Advances in FDR for fMRI

Ruth Heller
University of Pennsylvania

The fundamental units of interests in fMRI are the spatially contiguous clusters of voxels that are activated together. The investigator may know
a-priori these cluster units or an approximation to them. Since the activation may be absent from part of each cluster, we define a cluster as active if there is activation somewhere within the cluster. Testing these cluster units has a two-fold statistical advantage over testing each voxel separately: the signal to noise ratio within the unit tested may be higher, and the number
of hypotheses compared is smaller. We suggest controlling the false discovery rate on clusters (FDRc), i.e. the expected proportion of clusters rejected erroneously out of all clusters rejected, or its extension to general weights (WFDRc). Once the cluster discoveries have been made, we suggest ’cleaning’ non-active voxels within the cluster discoveries. For this purpose we develop
a hierarchical testing procedure that tests clusters first, then voxels within rejected clusters. Next, we address the problem of testing whether at least u out of n conditions considered activate the clusters. It offers an in-between approach to testing that non of the conditions activate the cluster (u=1) and that not all of
the conditions activate the cluster (u=n). We suggest powerful test statistics that are valid under dependence between the individual condition p-values as well as under independence. We address the problem of testing many such partial conjunction hypotheses simultaneously using the FDR approach. If inference at all levels u = 1, . . . , n is of interest we suggest a procedure that
controls an appropriate FDR measure, called the overall FDR, and produces an informative display of the findings. We use the above approach,
replacing conditions by subjects, to produce informative group maps that offer an
alternative to mixed/random effect analysis.

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