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")