Control of false positive rates in clusterwise fMRI inferences

Random field theory (RFT) provided a theoretical foundation for cluster-extent-based thresholding, the most widely used method for multiple comparison correction of statistical maps in neuroimaging research. However, several studies questioned the validity of the standard clusterwise inference in fMRI analyses and observed inflated false positive rates. In particular, Eklund et al. [Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates, Proc. Natl. Acad. Sci. 113 (2016), pp. 7900–7905. Available at http://www.pnas.org/content/113/28/7900.abstract] used resting-state fMRI as null data and found false positive rates of up to $ 70\% $ 70%, which immediately led to many discussions. In this study, we summarize the assumptions in RFT clusterwise inference and propose new parametric ways to approximate the distribution of the cluster size by properly combining the limiting distribution of the cluster size given by Nosko [Local structure of Gaussian random fields in the vicinity of high-level shines, Sov. Math. Dokl. 10 (1969), pp. 1481–1484] and the expected value of the cluster size provided by Friston et al. [Assessing the significance of focal activations using their spatial extent, Hum. Brain Mapp. 1 (1994), pp. 210–220. Available at http://dx.doi.org/10.1002/hbm.460010306]. We evaluated our proposed method using four different classic simulation settings in published papers. Results show that our method produces a more stringent estimation of cluster extent size, which leads to a better control of false positive rates.