Comparing extent of activation: A robust permutation approach

The number of contiguous voxels activated in a brain image can differ between groups or conditions even though the amplitude of activation does not markedly differ. Existing techniques test for differences in amplitude given that extent (number of contiguous voxels) exceeds some threshold. We present a technique that tests for differences in extent of activation given that amplitude of activation exceeds some threshold. The technique was motivated by apparent differences in extent of regional cerebral blood flow (rCBF) between hypertensive and normotensive participants performing cognitive tasks. These data are used to illustrate our test for extent of activation. We threshold the estimated parameter map for each subject, count the number of voxels exceeding the threshold over a defined region enclosing activated cortical area, and test the hypothesis of difference in the number of activated voxels between the two groups. Due to the large number of zeros resulting from the thresholding and the occurrence of extreme observations, we use a Robust permutation test [Lambert, D., 1985. Robust two-sample permutation tests. Ann. Stat., 13, 606-625], which is based on the sum of censored log-likelihood ratios. This statistic has desirable properties relative to the usual permutation test in contaminated distributions, i.e., idealized histogram with outliers, and provides an appropriate and robust test of extent of activation between conditions or groups.