Replicable multivariate BWAS with moderate sample sizes

Abstract Brain-Wide Association Studies (BWAS) have become a dominant method for linking mind and brain over the past 30 years. Univariate models test tens to hundreds of thousands of brain voxels individually, whereas multivariate models (‘multivariate BWAS’) integrate signals across brain regions into a predictive model. Numerous problems have been raised with univariate BWAS, including lack of power and reliability and an inability to account for pattern-level information embedded in distributed neural circuits1–3. Multivariate predictive models address many of these concerns, and offer substantial promise for delivering brain-based measures of behavioral and clinical states and traits2,3. In their recent paper4, Marek et al. evaluated the effects of sample size on univariate and multivariate BWAS in three large-scale neuroimaging dataset and came to the general conclusion that “BWAS reproducibility requires samples with thousands of individuals”. We applaud their comprehensive analysis, and we agree that (a) large samples are needed when conducting univariate BWAS of individual differences in trait measures, and (b) multivariate BWAS reveal substantially larger effects and are therefore more highly powered. However, we disagree with Marek et al.’s claims that multivariate BWAS provide “inflated in-sample associations” that often fail to replicate (i.e., are underpowered), and that multivariate BWAS consequently require thousands of participants when predicting trait-level individual differences. Here we substantiate that (i) with appropriate methodology, the reported in-sample effect size inflation in multivariate BWAS can be entirely eliminated, and (ii) in most cases, multivariate BWAS effects are replicable with substantially smaller sample sizes (Figure 1).