Large number of correlations with MRI region of interest (ROI) variables: What adjustment should I perform? In our group, we have measured grey matter volumes of about 20 regions of interest (ROI) and frequency of cannabis use. Now, we would like find out whether cannabis use is associated with grey matter volumes of any of the measured brain regions. Furthermore, we would like find out whether these associations differ in subgroups of our sample.
For each of the 20 ROIs, we have performed an ANCOVA with the ROI as dependent variable and cannabis use, group, sex, age, and total grey matter volume as independent variables. We are mainly interested in the effects of cannabis. The other independent variables in the models serve as control variables. To investigate group specific associatons between cannabis use and ROIs, we have specified interaction terms between cannabis use and group.
What kind of adjustment for multiple comparisons would you use in such an analysis?
I have already adjusted my p-values with the Benjamini-Hochberg procedure, but I'm concerned that it is too conservative because the ROI variables and consequently the associations between ROIs and cannabis use are not independent. I guess it would be more appropriate to analyze these associations in a single model such that the non-independency of the associations could be taken better into account. I was thinking about a mixed effects models in which the regression coefficient for cannabis use is allowed to randomly vary between ROIs. A big advantage of such an approach would be that one could adjust not only the standard errors of the regressions coefficients but also the parameter estimates themselves (due to shrinkage). Andrew Gelman has proposed such an approach in the following papers:
http://pps.sagepub.com/content/4/3/310.short
http://www.stat.columbia.edu/~gelman/research/unpublished/multiple2.pdf
Do you think this would be feasible in my situation? How would such a model be specified in R?
 A: The answer depends on the type of inference you wish to make. Do you wish to make statements about each ROI or do you want to quantify the distribution of effect over ROIs?
If you wish to infer on each ROI, multiplicity correction is the way to go. The fact that you do not need to define the exact dependence between the test statistics at each ROI isan generally an advantage. Unless, of course, you still lack power. Assuming you are able to quantify the exact dependence between ROIs, you can look for a rejection region that controls the FDR at the desired level using simulation (deriving it analytically might be rather hard).  If you are pleased with your findings using "vanilla" Benjamini-Hochberg, I would use it as is. 
On the other hand, if you wish to infer over all ROIs, there is a point in assuming the distribution of effects over ROIs. In which case you could indeed compute the mean activation over ROIs and the conditional distribution of the effect given the observed. Personally, I find this sort of analysis hard to interpret. Especially since the ROIs are defined only within your study (as such, they are random entities). I do suspect that en empirical Bayesian  (such as Gelman) might disagree with me on this point.
A: In case your approach is not look at the volume of a particular ROI but to "screen through" the whole brain to look for differences associated with cannabis use, maybe running voxel-based morphometry (http://dbm.neuro.uni-jena.de/vbm/) would be a more sensitive approach?
