Power, positive predictive value, and sample size calculations for random field theory-based fMRI inference

Recent discussions on the reproducibility of task-related functional magnetic resonance imaging (fMRI) studies have emphasized the importance of power and sample size calculations in fMRI study planning. In general, statistical power and sample size calculations are dependent on the statistical inference framework that is used to test hypotheses. Bibliometric analyses suggest that random field theory (RFT)-based voxel- and cluster-level fMRI inference are the most commonly used approaches for the statistical evaluation of task-related fMRI data. However, general power and sample size calculations for these inference approaches remain elusive. Based on the mathematical theory of RFT-based inference, we here develop power and positive predictive value (PPV) functions for voxel- and cluster-level inference in both uncorrected single test and corrected multiple testing scenarios. Moreover, we apply the theoretical results to evaluate the sample size necessary to achieve desired power and PPV levels based on an fMRI pilot study.