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in the following papers: http://pps.sagepub.com/content/4/3/310.short http://www.stat.columbia.edu/~gelman/research/unpublished/multiple2.pdf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?