Discussion and Conclusions

In the introduction to this review, it was stated that classically the analysis is separated for each voxel, and separated for each subject. This is true in terms of estimation of the fixed effect and given that OLS is desired (although may not be optimal), but the estimation of the covariance structure does not imply separation (even if on some occasions one simply pools over all the subjects and groups). It might be desirable as well not to completely separate the analysis for voxels (which is normally the case, apart from the final stage of cluster-based thresholding). This restriction was, for example, lifted in the ``variance ratio smoothing'' method, and mentioned in the previous section. Thus, a point which should be addressed is the sample size required to do an fMRI-GLM analysis. It has been already pointed out that for a random subject effect analysis, this is crucial for good power. This fact is dependent on another point not discussed in this paper but crucial which can be summarised in a question: ``are these voxels representing the same variables over different time and subjects?". A short answer would be: ``this is a matter of data registration before multi-group subjects statistical analysis!" (see [15] for a good discussion of this). In the present paper when assessing activation two types of variation have been discussed: the within subject variation (repeated measures and registration error of the time course), and the between subject variation (population variation of the signal at a given voxel). A third type of variation has not been discussed, which is crucial when looking at multi-subject fMRI experiments, the variation due to error of co-registration of subjects confounded or not with the natural anatomic-functional variation from subject to subject. These three types of variation can be characterised as (i) measurement error and time variation, (ii) point population variation, (iii)spatial population variation and error, where here, error and variation are used to emphasise differences in variation due to the technical process of measurement (i.e. purely instrumental error but also within variation), and variation due to more natural causes(i.e. population variation). The analysis presented in this paper did not address the third type of variation (measurement error and time variation were also confounded). This spatial variation has obviously a greater impact in random subject analysis than in fixed subject analysis, as it plays a role in the location or estimation of possible activation (fixed and random approach) but also in the decision of significant activation through the variance estimation (only the random approach). A simple way to account for it is to perform ROI analysis or spatial smoothing before second level analysis. According to the activation estimation, these introduce a loss of specificity but also in sensitivity if the smoothing ``width" is larger than the activation ``area". Is this loss going to be counterbalanced by smaller variances achieved by smoothing? A way of keeping sensitivity when smoothing is to use a max-min filter [13] retaining for every subject only a maximum or minimum value on a neighbourhood of a given voxel (though activation would give a larger absolute value for the maximum, and deactivation would give a larger absolute value for the minimum). This approach was performed successfully [13] with permutation testing for fixed subject analysis in combining the z-maps, but could be more appropriate for random subject analysis (the filter is performed on the parameter maps) as a valid population method less conservative than its unfiltered counterpart.