Statistical analysis

All statistical analyses were conducted in R version 4.1.1. Formulas are described using the Wilkinson notation.

First, we identified the best generalized linear mixed-effects model for explaining the data. We used both a categorical and dimensional representation of ADHD on whole-brain FA to identify the most explanatory model for both approaches. The base model contained whole-brain FA (continuous) as dependent variable, in-scanner motion (continuous) as variable of interest and age (continuous), sex (categorical: male, female), IQ (continuous), and acquisition site (categorical: three sites) as confounding factors. The acquisition site was included to account for different scanning sites (compare [12, 41]). The categorical analysis compared the base model to extended models that included the ADHD category (categorical: ADHD-IN, ADHD-C, No ADHD) as a fixed effect and an interaction effect between the ADHD category and in-scanner head motion. The same procedure was applied for the dimensional analysis with the SWAN-HY score (continuous). To compare the models, we excluded participants with an ADHD-HI diagnosis from the dimensional analysis as well. Nested models were compared using an ANOVA (Supplement H). To further determine which model better explains the given data, we directly compared the categorical and the equivalent dimensional models with the same number of predictors using the Akaike information criterion (AIC) and the Bayesian information criterion (BIC).

We used a causal mediation analysis [88] to investigate whether differences in whole-brain FA and tract-wise FA can be explained by a mediating effect of in-scanner head motion rather than the disorder (see Fig. ​Fig.3).3). Based on the selected model (here the dimensional model), Model M0 to assess the direct effect of SWAN-HY on whole-brain and tract-wise mean FA disregarding the effect of in-scanner head motion was defined as

Model Y (orange) captures the average direct effect (ADE) of SWAN-HY on FA. Model M (yellow) reflects the effect of SWAN-HY on motion regardless of FA. The indirect effect of SWAH-HY on FA through the mediation of motion is the average causal mediation effect (ACME) (blue). Model M0 (green) captures the relationship of SWAN-HY on FA disregarding any effect of motion. SWAN-HY, Strengths and Weaknesses Assessment of Normal Behavior Rating Scale for ADHD Hyperactivity Score; FA, fractional anisotropy.

Model M0: FA ~ Age + Sex + IQ + Site + SWAN-HY.

Model M to assess the effect of SWAN-HY on in-scanner head motion was defined as

Model M: Motion ~ Age + Sex + IQ + Site + SWAN-HY.

Model Y, which comprises the effect of SWAN-HY and the effect of in-scanner head motion on FA, was defined as

Model Y: FA ~ Age + Sex + IQ + Site + Motion + SWAN-HY.

Models M and Y were used as input for causal mediation analysis. Figure ​Figure33 depicts the mediation relation analyzed in this study. The causal mediation analysis was calculated using the R package for causal mediation analysis with nonparametric bootstrap for confidence intervals and 5000 Monte Carlo draws [88]. Effect sizes for the causal mediation analysis are reported as portions of variance [89]. Because these measures are not squared but are results of arithmetic operations, they can be negative, indicating suppression effects [89, 90]. Prior to the causal mediation analysis, we confirmed a main effect of SWAN-HY in either Model M0 or M (Table ​(Table2),2), which is a premise for consecutive causal mediation analysis [91, 92]. In particular, the main effect of SWAN-HY on motion shows how ADHD symptomatology is associated with an increase in-scanner head motion.

Summary of regressions of Models M0 and M as premise for causal mediation analysis using the dimensional model.

SWAN-HY Strengths and Weaknesses Assessment of Normal Behavior Rating Scale for ADHD Hyperactivity Score, FA fractional anisotropy, CC corpus callosum, CST corticospinal tract, SLF superior longitudinal fasciculus, CI 95% confidence interval, r²_SF portion of variance in FA explained by SWAN-HY, r²_SM portion of variance in motion explained by SWAN-HY.