Providing Evidence for the Null Hypothesis in Functional Magnetic Resonance Imaging Using Group-Level Bayesian Inference

Abstract

Classical null hypothesis significance testing is limited to the rejection of the point-null hypothesis; it does not allow the interpretation of non-significant results. This leads to a bias against the null hypothesis. Herein, we discuss statistical approaches to ‘null effect’ assessment focusing on the Bayesian parameter inference (BPI). Although Bayesian methods have been theoretically elaborated and implemented in common neuroimaging software packages, they are not widely used for ‘null effect’ assessment. BPI considers the posterior probability of finding the effect within or outside the region of practical equivalence to the null value. It can be used to find both ‘activated/deactivated’ and ‘not activated’ voxels or to indicate that the obtained data are not sufficient using a single decision rule. It also allows to evaluate the data as the sample size increases and decide to stop the experiment if the obtained data are sufficient to make a confident inference. To demonstrate the advantages of using BPI for fMRI data group analysis, we compare it with classical null hypothesis significance testing on empirical data. We also use simulated data to show how BPI performs under different effect sizes, noise levels, noise distributions and sample sizes. Finally, we consider the problem of defining the region of practical equivalence for BPI and discuss possible applications of BPI in fMRI studies. To facilitate ‘null effect’ assessment for fMRI practitioners, we provide Statistical Parametric Mapping 12 based toolbox for Bayesian inference.

No changes in triple network engagement following (combined) noradrenergic and glucocorticoid stimulation in healthy men

“…In order to investigate whether the absence of network differences between groups reflected evidence for the null hypothesis, we additionally conducted group-level Bayesian parameter inference (BPI) in SPM12 (Statistical Parametric Mapping; http://www.fil.ion.ucl.ac.uk/spm ; v7771) using the BayInf toolbox ( Masharipov et al. , 2021 ).…”

“…BPI evaluates the posterior probability of finding the experimental effect within or outside the region of practical equivalence (ROPE) to the null value. Parameter estimation of the BayInf toolbox is based on a parametric empirical Bayes approach with a ‘global shrinkage’ prior ( Masharipov et al. , 2021 ).…”

“…Estimated ES thresholds were: 0.85 for the DMN, 0.93 for the SN, and 0.79 for the ECN. The posterior probability threshold was P thr = 95%, which is equal to Log Posterior Odds (LPO) > 3 ( Masharipov et al. , 2021 ).…”