Dear Jake,
> We have a question regarding correction for multiple comparisons in a
> diffusion tensor imaging study:
>
> We have conducted a DTI study in which we have a priori areas of
> interest
> in our voxel-based analysis. We've pulled out the areas of interest
> and
> are only evaluating them initially, so the correction for multiple
> comparisons should be based on the number of voxels considered, with
> smoothing/clustering criteria taken into account.
>
> So far, this is all fine. However, the problem arises when I realize
> that
> the registrations that FSL uses to put DTI data into standardized
> space
> (using an MNI template), takes 2x2x2 data and registers it into a
> 1x1x1
> volume. The voxel-based contrast is done on the registered 1x1x1
> images,
> and thus, eight times the number of comparisons are made than would
> have
> been made on the original data. So the question is: How do we
> correct for
> multiple comparisons? It doesn't make sense to me to "increase"
> resolution and the number of comparisons without actually adding real
> information.
There are two principal ways that people do corrections for multiple
comparisons in imaging. One is through something called "Gaussian
Random Field theory" (GRF). Slightly simplified one might say that one
estimates the smoothness of the data (i.e. how dependent adjacent
voxels are) and from that calculates the number of
"resels" (resolution elements). The correction for multiple
comparisons is then based on the number of resels, not the number of
voxels. That means that if you just up-sample your data by a factor of
two, the number of resels will not change (and hence not the
correction).
The other way is by permuting the design matrix (e.g. switching labels
between patients and controls) and through this build an empirical
estimate of the sampling distribution of the maximum t-value within
the volume of interest. If we reject the null hypothesis anywhere, we
will reject it at the maximum voxel (or, analogously, the largest
cluster) so by finding a threshold that the maximum t-value exceeds
only one time out of 20, we control for family wise error at the 0.05
level. Also this case is (of course) independent of any up-sampling of
the data.
Good Luck Jesper
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