DiscussionGenerative and recognition models for neuroanatomy☆
Section snippets
The issue
As with previous critiques of voxel-based morphometry (e.g., see Bookstein, 2001, Mehta et al., 2003), Christos Davatzikos (2004) reprises issues that have engaged the functional neuroimaging community for many years. In this instance, the issue is the distinction between multivariate and mass-univariate analyses of imaging data. Put simply, Davatzikos is pointing out that pathology can be expressed, anatomically, in a distributed and complicated fashion over the brain. Critically, its
Voxel-based morphometry
Voxel-based morphometry is the application of statistical parametric mapping to (spatially normalized, scalar) images that index some aspect of local brain structure, for example, grey matter density following segmentation or compression maps based on the Jacobian of deformation fields. As such, VBM uses a mass-univariate approach. VBM was proposed and designed for the analysis of regionally specific differences in structural indices. The nature of these indices and ensuing interpretation
Distributed versus dependent
It is important to distinguish between the presence of distributed effects over the brain and dependencies among these effects. It is perfectly possible for VBM to detect a distributed pattern of regionally specific effects. However, VBM is not appropriate for the analysis of statistical dependencies among measures from different regions. The example shown in Fig. 1 (left-hand panel) of Davatzikos's paper is, in fact, a rather bad example to use from his point of view. This is a linear
Multivariate versus mass-univariate
In functional anatomy, this dichotomy is closely related to the distinction between functional specialization and functional integration in the brain. Most analyses of neuroimaging data are predicated on the specialization or segregation model and are happy to limit their inferences to regionally specific effects using univariate approaches. The alternative is to characterize treatment-related responses in one brain area, in relation to responses elsewhere. This calls for multivariate models
Using VBM to assess interregional dependencies
Usually, interregional dependencies are accommodated by treating the region as a factor in multivariate statistical models and looking for region × treatment interactions. However, there are ways of using univariate VBM to assess these sorts of effects. This entails using the response variable in one region as an explanatory variable for other regions. For example, to test for the negative correlations in Fig. 2b (middle panel), one would simply construct an SPM using the measures in voxel 1
Characterization versus classification
Finally, Davatzikos makes an important point that procedures for making statistical inferences about regionally specific effects (i.e., VBM) are not necessarily the best for classifying patients. This is absolutely right. VBM is a research tool that enables people to ask specific questions of their data. It is not a diagnostic or classification device. Although there is a close mathematical relationship between CVA and discriminant function analysis, the objectives of classification procedures
Summary
In conclusion, there is a clear distinction between multivariate and mass-univariate characterizations of brain imaging data. The application of standard univariate approaches to structural data, namely VBM, has proved extremely successful. Part of this success can be explained by the fact that VBM allows researchers to frame and report their analyses in terms of regionally specific effects that refer directly to structure–function relationships. The main point made by Davatzikos is that
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A response to “Why voxel-based morphometric analysis should be used with great caution when characterizing group differences,” by Christos Davatzikos (doi:10.1016/j.neuroimage.2004.05.010).