Robust circular cluster-based statistics for respiration-brain coupling

The rapidly developing research field of brain-body neuroscience faces methodological challenges, as analysts continue to develop new analysis strategies in the absence of established best practices. This quest for valid methods is further complicated by the (naturally) circular data involved in the study of phase-locked effects, e.g., in respiration-brain coupling. Various available approaches for phase extraction, constructing adequate surrogate data for statistical comparison, and accounting for the circularity of respiratory data lead to poor cross-study generalisability of results. Interpretation of effects is particularly affected by the problem of multiple comparisons in phase-related inferential statistics. In this tutorial, we propose a robust pipeline for respiration phase-related analyses based on a novel circular extension of cluster-based permutation testing. We highlight and offer guidance on critical parameters in the analysis, systematically compare various approaches being used in the field today, and provide open-access software code for flexible use and future development of our proposed pipeline.