The Etiological Structure of Cognitive-Neurophysiological Impairments in ADHD in Adolescence and Young Adulthood

Objective: Previous studies in children with ADHD identified two partially separable familial factors underlying cognitive dysfunction, but evidence in adolescents and adults is lacking. Here, we investigate the etiological structure of cognitive-neurophysiological impairments in ADHD in adolescents and young adults. Method: Factor analyses and multivariate familial models were run in 356 participants from ADHD and control sibling pairs aged 11 to 27 years on data on IQ, digit span forward (DSF) and backward (DSB), and cognitive-performance and event-related potential (ERP) measures from three cognitive tasks. Results: Three familial factors (cF1-3), showing substantial familial overlap with ADHD, captured the familial covariation of ADHD with nine cognitive-ERP measures. cF1 loaded on IQ, mean reaction time (MRT), and reaction-time variability (RTV); cF2 on DSF and DSB; and cF3 on number of errors and ERPs of inhibition and error processing. Conclusion: These results identify three partially separable etiological pathways leading to cognitive-neurophysiological impairments in adolescent and adult ADHD.

contacted by telephone and scheduled for a single testing session including clinical, cognitive and EEG assessments. Retention rate at follow-up was 77%.

ERP analysis
ERP measures which showed ADHD-control differences in our previous work on this sample were included in this study, following the same ERP protocol used in our previous analyses showing ADHDcontrol differences in these tasks (Cheung et al., 2017, Michelini et al., 2016. ERPs from the cued performance task (CPT-OX) included the Cue-P3, the CNV and the NoGo-P3 . ERP components in this task were measured without applying a pre-stimulus baseline correction in line with previous ERP analyses on the same paradigm (Albrecht et al. 2013;McLoughlin et al. 2010;Cheung et al., 2016). The Cue-P3 amplitude was measured as the maximum positive peak between 250-600ms following cue trials at Pz. The CNV was analysed as mean amplitudes between 1300 and 1650ms following cues at Cz. The NoGo-P3 amplitude was measured as the maximum positive peak between 250-600 ms following NoGo trials at Cz. In the other tasks characterized by inactive pre-stimulus states or analysed by peak-to-peak ERP measures, pre-stimulus baseline correction was applied prior to extracting ERP peaks. As in our previous work (Michelini et al., 2016), ERPs from the arrow flanker task included the N2, the ERN and the Pe from the incongruent condition only, as an N2 reduction in ADHD compared to neurotypical individuals is only observed in the incongruent condition (but not in the congruent condition) of this task (Albrecht et al., 2008;McLoughlin et al., 2009), and a sufficient number of errors to allow at least 20 ERP segments for robust ERP averaging is made in incongruent trials only (McLoughlin et al., 2009). Baseline correction was applied prior to extracting ERP peaks, using the -300 to -100 ms pre-target (-200 to 0 ms pre-flanker) interval. The N2 amplitude was measured as maximum negative peak at Fz and FCz between 250-450 ms after target onset. The ERN amplitude was defined with a peak-to-peak amplitude approach with respect to the preceding positivity (PNe, -100-50 ms) to obtain a more robust measure of this 3 component (Albrecht et al., 2008;McLoughlin et al., 2009;Nieuwenhuis, Ridderinkhof, Blom, Band, & Kok, 2001), and was measured at FCz between 0-150 ms. The Pe amplitude was measured as maximum positive peak at CPz between 150-450 ms. In the slow-unrewarded baseline condition of the Fast task, the P3 amplitude (baseline-P3) was measured, following pre-stimulus baseline correction in the interval between -200 and 0 ms, as the area amplitude measure at Pz between 250 and 450 ms (Cheung et al., 2017). CNV, Cue-P3, NoGo-P3, N2 and baseline-P3 were stimulus-locked and measured on correct trials only, while the ERN and Pe were response-locked and measured when an erroneous response was made.

Further information on the exploratory factor analysis (EFA)
Our analysis started with an examination of the correlated factors solution of the Cholesky decomposition, which gives separate correlation matrices for the underlying familial and non-familial influences. On the basis of the familial and non-familial correlation matrices between all 9 cognitive-ERP measures, data were simulated in R for 1000 participants within two EFAs, separately for familial and non-familial influences. EFA approaches give an indication of the underlying factor structure, but no specification of the underlying covariance matrices can be deduced. Factors were extracted using an unweighted least squares estimator approach following previous work (Loken, Hettema, Aggen, & Kendler, 2014). An unweighted least squares estimator was chosen over other extraction methods as it has shown robust as a method of factor analysing ordinal data yielding polychoric correlations (Forero, Maydeu-Olivares, & Gallardo-Pujol, 2009;Lee, Zhang, & Edwards, 2012). Factors with an eigenvalue of greater than 1 ( Figure S1) were extracted and rotated using an oblique (oblimin) rotation, which allows correlation between factors. The extracted factor structure and factor loadings (Table S3) were specified separately for familial and non-familial influences in a confirmatory factor model in OpenMx. This confirmatory model was aimed at examining the covariation between the factors capturing the cognitive-ERP measures and ADHD.

Further explanation on constrained correlation bivariate models and variable selection
Using our large cognitive battery, previous phenotypic analyses on this sample found that individuals with ADHD showed atypical profiles, compared to controls, in the following 22 cognitive and ERP variables (Cheung et al., 2017;Cheung et al., 2016;Michelini et al., 2016) ). Since our aim was to identify measures associated with ADHD and that would inform on the underlying familial relationships with the disorder, preliminary analyses were thus carried out to objectively select variables more strongly related to ADHD and that showed evidence of underlying familial influences.
We ran constrained correlation bivariate models between ADHD and each of the 22 cognitive-ERP variables (Table S1) extracted from our large cognitive-neurophysiological battery, in order to select variables that had (1) modest-to-large (Cohen, 1988) phenotypic correlation with ADHD (phenotypic correlation above .20) and (2) significant cross-sibling/within-trait sibling correlations, suggesting the influence of familial factors (Table S1). These models give maximum likelihood estimates of correlations between two traits within and across pairs while applying specific constraints. Applied constraints reflect the assumptions of the familial model, i.e. that phenotypic correlations across traits within individuals are the same across siblings and that cross-sibling/cross-trait correlations are independent of sibling order. Given the selected nature of this sample (selection of ADHD probands) 5 and ADHD modelled as present/absent, we further included constraints reflecting the assumptions of the liability distributions underlying ADHD status: we fixed the sibling correlation for ADHD status to .40 and the threshold on ADHD liability to a z-value of 1.64, corresponding to a population prevalence of 5%. Cognitive-ERP variables were modelled as continuous if their age-and sex-residuals were normally distributed or could be normalised using transformations methods, and included with ADHD status in combined continuous-ordinal bivariate models. In these analyses, a model for the thresholds of ordinal variables in specified along with a model for the means of continuous variables. Cognitive-ERP variables which could not be normalised using any transformation methods were modelled as ordinal using equal-sized categories, and included with ADHD status in bivariate ordinal liabilitythreshold models, estimating age and sex effects on their mean. Ordinal models and combined continuous-ordinal models were used to derive, respectively, the polychoric and polyserial phenotypic correlations between ADHD and each cognitive-ERP variable, the cross-sibling/within-trait sibling correlation for each cognitive-ERP variable, and the cross-sibling cross-trait sibling correlation between ADHD and each cognitive-ERP variable (Table S1).
Information about the precision of parameter estimates was obtained by likelihood-based confidence intervals (CIs). According to the criteria outlined above, IQ, DSF, DSB; MRT and RTV from the fast task (baseline condition); RTV, OE and NoGo-P3 ( Figure S3) from the CPT-OX; and RTV in the congruent and incongruent condition, congruent errors (CongE) and ERN ( Figure S2) from the arrow flanker task could be retained for inclusion with ADHD status in the multivariate models, as they met both inclusion criteria. Since all measures of RTV across tasks showed large correlations with one another (r=.45-.76), only RTV from the baseline condition of the fast task was included, as this variable showed the strongest phenotypic correlation with ADHD (Table S1).

Model comparisons 6
The Akaike information criterion (AIC) and χ 2 difference tests were used to inform on model fit when comparing models. The confirmatory 3-factor model showed a significantly better fit compared to the Cholesky decomposition (p=.08) (Table S4), indicating support for this more parsimonious description of the data.
As a sensitivity test, the 3-factor model was also compared to a 1-factor model. In this 1-factor model, all cognitive-ERP variables were influenced by 1 familial factor and 1 non-familial factor, with correlation paths to the familial and non-familial influences on ADHD, respectively. The 1-factor model provided a significantly worse fit than the 3-factor model (p<.01). This suggests that, although the 3 familial and non-familial factors are inter-correlated, they represent processes that are at least partly separable and cannot be accounted for by a single factor.

Proportion of phenotypic correlation due to familial and non-familial factors
The proportion of phenotypic correlation between ADHD and each cognitive-ERP variable explained by contributions of shared familial and non-familial influences could be further derived from the factor model (note that these phenotypic correlations could be slightly different from those estimated from the saturated Cholesky model in Table 1). For example, the proportion of phenotypic correlation between IQ and ADHD is calculated by two pathways: (1) via linked familial factors: the product of the standardised factor loading of IQ (path from cF1 to IQ), the correlation between cF1 and the ADHD-  (Table S5).   Notes: Significant differences are indicated in bold. Group differences between ADHD and control participants were reported in previous analyses on this sample Michelini et al., 2016).