Logical circularity in voxel-based analysis: normalization strategy may induce statistical bias.

Recent discussions within the neuroimaging community have highlighted the problematic presence of selection bias in experimental design. Although initially centering on the selection of voxels during the course of fMRI studies, we demonstrate how this bias can potentially corrupt voxel-based analyses. For such studies, template-based registration plays a critical role in which a representative template serves as the normalized space for group alignment. A standard approach maps each subject's image to a representative template before performing statistical comparisons between different groups. We analytically demonstrate that in these scenarios the popular sum of squared difference (SSD) intensity metric, implicitly surrogating as a quantification of anatomical alignment, instead explicitly maximizes effect size--an experimental design flaw referred to as "circularity bias." We illustrate how this selection bias varies in strength with the similarity metric used during registration under the hypothesis that while SSD-related metrics, such as Demons, will manifest similar effects, other metrics which are not formulated based on absolute intensity differences will produce less of an effect. Consequently, given the variability in voxel-based analysis outcomes with similarity metric choice, we caution researchers specifically in the use of SSD and SSD-related measures where normalization and statistical analysis involve the same image set. Instead, we advocate a more cautious approach where normalization of the individual subject images to the reference space occurs through corresponding image sets which are independent of statistical testing. Alternatively, one can use similarity terms that are less sensitive to this bias.