Adaptive control of the false discovery rate in voxel-based morphometry

Voxel-based morphometry (VBM) is widely used as a high-resolution approach to understanding the relationship between anatomical structures and variables of interest. Controlling for the false discovery rate (FDR) is an attractive choice for thresholding the resulting statistical maps and has been commonly used in fMRI studies. However, we caution against the use of nonadaptive FDR control procedures, such as the most commonly used Benjamini-Hochberg procedure (B-H), in VBM analyses. This is because, in VBM analyses, specific risk factors may be associated with volume change in a global, rather than local, manner, which means the proportion of truly associated voxels among all voxels is large. In such a case, the achieved FDR obtained by nonadaptive procedures can be substantially lower than the nominal, or controlled, level. Such conservatism deprives researchers of power for detecting true associations. In this article, we advocate for the use of adaptive FDR control in VBM-type analyses. Specifically, we examine two representative adaptive procedures: the two-stage step-up procedure by Benjamini, Krieger and Yekutieli ([2006]: Biometrika 93:491-507) and the procedure of Storey and Tibshirani ([2003]: Proc Natl Acad Sci USA 100:9440-9445). We demonstrate mathematically, with simulations, and with a data example that these procedures provide improved performance over the B-H procedure.