gamma((50 - 3) / 2) / gamma((50 - 2) / 2))^2 * (50 - 4) / 2) * c^2
z = rep(NA, length(x))
for (i in 1:length(x)) {
z = metagen(c(a, b, c), sqrt(c(vara, varb, varc)))$zval.random
}
plot(x, z, type = "l")

Hi Joaquim,

Many thanks for investigating this! The graph and your explanation was very helpful in visualising how it works.

I'm wondering if you will be doing something clever like you have done in MetanSUE instead of assuming a null effect size in the next SDM version..

Best wishes,

Matthew