Spatial confidence sets for raw effect size images

Abstract The mass-univariate approach for functional magnetic resonance imaging (fMRI) analysis remains a widely used statistical tool within neuroimaging. However, this method suffers from at least two fundamental limitations: First, with sufficient sample sizes there is high enough statistical power to reject the null hypothesis everywhere, making it difficult if not impossible to localize effects of interest. Second, with any sample size, when cluster-size inference is used a significant p-value only indicates that a cluster is larger than chance. Therefore, no notion of confidence is available to express the size or location of a cluster that could be expected with repeated sampling from the population. In this work, we address these issues by extending on a method proposed by Sommerfeld et al. (2018) (SSS) to develop spatial Confidence Sets (CSs) on clusters found in thresholded raw effect size maps. While hypothesis testing indicates where the null, i.e. a raw effect size of zero, can be rejected, the CSs give statements on the locations where raw effect sizes exceed, and fall short of, a non-zero threshold, providing both an upper and lower CS. While the method can be applied to any mass-univariate General Linear Model, we motivate the method in the context of blood-oxygen-level-dependent (BOLD) fMRI contrast maps for inference on percentage BOLD change raw effects. We propose several theoretical and practical implementation advancements to the original method formulated in SSS, delivering a procedure with superior performance in sample sizes as low as N = 60 . We validate the method with 3D Monte Carlo simulations that resemble fMRI data. Finally, we compute CSs for the Human Connectome Project working memory task contrast images, illustrating the brain regions that show a reliable %BOLD change for a given %BOLD threshold.