Cluster extent inference revisited: quantification and localisation of brain activity

Cluster inference based on spatial extent thresholding is a popular analysis method multiple testing in spatial data, and is frequently used for finding activated brain areas in neuroimaging. However, the method has several well-known issues. While powerful for finding regions with some activation, the method as currently defined does not allow any further quantification or localisation of signal. In this paper, we repair this gap. We show that cluster-extent inference can be used (1) to infer the presence of signal in any region of interest and (2) to quantify the percentage of activation in such regions. These additional inferences come for free, i.e. they do not require any further adjustment of the alpha-level of tests, while retaining full family-wise error control. We achieve this extension of the possibilities of cluster inference by embedding the method into a closed testing procedure, and solving the graph-theoretic k-separator problem that results from this embedding. We demonstrate the usefulness of the improved method in a large-scale application to neuroimaging data from the Neurovault database.