Study design features that improve effect sizes in cross-sectional and longitudinal brain-wide association studies.

Brain-wide association studies (BWAS) are a fundamental tool in discovering brain-behavior associations. Several recent studies showed that thousands of study participants are required to improve the replicability of BWAS because actual effect sizes are much smaller than those reported in smaller studies. Here, we perform analyses and meta-analyses of a robust effect size index (RESI) using 63 longitudinal and cross-sectional magnetic resonance imaging studies from the Lifespan Brain Chart Consortium (77,695 total scans) to demonstrate that optimizing study design is critical for improving standardized effect sizes and replicability in BWAS. A meta-analysis of brain volume associations with age indicates that BWAS with larger covariate variance have larger effect size estimates and that the longitudinal studies we examined have systematically larger standardized effect sizes than cross-sectional studies. We propose a cross-sectional RESI to adjust for the systematic difference in effect sizes between cross-sectional and longitudinal studies that allows investigators to quantify the benefit of conducting their study longitudinally. Analyzing age effects on global and regional brain measures from the United Kingdom Biobank and the Alzheimer's Disease Neuroimaging Initiative, we show that modifying longitudinal study design through sampling schemes to increase between-subject variability and adding a single additional longitudinal measurement per subject can improve effect sizes. However, evaluating these longitudinal sampling schemes on cognitive, psychopathology, and demographic associations with structural and functional brain outcome measures in the Adolescent Brain and Cognitive Development dataset shows that commonly used longitudinal models can, counterintuitively, reduce effect sizes. We demonstrate that the benefit of conducting longitudinal studies depends on the strengths of the between- and within-subject associations of the brain and non-brain measures. Explicitly modeling between- and within-subject effects avoids conflating the effects and allows optimizing effect sizes for them separately. These findings underscore the importance of considering study design features to improve the replicability of BWAS.

Accurate Confidence and Bayesian Interval Estimation for Non-centrality Parameters and Effect Size Indices.

Reporting effect size index estimates with their confidence intervals (CIs) can be an excellent way to simultaneously communicate the strength and precision of the observed evidence. We recently proposed a robust effect size index (RESI) that is advantageous over common indices because it's widely applicable to different types of data. Here, we use statistical theory and simulations to develop and evaluate RESI estimators and confidence/credible intervals that rely on different covariance estimators. Our results show (1) counter to intuition, the randomness of covariates reduces coverage for Chi-squared and F CIs; (2) when the variance of the estimators is estimated, the non-central Chi-squared and F CIs using the parametric and robust RESI estimators fail to cover the true effect size at the nominal level. Using the robust estimator along with the proposed nonparametric bootstrap or Bayesian (credible) intervals provides valid inference for the RESI, even when model assumptions may be violated. This work forms a unified effect size reporting procedure, such that effect sizes with confidence/credible intervals can be easily reported in an analysis of variance (ANOVA) table format.