Effects of large-scale nonstationarity on parametric maps. A study of rest perfusion CASL data

This study investigates the emergence of characteristic patterns in clusters thresholded at uncorrected significance levels, using as a case study rest perfusion images obtained with the continuous arterial spin labelling technique (CASL). The origin of these patterns is traced back to the existence of large-scale spatial covariance, a violation of the stationarity assumption on the spatial distribution of residual errors. It is shown that in the presence of large-scale covariance, several principles or intuitions common among experimenters when evaluating the inferential strength of their analyses are not applicable. Thresholded maps and clusters are confounded by the spatial patterns of large-scale covariance, irrespective of the existence of a true effect, as shown in t maps constructed by resampling groups at random from a large pool of volumes. Filtering clusters according to their size made the problem worse, and corrections on cluster size based on random field theory models of smoothness had only a minor impact on their tendency to appear in characteristic locations. A formal analysis shows that the large-scale covariance at the origin of these problems is retained in the parametric map irrespective of sample size. Therefore, neither sample independence nor sample size protect from replications of effects being confounded by replications of the spatial covariance of residual errors. In contrast, cluster peaks were not affected by large-scale covariance but only by local differences in smoothness levels, as predicted by random field theory for the distribution of maxima, highlighting the different inferential robustness of cluster-based and maxima-based statistics. A framework is provided to generalize these results to mixed effects models with nested random effects, applicable also to activation studies. Large-scale nonstationarity is most problematic when the variance source at the origin of the characteristic patterns is not specific to a function or variable involved in the inferential process, as typically in observational studies of individual differences. These results raise the question of the existence and impact of large-scale nonstationarity in studies with data obtained with other techniques.