Coordinate based meta-analysis of functional neuroimaging data using activation likelihood estimation; full width half max and group comparisons.

Coordinate based meta-analysis (CBMA) is used to find regions of consistent activation across fMRI and PET studies selected for their functional relevance to a hypothesis. Results are clusters of foci where multiple studies report in the same spatial region, indicating functional relevance. Contrast meta-analysis finds regions where there are consistent differences in activation pattern between two groups. The activation likelihood estimate methods tackle these problems, but require a specification of uncertainty in foci location: the full width half max (FWHM). Results are sensitive to FWHM. Furthermore, contrast meta-analysis requires correction for multiple statistical tests. Consequently it is sensitive only to very significant localised differences that produce very small p-values, which remain significant after correction; subtle diffuse differences between the groups can be overlooked. In this report we redefine the FWHM parameter, by analogy with a density clustering algorithm, and provide a method to estimate it. The FWHM is modified to account for the number of studies in the analysis, and represents a substantial change to the CBMA philosophy that can be applied to the current algorithms. Consequently we observe more reliable detection of clusters when there are few studies in the CBMA, and a decreasing false positive rate with larger study numbers. By contrast the standard definition (FWHM independent of the number of studies) is demonstrated to paradoxically increase the false positive rate as the number of studies increases, while reducing ability to detect true clusters for small numbers of studies. We also provide an algorithm for contrast meta-analysis, which includes a correction for multiple correlated tests that controls for the proportion of false clusters expected under the null hypothesis. Furthermore, we detail an omnibus test of difference between groups that is more sensitive than contrast meta-analysis when differences are diffuse. This test is useful where contrast meta-analysis is unrevealing.