Robust estimation of the probabilities of 3-D clusters in functional brain images: application to PET data

Recently, we presented a method (the CS method) for estimating the probability distributions of the sizes of supra threshold clusters in functional brain images [Ledberg A, Akerman S, Roland PE. 1998. Estimating the significance of 3D clusters in functional brain images. NeuroImage 8:113-128]. In that method, the significance of the observed test statistic (cluster size) is assessed by comparing it with a sample of the test statistic obtained from simulated statistical images (SSIs). These images are generated to have the same spatial autocorrelation as the observed statistical image (t-image) would have under the null hypothesis. The CS method relies on the assumptions that the t-images are stationary and that they can be transformed to have a normal distribution. These assumptions are not always valid, and thus limit the applicability of the method. The purpose of this paper is to present a modification of the previous method, that does not depend on these assumptions. This modified CS method (MCS) uses the residuals in the linear model as a model of a dataset obtained under the null hypothesis. Subsequently, datasets with the same distribution as the residuals are generated, and from these datasets the SSIs are derived. These SSIs are t-distributed. Thus, a conversion to normal distribution is no longer needed. Furthermore, no assumptions concerning the stationarity of the statistical images are needed. The MCS method is validated on both synthetical images and PET images and is shown to give accurate estimates of the probability distribution of the cluster size statistic.