Fig. 4: Multivariate brain-wide associations.
From: Reproducible brain-wide association studies require thousands of individuals
a–f, In-sample brain–behavioral phenotype associations as a function of out-of-sample associations and sample size. Mean multivariate brain–behavioral phenotype associations across 100 bootstrap samples at n = 200 (red dots) and for the full sample (black dots). Grey dashed lines represent the significance threshold for out-of-sample correlations (>99% confidence interval of permutations), determined on the full sample (see Methods, ‘Multivariate out-of-sample replication’). Data are from the ABCD Study; full sample sizes: cortical thickness n = 1,814; RSFC n = 1,964. a, b, For SVR, out-of-sample association strength is reported as the correlation between predicted and observed phenotype scores (rpred) using models trained on the discovery set. SVR of cortical thickness (a) and RSFC (b), with cognitive ability (green, left) and psychopathology (purple, right). c, d, For CCA, out-of-sample association strength is reported as the correlation of phenotypic and brain scores in the first canonical variate pair (rCV1) when discovery set weights are applied to the replication set. CCA of cortical thickness (c) and RSFC (d), with all NIH Toolbox (green, left) and CBCL (purple, right) subscales. e, Differences between out-of-sample (SVR: rpred; CCA: rCV1) and corresponding in-sample associations by multivariate method (left), imaging modality (middle) and behavioural phenotype (right); normalized to per-panel maximum. On average, out-of-sample associations (mean r = 0.17) were smaller (∆r = −0.29; 63% reduction) than in-sample associations (mean r = 0.46), similar to replication effect size reductions in cancer biology49 and psychology50. f, SVR out-of-sample association (rpred) as a function of univariate effect size (r; top 1% for each phenotype) across the 41 phenotypes (bivariate linear r = 0.79, orange line).
