Deficits in working memory tasks have been widely documented in Attention Deficit Hyperactivity Disorder (ADHD) studies. The aim of this study is to evaluate the effects of working memory load in impulsivity during decision-making processes. A delayed discounting (DD) paradigm was used, comparing children with ADHD and age-matched controls.Thirty-two children equally divided between typically developing and ADHD, from 8 to 10 years of age were assigned to sessions of a dual-task paradigm. In the primary task the child has to choose between two different amounts of money at different time delays, while in the secondary task the child has to repeat a random series of digits with different lengths. The experiment was conducted in a school setting.Compared to peers with typical development, delayed discounting was significantly stronger in children with ADHD and discounting rates increased in both groups for heavier memory loads. Furthermore, the memory load impact on frequency of immediate rewards was stronger in children with ADHD compared to typically developing children.Results are discussed in terms of the relation between working memory load and decision-making processes, their impact on impulsive behaviour in ADHD and the need for future research to understand possible neurocognitive correlates and use that information to develop better inclusive policies. Delayed Discounting (DD) refers to the human preference for smaller but quicker rewards rather than larger but delayed rewards  due to tChildren with ADHD are characterized by elevated inattention, hyperactivity, and impulsivity , and morThe process of decision-making is based on the choice between alternative behaviours. Psychological and economic studies consider ways in which gain, losses and probabilities are associated and combined to generate informed choices. In such studies, the attention has been focused on determining whether, in choices that may involve a short-term sacrifice for a long-term gain, the promptness with which a reward is obtained is perceived as an important factor in the process of decision-making –10. DelaThe DD task, in which one chooses between sooner/smaller or later/larger rewards, has proven useful in revealing deficits in executive functioning in various clinical groups , 13. IndV of a reward can be estimated using the present value A of the delayed reward and is described mathematically as a hyperbolic curve with the following equation:Most studies using the DD paradigm characterize an individual’s choice by generating a discount function that models the effect of delay on subjective value of later rewards , 17. TheD is the delay in the delivery of the reward, and k is a free parameter that describes the rate of discounting [k indicate a lack of discounting and a preference for delayed rewards, while higher values indicate strong discounting and a preference for immediate rewards.counting . Smallerk are indicative of high levels of impulsivity [Higher rates of DD are found in subjects who are willing to decline greater rewards available in the near future, and that show a preference for smaller rewards available immediately . Greaterulsivity .Some aspects of the cognitive components of temporarily myopic decisions can be explained in terms of working memory (WM) , 22, 23.The multi-component model of WM theory proposes a hierarchical structure with three slave subsystems to store and manipulate information and contains a temporary representation of the flow of information into and out of memory . The thrThe master subsystem is the Executive Working Memory (EWM) and it functions as a control centre, directing information between phonological, visuospatial and episodic components. The central executive is also responsible for: (1) directing attention to relevant information; (2) shift attention between information used to perform tasks of planning and decision making; (3) suppressing irrelevant information and inappropriate actions and (4) coordinates cognitive processes when more than one task is carried out at the same time .Optimal choice between two or more alternatives involves greater EWM capacity, because the subject should: (1) shift attention between the different options; (2) keep in mind short- and long-term goals; (3) inhibit distraction from decision-irrelevant information; (3) weight the options through the assessment of costs and benefits; (4) access long-term memory for knowledge aiding the decision. Therefore, EWM can be studied through tasks monitoring the completion of goal-directed actions during distractions and dual task paradigms .A few previous studies showed evidence for the effect of WM load on DD, where a decreased WM capacity increases impulsive decision-making , 31. We k. Instead, adults are more tolerant with delays and show relatively low k values [Previous studies have demonstrated a developmental progression of DD: children show very high values of k values , 35. Howk values  showed tk values –39.n = 231) and found contrasting evidence for DD in ADHD. Only three of five studies found greater temporal reward discounting for ADHD children. An age and IQ effect on DD was reported for most studies with younger ages and lower intelligence associated with greater discounting. Four of the studies [A recent systematic review  selected studies –44 used,d = .332). According to Dias and colleagues [d = .442). Nevertheless, in the comparison analysis in correlation analysis controlling age and gender and correcting for multiple comparisons, only the correlations with the AUC measures remained significant, considering the diagnoses (d = .327). Authors also used functional Magnetic Resonance Imaging (fMRI) to divide children into three subgroups, according to the connectivity pattern. It was observed that in one of the subgroups, children with ADHD performed significantly worse than controls, and when compared to children with ADHD from one of the other two subgroups. Authors also described a strong correlation between DD gradient ln(k) and Area Under the Curve (AUC) with the connectivity from the nucleus accumbens (NAcc) to the Prefrontal Cortex (PFC), including the ventromedial PFC and the left anterior PFC.The first two studies used long delays (7 to 180 days). Antonini and colleagues  reportedlleagues , ADHD-C d = .480). The second study [η2partial = .092) but only in the condition with hypothetical rewards and real delays.The other two studies used a short range of delays (0.5 to 60 s). The first  found grnd study  observedA possible interaction effect between DD and ADHD could be the role of working memory. Previous studies have shown that WM deficits are associated with ADHD and impulsivity –48. For To our knowledge there is only one study comparing ADHD and TD on DD task with cognitive loads  using a In agreement with the results of Hinson, Jameson and Whitney  this stuPrevious studies showed contrasting results for DD tasks in children with ADHD, especially when the task involves hypothetical rewards. Only few studies have researched the impact of memory load on DD and showed different pattern of results in typical and clinical populations. To our knowledge there were no studies investigating the effect of WM load in children with typical development or ADHD.Therefore, the hypotheses of this study are as follows: (1) Children with ADHD in the Experimental Group (EG) will find more difficult than Control Group (CG) to defer a reward; (2) once the memory load increases the deferment of rewards becomes increasingly hard for all participants (both EG and CG) and (3) the increase of memory load have a larger impact on the performance of EG than CG.Inclusion criteria for all participants were as follows: (1) between 8 and 10 years of age; (2) have a score above 70 in the verbal and performance IQ on the Wechsler Intelligence Scale for Children - IV Edition (WISC-IV); and (3) have no history of brain damage, epilepsy, psychosis, autism spectrum disorder (ASD), bipolar disorders (early-onset bipolar disorder), Tourette’s syndrome, childhood depression; (4) have no current aggressive behaviour or severe oppositional tendency; (5) have no hearing, visual, or physical disabilities, and (6) not being under psychiatric medication.Children with comorbid disorders were excluded to increase the specificity of the results and avoid confounders. More specifically, children with ODD can be uncooperative, hostile toward authority and behave with the aim of annoying others. Including children with ODD in the study could have raised the doubt that a lower score could have been due to uncooperativeness or plain opposition to the task instead of a neurocognitive deficit.The hypothetical monetary DD task has been used extensively with adolescents and occasionally with children. However, a recent study found that the generated data suggest a disengagement or misunderstanding of the task . Thus, tParticipants included in the EG also have a cut-off severity scores of 14 or higher in both ADHD-I (inattentive subgroup) and ADHD-H (hyperactive subgroups) subscales, i.e. ADHD-C criteria (combined inattentive and hyperactive subgroups) on the Italian versions of the ADHD Rating Scale for Teachers (SDAI) , 55 and N = 414 Italian children, aged 8 to 10 years old, attending 4th or 5th grade of twelve public primary schools in Lombardy, Northern Italy, were recruited. Referrals for children with ADHD were obtained from professionals taking part in an ongoing research and placement training program. All contacted schools agreed to participate in the research and were located in urban areas with an average socio-economic status (SES), private schools were not included. A first screening, administered by teachers, based on SDAI and the Disruptive Behavior Disorders Rating Scale (DBDRS) [ (DBDRS)  were useTeachers were asked to observe the recruited children for 2 weeks and to complete SDAI and DBDRS for each child. Subsequently, they had to report the frequency of any problematic behaviour according to a Likert scale from 0 (problematic behaviour never presents) to 3 scores (very often present) for each questionnaire.N = 22 children were eligible for the EG.Thirty children were eligible for the EG according to the ADHD-C criteria on SDAI and were further assessed using CTMQ. Each participant was asked to answer 16 open-ended questions on knowledge regarding the values of money and time. Based on the results, N = 6 children were excluded because diagnosed with ODDs  fully met the inclusion criteria and were enrolled as EG in the present study.In the final sample there were 14 classes from 11 schools with either 1 or 2 children for each of the twelve participating classes in each group.The selection was performed separately for each participating school and class to ensure the best matching among social and educational exposure and experimental setting.N = 16 children  were randomly assigned to the CG.We used a randomized block selection among children eligible for the CG to ensure that the groups were balanced for number of children, class, and gender. All selected children for CG participated in the study and were assessed using the same method used for the EG. All children in the CG meet the inclusion criteria. We had no dropouts.t(22.4) = 38.5, p < .001, SDAI inattention subscales, t(15.0) = 70.5, p < .001, while there were no significant statistical differences in IQ, t(30) = 1.29, p = .208 and Digit Span Forward task, t(30) = .582, p = .565. Furthermore, there were no difference in time and money understanding on CTMQ: Time scale, t(28.7) = 1.17, p = .253, Money scale, t(22.6) = 1.85, p = .077.The EG displayed significantly higher scores than CG on both SDAI hyperactivity, The Control Group was comparable to the EG regarding IQ, age, year of education, Digit Span and CTMQ scores. All children in the CG showed no clinical signs of ADHD or other developmental conditions.Demographic and assessment data for both experimental and control groups are summarised in Table r > 0.95 [The SDAI is an ADHD questionnaire widely used in Italy, validated and standardized for the Italian population , 59. It r > 0.95 ;. Its ter > 0.95 .The DBDRS is a 45-question screening measure, completed by either parents or teachers, designed to identify symptoms of ADHD, ODD, and conduct disorder in children and adolescents.The CTMQ was developed for this study and is reported in the A dedicated application was developed for the administration of the individual sessions. All sessions were administered in a quiet classroom of the school, equipped with computers, monitors, chairs and desks. All participants were asked to sit in front of a monitor in order to complete the tasks. Each session consisted of one preliminary trial and 3 blocks with different memory loads with 16 experimental trials for each block comprising the random combination of 4 delay and 4 reward conditions. Each session lasted 20 min.N = 32 participant was asked to engage in a second individual assessment of memory span using the software developed to run the experiment instead of the WISC-IV [Each of the  WISC-IV . The aimFor the preliminary assessment of maximum memory load, the first sequence was 3-digits long. The number of digits to repeat would increase if the participants successfully managed to repeat all of them. A new number sequence was randomly generated before each trial.In the memory load task, the participant was required to listen and repeat the assigned sequence of random numbers.Three different conditions were tested and counterbalanced among participants: (1) delayed reward option task without the memory load task; (2) dual-task with the delayed reward option task and the memory load task with half memory load and (3) dual task with full memory load.n-1), while the half load was set to n/2 if n was even and (n-1)/2 if n was odd.The initial full load was set to the maximum digit span assessed in the preliminary task minus one (We choose (n-1) as the full load condition to minimize the number of errors while maintaining a high load on WM. This task not only functions as an interference but it’s also a measure of the attention to the experiment. A high number of errors in this task would mean that participants are deploying their attentional resources mainly on the primary task instead of splitting them between the two tasks.In the conditions with half and full memory load, the random number sequence was presented before the choice task, participants were therefore asked to remember the sequence and repeat it aloud through the choice task. To ensure that the participants’ cognitive resources were focused on the memory load task, if an error in repeating the digits was made, another series of the same digits was presented; if the participant failed also to repeat the second series, the task was stopped and the number of correct digits was recorded as the maximum digit span of the participant for that specific trial.The primary task consisted of a series of choices between a small monetary reward obtained after a shorter time and a larger monetary reward obtained after a longer time. The delayed reward option task comprised a series of 16 trials. In each trial, the participant was asked to select between two options e.g. the first option was always a smaller amount of money the same day, whilst the second option was a larger amount of money deferred in different periods of time. Each participant knew that there were no right or wrong choices. Trials comprised 4 possible reward combinations: €1–€11, €2–€12, €3–€13 and €4–€14, with a reward difference always set to €10; and 4 possible time delays of 1 week, 1 month, 6 months and 1 year. An algorithm specifically designed for the test had selected the order of the 16 trials randomly and balanced them among participants.The full set of responses from the money/time option task and digit spans for different memory load condition are reported in the Supplementary Materials, sheet k) were submitted to repeated measure ANOVA with one between-subject factor (group), and two within-subject factors: (1) three memory load conditions  and (2) four time delays ; trials within the same condition but different monetary rewards were averaged together. The alpha-level was set to .05 for all statistical tests. All effect sizes and post-hoc tests’ power are reported in sheet St-test and ANOVA, alpha-level was Sidak’s corrected. Greenhouse-Geisser correction was used for effects failing the Mauchly’s test of sphericity.All statistical analyses were run through SPSS software . The descriptive statistics of the dependent variables were examined. The dependent variable  as units. The specific units of measurement that have been chosen change the results only by a multiplicative factor, the choice is therefore irrelevant for the purposes of statistical analysis.With reference to the primary task parameter, the inverse formula of Preliminary ANOVA was carried out to examine the secondary task performance, assuming digit span as the dependent variable to ensure that the relevant variable was the memory load and not the memory span. Correlations among variables were calculated to assess their impact on the analysis.DR = −ln(k) is also commonly reported in the literature, especially when researchers prefer to use logistic regression instead of the inverse formula to compute k [Delayed discounting rate defined as ompute k . TherefoFor both groups of participants, the percentage of errors on the memory load task was 0% in the half load condition and 15% in the full load condition.The preliminary analysis revealed no effects of the maximum digit span on the primary task results (see sheet Sk and ln(k) for different WM load conditions . Outcome variables among different WM load conditions were highly correlated, k  and ln(k) (r = .758 to r = .882. p < .001). Furthermore, IQ was correlated with CTMQ-Time  and Digit Span was correlated with CTMQ-Money . IQ, age and CTMQ were not correlated with outcome variables (p > .155) with the exception of a trend between IQ and k in the zero WM load condition  and CMTQ-Money and k in the zero WM load condition .Correlation among SDAI and DBRDS subscales was very high (.906 to .988) and also their correlation with outcome variable F  = 33.8, p < .001, η2p = .700, and time delay, F  = 110, p < .001, η2p = .922, were significant main effect on k in the multivariate test.In the primary multivariate analysis, both memory load, F  = 228, p < .001, η2p = .884, post-hoc comparison showed that EG > CG, with M = 1.04, S.E. = .041 for EG and M = .150, S.E. = .041 for CG, indicating that the EG showed higher k value than CG. Furthermore, a significant Group × Memory Load interaction effect was found, F  = 17.2, p < .001, η2p = .543, post-hoc comparison showed that k increased more in EG when the memory load was heavier as depicted in Fig. ANOVA revealed also a significant main effect of Group F  = 75.3, p < .001, η2p = .890, post-hoc comparison showed a larger decrease of k with time in the EG compared to CG, and a larger difference for shorter reward delays. We also found a Memory Load × Delay interaction effect, F  = 11.8, p < .001, η2p = .740. A post-hoc comparison showed a larger effect of memory load for shorter reward delays.All the other 2-ways and the 3-ways interactions were also significant. Group ×Delay interaction effect, F  = 5.69, p = .001, η2p = .577, revealed that the heightened effect of memory load for shorter reward delays was more accentuated for the EG. Group comparison for each condition is reported in Table Finally, we found the 3-ways interaction effect among Memory Load, Delay and Diagnosis, F 6,5 = 5.69,ln(k) as a dependent variable led to a significant within subject effect for memory load, F  = 14.7, p < .001, η2p = .509 and between subject effect for group, F  = 114, p < .001, η2p = .792. The Group×Memory Load interaction effect was not significant when ln(k) was used as a dependent variable, F  = .272, p < .764, η2p = .018.The ancillary analysis with k, to avoid any theoretical assumption on the shape of the discounting curve. In both analyses all effects were significant and in the same direction as the primary analysis. Hence, the effects are not an artefact of the specific formula used to study DD.To test the robustness of the results we ran two other ancillary analysis: in the first one we used a simple ranking for the delays  instead of the number of weeks , to approximate a contraction of perceived time for longer delays; in the second one, we used the number of delayed reward responses as the dependent variable instead of The three ancillary analyses are reported in the supplementary materials in sheets SGender differences in ADHD was not one of the aims of the study. However, for future comparisons, it was possible to run the primary analysis excluding female participants.F  = 163, p < .001, η2p = .881, and Group × Memory Load interaction, F  = 9.85, p < .001, η2p = .309.Results were in line with the ones found for the whole group. ANOVA revealed a significant main effect of Group All hypotheses of the study have been confirmed: (1) children with ADHD show higher levels of DD than control subjects, (2) once the memory load increases, deferring a reward becomes harder for both children with ADHD and with typical development, and (3) the performances of children with ADHD are significantly worsened by the addition of a memory load compared to the control ones.For the sake of clarity, we will discuss the results based on proportion of delayed reward, for each group and each condition. Data is reported in supplementary materials in sheet Sin all conditions and for both groups: ZML > HML > FMLIn all conditions: EG < CG, with the exception of 1-year delay.In almost all conditions we have a decrease in delayed rewards responses with the increase of time delays, with a few exceptions that are not statistically significant:For the 1-year delay EG and CG are comparable, but in the CG there was  a huge change in the discounting slope. Wittmann and colleagues , 66 haveThe decrease in group differences between high impulsivity (ADHD-C) and low impulsivity (TD) groups for increasing time delays, also suggest the presence of a non-linear scaling, as expected using hyperbolic delayed reward discounting curves that take into account the contraction of time for future events .The analysis of the results also found that the number of delayed choices decreases in ratio with the increasing of time gap between immediate and delayed options. This data confirms that the value that the individual attributes to the different choices decreases as the reward becomes more distant in time , 68.k, influenced by the chosen behaviours of the subject. As Green and colleagues [k value increases.The findings of this experiment are consistent with the literature of the discounting parameter lleagues , 68 statlleagues  or a higd = .302 for Antonini and colleagues, and d = .442 for Dias and colleagues, but did not survive correction for multiple comparisons, p = .054). In contrast, for the condition without memory load, we found a very large effect size, d = 2.59. The smaller sample size could have inflated our results, thus caution in interpretation of our data is mandatory. However, a careful examination of the data  does not vary differently between the experimental and the control group. Nevertheless, we found a greater effect of a WM loading ADHD compared to control for both k and the proportion of delayed choices.A significant finding in this study is that a WM load, designed to deplete EWM capacity, substantially increased delay discounting rates for all subjects. The current study extends the work of Finn and colleagues  on adultWe chose a restricted range of age (8 to 10 years old) and IQ within the normal range, to avoid the confounding effect of intellectual ability and maturational processes, that choice impacts on the generalisability of the study. Moreover, although the selection process adopted by this study made possible to create a detailed assessment of the participants, it reduced considerably the number of final participants, lowering the power of the study even if the results were statistically significant.Previous studies suggested differences in symptoms between males and females with ADHD , 72 withThe selection process was performed sequentially, therefore we cannot compare children who failed the screening tests (e.g. CMTQ) with children who passed them on outcome measures. Moreover, comorbidities are common in neurodevelopmental disorders, and our choice to exclude children with comorbidities further reduced the generalisability of the results. Nevertheless, we are confident that our choices increased the putative validity of the link between the experimental results and executive functioning circuitry specific to the condition.A school setting has been chosen for this study for practical reasons and the children had to leave the class to do the assessment. Thus, the level of cognitive resources available to the child while performing the tasks cannot be assured. In addition, as the children were from different schools and there were different examiners, the settings where the assessments were carried out and the examiners that assessed the children differed. That might have reduced the controllability of the experiment. However, it could have increased its ecological validity. Furthermore, for each school/setting the number of children in the EG and CG were the same, therefore confounding factors linked to the specific setting should be negligible in the group comparison.k, which is supposed to be a constant, and that has been found to vary in relation to different temporal intervals. Meaning that the equation chosen to define DD might be too simplistic. However, the supplementary analysis employed to double-check the results using different formulae showed that the behavioural results are robust enough to remain statistically significant regardless of the specific equation used to compute discounting.Finally, one limitation of this study is given by the specific formula used to compute the parameter The present study is the first to show the impact of WM on DD in children with ADHD. Moreover, even if the results are statistically significant, the small sample size of the study reduces their strength. Therefore, the study could be seen as an initial step towards more definitive evidence to investigate further the four implications described below.k should be a constant, but the results we presented showed a variability of k with time. According to Body, Bradshaw and Szabadi [k in a more precise way using generalized hyperbolic functions or other more sophisticated models instead of the standard hyperbolic discounting. A more complex model, that also includes the many intervening variables, could lead to a richer explanation of decision making in typical development and ADHD.First, given the same experimental condition,  Szabadi  time delSecond, under the conditions of increased memory load, both the ADHD and the control group reported higher discounting. Therefore, in line with already discussed evidence highlighting the hierarchical structure of the executive system we found a link between the executive working memory and inhibition of impulsive behaviour . Taxing k than their peers even if they have the same IQ, WM capacity and WM load. Thus, we suggest that even if WM has a significant role in the decision-making and DD processes and reducing its capacity lead to choice impulsivity in children with ADHD, it could not be the solely responsible for the behaviour. Therefore, this paper invites future research to focus not only on replicating those findings, but to expand them, exploring the different dimensions of specific ADHD characteristic and comorbidities, possible differences in the mechanisms involved underlying DD under different ranges of delays, and their maturational changes during development.Third, as expected, the ADHD-C group showed significantly higher levels of k in the zero WM load condition and CMTQ-Money and k in the zero WM load condition. Those results invite future researchers to design experiments to better understand, and control for, the influence of conceptual understanding of time and monetary value in DD research.Fourth, despite the small range in variability among the demographic variables, we found a correlation between IQ and CTMQ-Time and between Digit Span and CTMQ-Money. Furthermore, we also found a trend for a correlation between IQ and Fifth, contrary to some of the previous studies , 72 repoDR = −ln(k) with an increase in WM load. Nevertheless, both k and the raw number of impulsive choices, increased more in ADHD than in typical children; for instance, the frequency of choices for immediate reward, in a 1 month delay condition without WM load, was 42% in ADHD and 12% in typical children, while in the full WM load condition, it was 90% in ADHD and 23% in controls. Based on the assumption of hyperbolic discounting and Fechner’s logarithmic psychological function of perception, we can assume that DR, a logarithmic function of the discounting coefficient, is proportional to the perceived delay [Finally, EG and CG showed a comparable increase in discounting rate ed delay . TherefoTaken together, these results suggest that those with ADHD, who already have elevated discounting rates and patterns of disinhibited decision-making, are very vulnerable to the effects of conditions which compromise EWM capacity, such as stress, emotional arousal, or high cognitive load, conditions that are frequently found in a school setting. Under such conditions, those with ADHD may be more likely to engage in impulsive /risky decisions that have significant negative consequences.This is the first DD experiment with ADHD children run in a school setting. Children were briefly taken from their class after hours of school that already taxed their executive control. Therefore, we can suggest that the larger effect size we found could be related to the specific setting. The behavioural and attentional request made in school, could deplete executive resources in children with ADHD, decreasing their capacity to learn and to inhibit impulsive behaviours. Future research should try to directly compare settings (laboratory vs. school) and fatigue (well rested vs. late hours). Moreover, a systematic assessment of different aspects of the WM system and of the role of different strategies used in task completion for different kinds of cognitive loads, would help tease apart the different factors that affect discounting rates / impulsive decision-making. If the results will be corroborated, and the setting will play an important role in the effect size of the results, they will also be informative for decisional bodies to develop better inclusive policies.Additional file 1 Table S1.1 Complete Participants’ Demographic Data and Assessment Scores. Table S2 Complete Experimental Data. Table S3.1 Multivariate Test, k in weeks. Table S3.2 Mauchly’s Test of Sphericity. Table S3.3 Tests of Within-Subjects Effects and Between-Subjects Effect, k in weeks. Table S3.4 Pairwise Comparisons, k in weeks. Table S3.5 Parameter Estimates, k in weeks. Table S4. Tests of Between-Subjects Effects, Preliminary ANOVA using Digit Span as a Covariate. Table S5. Correlation among Demographic and Outcome Variables. Table S6. Group Comparison among Different Conditions. Table S7.1 Multivariate Test, k computed using ranked delays. Table S7.2 Mauchly’s Test of Sphericity, k computed using ranked delays. Table S7.3 Tests of Within-Subjects Effects and Between-Subjects Effect, k computed using ranked delays. Table S8.1 Multivariate Test, Using Number of Delayed Choices as a Dependent Variable. Table S8.2 Mauchly’s Test of Sphericity, Using Number of Delayed Choices as a Dependent Variable. Table S8.3 Tests of Within-Subjects Effects and Between-Subjects Effect, Using Number of Delayed Choices as a Dependent Variable. Table S9.1 Multivariate Test, Using ln(k) as a Dependent Variable. Table S9.2 Mauchly’s Test of Sphericity, Using ln(k) as a Dependent Variable. Table S9.3 Tests of Within-Subjects Effects and Between-Subjects Effect, Using ln(k) as a Dependent Variable. Table S10. Group Comparison of Delayed Choice among Different Conditions.Additional file 2.


Objective: Previous studies in children with ADHD identified twopartially separable familial factors underlying cognitive dysfunction, butevidence in adolescents and adults is lacking. Here, we investigate theetiological structure of cognitive-neurophysiological impairments in ADHD inadolescents and young adults. Method: Factor analyses andmultivariate familial models were run in 356 participants from ADHD and controlsibling pairs aged 11 to 27 years on data on IQ, digit span forward (DSF) andbackward (DSB), and cognitive-performance and event-related potential (ERP)measures from three cognitive tasks. Results: Three familialfactors (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-timevariability (RTV); cF2 on DSF and DSB; and cF3 on numberof errors and ERPs of inhibition and error processing. Conclusion:These results identify three partially separable etiological pathways leading tocognitive-neurophysiological impairments in adolescent and adult ADHD. The majority of children clinically diagnosed with ADHD continue to meet ADHDdiagnostic criteria in full or in partial remission in adolescence and adulthood. In addiTwin and family studies have consistently reported high genetic/familial influencesand limited-to-no role of the shared environment on ADHD . In chilIn our recent follow-up study of adolescents and young adults with a childhoodcombined-type ADHD diagnosis, we found a separation between impairments in cognitiveand brain function processes in relation to ADHD outcomes (persistence/remission) atfollow up. Cognitive and neurophysiological measures of preparation-vigilanceprocesses , error detection, and IQ were uniquely linked to ADHDpersistence/remission at follow up ,as indiThe present study aims to investigate, for the first time, the etiological structureunderlying cognitive-neurophysiological processes in ADHD in adolescence and earlyadulthood, in our follow up of individuals from ADHD and control sibling pairsinitially assessed in childhood . In prevDiagnostic and Statistical Manual ofMental Disorders [4th ed.; DSM IV; Supplementary material). At initial assessment , ADHD participants recruited from specialist clinics and their closest-agesiblings were invited to participate. Control participants were recruited fromschools. At follow up, which took place on average 5.8 years(SD = 1.24) after the childhood assessment, 30 childhoodADHD probands were excluded for no longer meeting DSM-IV ADHDcriteria (n = 25), not having combined-type ADHD in childhood(n = 3), or due to EEG equipment failure(n = 2). Nine siblings of ADHD probands were excluded asthey were unaffected in childhood but met DSM-IV ADHD criteriaat follow up (n = 3) or their diagnostic status could not bedetermined due to missing parent-reported data on impairment (n= 6). Nine controls were excluded due to meeting ADHD criteria at follow upbased on parent-reported ADHD ratings  met criteria for the combinedsubtype, 32% (n = 28) met criteria for predominantlyinattentive subtype, and 8% (n = 7) met criteria forpredominantly hyperactivity-impulsivity subtype at follow up. Written informedconsent was obtained from all participants and the study was approved by theLondon-Surrey Borders Research Ethics Committee (NRES 09/H0806/58).The sample consisted of 404 participants, including 226 participants from ADHDsibling pairs  inthis sample, whereas the same objective markers showed limited agreement withself-reported ADHD , a 48-hr ADHDmedication-free period was required prior to cognitive-EEG assessments.Participants attended a single 4-hr research session (including breaks) for IQ,digit span, and cognitive-EEG assessments . For eacSupplementary material).The EEG was recorded from a 62 channel DC-coupled recording system (extended10-20 montage), using a 500 Hz sampling rate, impedances under 10 kΩ, and FCz asthe recording reference. The electro-oculograms (EOGs) were recorded fromelectrodes above and below the left eye and at the outer canthi. EEG data wereanalyzed using Brain Vision Analyzer 2.0 . Raw EEGrecordings were down-sampled to 256 Hz, re-referenced to the average of allelectrodes, and filtered using Butterworth band-pass filters . Electrical or movement artifacts were removed following visualinspection. Ocular artifacts were corrected using the infomax IndependentComponent Analysis (ICA) algorithm . Sectionzscore set at 1.64). For further explanation of this approach, see Supplementary material and Sibling-data model fitting was accomplished by structural equation modelfitting analyses (SEM) using the OpenMx package in R . As siblTable S1). Following preliminary analyses, nine variableswere included with ADHD status in multivariate models (Table S2): IQ, digit span forward (DSF), digit span backward(DSB); ERN , and congruent errors (CongE) from the arrowflanker task; NoGo-P3  and OE from the CPT-OX; and mean reaction time(MRT) and RTV from the Fast task (baseline condition). ERN, NoGo-P3, and MRTwere transformed to normality using the square root transformation, whileRTV was log-transformed. IQ, DSF, and DSB residuals were normallydistributed. These measures were included as continuous variables. OE andCongE were highly skewed and could not be normalized using anytransformation methods. They were therefore modeled as ordinal using 3 and 4equal-sized categories, respectively. Age and sex were controlled for in allanalyses as is standard practice for family model-fitting studies . Separate EFAs were carried out onthe familial and nonfamilial correlations between the nine cognitive-ERPvariables. This allowed detection of possible differences between thefamilial and nonfamilial effects on the number of extracted factors or inhow they load on variables. Three factors with an eigenvalue >1 wereidentified in both EFAs . Each factor explained >10% of the totalvariance in either EFA (Table S3). As cognitive-ERP variables mapped onto cognitiveprocesses which are likely to be interrelated (Table S3) separately for familial and nonfamilial influencesin a confirmatory three-factor model, including also ADHD, using OpenMx.Familial and nonfamilial paths from the extracted common factors werespecified for each variable from the factor with strongest loading in theEFAs, while ADHD and its fixed familial and nonfamilial influences weremodeled separately . ADHD showed moderate negative correlations with IQ, DSF, DSB,ERN, NoGo-P3, and moderate positive correlations with MRT, RTV, OE, andCongE.Phenotypic correlations between cognitive-ERP variables and ADHD were allsignificant, with positive correlations ranging from .17 to .88 and negativecorrelations from −.19 to −.39 . The onlFamilial correlations of ADHD with IQ, DSB, RTV, OE, and CongE were significantand moderate-to-large, and moderate but nonsignificant with DSF, ERN, NoGo-P3.NonfamiFigure S1). This factor structure informed the confirmatoryfactor model, which provided the best fit to the data (Table S4). The first familial factor (cF1) loadedonto IQ, MRT, and RTV; the second factor (cF2) onto DSF and DSB; andthe third factor (cF3) onto ERN, NoGo-P3, OE, and CongE , but by specificinfluences, apart from MRT and RTV which were more strongly influenced by acommon nonfamilial factor (cNf1) (Table S5).The factor structure of nonfamilial influences resembled that of familialinfluences, except for IQ which loaded on the same factor capturing DSF and DSB. Themajr (cNf1) . The nonThis study represents the first comprehensive investigation to date, using a broadrange of cognitive-performance and brain activity (EEG) measures, into the etiologyunderlying cognitive-neurophysiological impairments in ADHD that has persisted fromchildhood to adolescence and early adulthood. We identified three familial and threenonfamilial factors underlying the association between impairments in these measuresand ADHD. The familial factors captured (a) response speed (MRT) and variability(RTV), and IQ; (b) short-term (DSF) and working (DSB) memory; and (c) sustainedattention , error processing (ERN), and, to a smaller extent, responseinhibition (NoGo-P3). Familial influences on ADHD overlapped strongly with both thefirst and third factors, but only moderately with the memory (second) factor. Thesame number of factors emerged for nonfamilial influences, with the only exceptionthat IQ clustered with memory rather than RT measures. These findings identifymultiple partially separable etiological processes that underliecognitive-neurophysiological impairments in persistent ADHD, extending ourunderstanding of the etiological pathways to widespread cognitive and braindysfunction in ADHD in adolescence and adulthood.rcF1-ADHD =.50;rcF2-ADHD = −.36;rcF3-ADHD = −.66) may underlie multiple familialprocesses. The factor structure for familial effects pointed to a separation betweena factor capturing IQ and RT performance (cF1), a factor capturing memoryperformance (cF2), and a factor capturing accuracy (number of errors) andbrain activity of inhibitory/error-detection processes (cF3). Theseparation between factors indicates that the co-occurring presence of impairmentscaptured by the same factor could be largely explained by shared familialinfluences. For example, the finding that one familial factor captured both IQ andRT performance indicates a strong familial association between these measures (morethan with other measures) in adolescents and adults. Conversely, impairments thatare captured by two separate factors may be driven by at least partially separatefamilial pathways. A dissociation of this kind is shown for memory and RTperformance, indicating that impairments in these processes may result from partlyindependent etiological pathways. In addition, to our knowledge, this is the firstfamily model-fitting study that simultaneously investigated multiple cognitive andbrain measures to obtain a deeper understanding of ADHD. Our results provide newinsights into how cognitive-performance impairments (omission and congruent errors)are etiologically associated with neural processes of error detection (ERN) andresponse inhibition (NoGo-P3), as these four measures clustered in one factor. Assuch, the etiological factors underlying atypical brain activity of inhibitory anderror-detection processes may overlap with those linked to task accuracy indices ofsustained attention deficits. The familial factor capturing these four measures(cF3) also overlapped with two thirds of the familial influences onADHD (rcF3-ADHD = −.66), indicating a strong etiologicalassociation between this cognitive-EEG factor and the disorder.Our results show substantial shared familial influences betweencognitive-neurophysiological impairments and ADHD in adolescents and young adults.The factor model further indicates that the association between these impairmentsand ADHD  highly correlated with ADHD, suggesting substantial overlap infamilial variance between these measures. The previous analyses in childhood,however, found a separation of genetic/familial influences on IQ from influences onADHD and other cognitive impairments , and of sustained attention andinhibitory/error-detection processes (cNf3) was largely measure-specificand not shared with ADHD. Nonfamilial influences include individual-specificenvironmental factors, representing any differences in the environment betweensiblings, and may include the effects of any treatment for ADHD. A possibleprediction is that nonpharmacological interventions, for example cognitive training,aimed at alleviating ADHD symptoms may be more effective if they target RT ratherthan memory or response-accuracy processes. This prediction is in line with evidencesuggesting that RTV may be more malleable than higher-level processes  on ADHD and impairments in cognitive andbrain function, extending current knowledge from childhood to later development. Thefamilial processes underlying both slower and more variable RTs and lower IQ inadolescents and young adults with ADHD may be partially distinct from familialinfluences on memory dysfunction and on impairments in sustained attention and brainactivity of inhibitory/error-detection processes. These partially distinctetiological pathways may underlie dysfunctional brain networks which are, in turn,associated with impaired cognition and behavior in the disorder. Future effortsshould examine the developmental trajectories of these etiological pathways, andtest treatment effects on these partially separate cognitive-neurophysiologicalfactors, which would refine causal models of the disorder and point to sensitivetargets for interventions.Click here for additional data file.Supplemental material, Supplement_JAD for The Etiological Structure ofCognitive-Neurophysiological Impairments in ADHD in Adolescence and YoungAdulthood by Giorgia Michelini, Celeste H. M. Cheung, Viryanaga Kitsune, DanielBrandeis, Tobias Banaschewski, Gráinne McLoughlin, Philip Asherson, FrühlingRijsdijk and Jonna Kuntsi in Journal of Attention Disorders


R2 = 2% and was robust to residualizing the effects of age, sex, race, parental income and education, handedness, pubertal status, and internalizing symptoms from ADHD symptomatology. This model used reduced activation in task positive regions and reduced deactivation in task negative regions to predict ADHD symptomatology. The best model with morphometry alone predicted ADHD symptomatology with an R2 = 1% but this effect dissipated when including covariates. The inhibitory control and reward tasks did not yield generalizable models. In summary, these analyses show, with a large and well-characterized sample, that the brain correlates of ADHD symptomatology are modest in effect size and captured best by brain morphometry and activation during a working memory task.Attention deficit/hyperactivity disorder is associated with numerous neurocognitive deficits, including poor working memory and difficulty inhibiting undesirable behaviors that cause academic and behavioral problems in children. Prior work has attempted to determine how these differences are instantiated in the structure and function of the brain, but much of that work has been done in small samples, focused on older adolescents or adults, and used statistical approaches that were not robust to model overfitting. The current study used cross-validated elastic net regression to predict a continuous measure of ADHD symptomatology using brain morphometry and activation during tasks of working memory, inhibitory control, and reward processing, with separate models for each MRI measure. The best model using activation during the working memory task to predict ADHD symptomatology had an out-of-sample  These deficits may be explained by reduced activation in brain regions, such as the dorsolateral prefrontal cortex (DLPFC), anterior cingulate cortex (ACC), posterior parietal cortex (PPC), ventrolateral prefrontal cortex (VLPFC), insula thalamus, and striatum, which have been found to differ in individuals with ADHD in meta-analyses of functional magnetic resonance imaging (fMRI) tasks of inhibitory control, working memory, and attention9. Differences in individuals with ADHD have also been found in activation in the ventral striatum, ventromedial prefrontal cortex (VMPFC), and ACC during monetary reward tasks10. Additionally, a recent review of morphometric differences measured by structural magnetic resonance imaging (sMRI) in adolescents with ADHD reported abnormalities in cortical thickness (CT) in the lateral prefrontal and parietal cortices, as well as gray matter volume of the thalamus as the most frequently identified effects11. However, these reviews and meta-analyses included few studies with more than 50 participants and none over 100.There is substantial evidence that individuals with Attention Deficit Hyperactivity Disorder (ADHD) have below average working memoryN > 1000) have aimed to characterize the neuroanatomical correlates of ADHD. These studies both investigated surface-based morphometry in a non-clinical sample of adolescents using the IMAGEN study dataset (https://imagen-europe.com/), which includes participants with a range of ADHD symptoms. They identified lower levels of CT in the ventromedial prefrontal cortex13 and cortical surface area (CSA) in the DLPFC and ACC14, which were also linked to performance on several neuropsychological measures known to be disrupted in individuals with ADHD. Additionally, a recent mega-analysis  found smaller gray matter volume (GMV) in children with ADHD in several subcortical structures 15. However, comparably powered studies have not been published for task fMRI.Two recent large studies of adolescents (16. A recent large machine learning study (N = 2713) found only modest prediction accuracies when distinguishing children with ADHD from controls using sMRI with more rigorous cross-validation17. It stands in contrast to prior smaller studies, which had shown much more optimistic predictions using more questionable approaches . However, the majority of existing machine learning work on ADHD focuses on only one imaging modality or task, making it difficult to compare classification accuracies across ADHD studies. Additionally, the use of non-linear modeling strategies makes the interpretation of model features in many machine learning models difficult.In response to concerns of mounting replication failures in the social sciences, reducing overfitting and assessing generalizability of models have become critical. To achieve this, methods such as regularized regression and cross-validation are frequently usedwww.ABCDstudy.org) study to predict current ADHD symptomatology using elastic net regression models with brain activation during fMRI tasks of working memory, inhibitory control, and the anticipation and receipt of monetary reward, as well as brain morphometry measured by sMRI. Among machine learning approaches, elastic net regression is particularly effective at making predictions when the predictors are highly intercorrelated, has been shown to be effective at making predictions using neuroimaging data18, and is one of the approaches in which model features are most interpretable, making it ideal for attempting to understand the specific brain regions most critical to ADHD. The current analyses also used cross-validation with an external test set to ensure that effects identified were replicable in an independent dataset.Another approach to improving replicability has been the initiation of large-scale open-data projects. The current study used baseline data from the Adolescent Brain and Cognitive Development . Furthermore, the use of a dimensional approach is more consistent with the National Institute of Mental Health’s Research Domain Criteria program25. Thus, the current study used a continuous measure of ADHD symptomatology, the “attention problems” scale of the child behavior checklist (CBCL)26.An additional weakness in the existing literature on the neurobiological basis of ADHD is a primary focus on categorical diagnoses of ADHD. There is strong empirical evidence that child psychopathology is better suited to dimensional measurementGiven the established relationship of working memory, inhibitory control, and reward processing with ADHD, we hypothesized that ADHD symptomatology would be predictable using each of the three fMRI tasks. We expected that the features used by these models would be regions activated by the tasks in prior studies, such as the DLPFC, VLPFC, and ACC for working memory and inhibition tasks and the striatum, VMPFC, and ACC for the reward task. Based on prior work linking structural MRI data to ADHD, we also hypothesized that structural MRI would predict ADHD symptomatology. We expected that the features used in these models would be the same as those whose morphometry had been found to be associated with ADHD in prior studies, such as the DLPFC, ACC, VMPFC, and striatum.sm Study (ABCD) is an ongoing multisite, longitudinal neuroimaging study following a cohort of 11,875 youths over 10 years. In this analysis, we use data from the baseline visits at which participants were 9–10 years old. All data used in the current study  were collected at a single visit or across two visits that occurred within 30 days of each other. The ABCD study® was approved by the institutional review board of the University of California, San Diego (IRB# 160091). Additionally, the institutional review boards of each of the 21 data collection sites approved the study. Informed consent was obtained from all parents and informed assent was obtained from participants. Data can be accessed through registration with the ABCD study at https://nda.nih.gov/abcd.The Adolescent Brain Cognitive Development27. For each fMRI task, participants were excluded for having any missing fMRI data on that task, having fewer than two fMRI scans pass the image quality control performed by the DAIRC (which was similar to the DAIRC Freesurfer QC reported above27), or failing to meet additional quality control criterion specific to this report. These additional quality control steps included having: (1) hemispheric mean beta-weights more than two standard deviations from the sample mean, (2) fewer than 200 degrees of freedom over the two runs, (3) mean framewise displacement > 0.9 mm for both runs, (4) failed to meet task-specific performance criteria . Because of a data processing error (https://github.com/ABCD-STUDY/fMRI-cleanup), participants were excluded who were collected on Philips scanners for all fMRI tasks. Additionally, for the SST only, a small group of participants were excluded because of a glitch in the SST task . This resulted in participant totals of 8596 for Structural MRI (sMRI), 5417 for the EN-Back task, 5959 for the monetary incentive delay (MID) task, and 5020 for Stop Signal Task (SST). Participant exclusion steps are reported in Supplemental Table Demographics for the full sample are shown in Table  having:  hemisphe30. Despite its name, the CBCL “Attention Problems” scale evaluates a broad constellation of ADHD symptomatology  and has been shown to be an excellent predictor of ADHD diagnosis derived from clinical interview32. Additionally, the CBCL internalizing composite was used as a covariate to account for depression and anxiety, which are frequently comorbid in children with ADHD. This composite is made up of the anxious/depressed scale, the withdrawn/depressed scale, and the somatic symptoms scale.The “Attention Problems” empirically derived syndrome scale of the CBCL parent-report questionnaire was used to evaluate symptoms of ADHD symptomatology as a continuous variableA demographics questionnaire was administered to the participant’s parent/guardian to determine demographic information including sex, age, race, household income, and parental education.33, which was completed by a parent/guardian and by the participant, with results of the two being averaged. This measure has been shown to have good reliability and to correspond with accepted self-report and biological measures of pubertal development33.Pubertal status was assessed using the pubertal development scale34 is a 4-item self-report scale that produces a handedness score of “right”, “mixed”, or “left” by asking about preferred hand used for writing, throwing, using a spoon, and using a toothbrush. The measure has been shown to have good reliability and to correlate highly with longer measures of handedness34.The Edinburgh Handedness Inventory – Short FormParents completed a survey in which they listed the names and dosages of all medications taken by the child. From this we created a binary variable if participants were taking one or more stimulant medications prescribed to treat ADHD . For a full list of medications included in this variable, see Supplemental Table 35 and are detailed in N items ago . The current task version incorporated added elements of facial and emotional processing, though these were not a focus of the current analysis. The task had two conditions: a 2-back as its active condition and a 0-back as the baseline condition. d’ (z(hit rate) − z) was used as the performance measure for the EN-back tasks. The MID task included both anticipation and receipt of reward and loss. In this task, participants viewed an incentive cue for 2 sec (anticipation) and then quickly respond to a target to win or avoid losing money ($5.00 or $0.20). Participants were then given feedback about their performance (receipt). The baseline used was “neutral” trials in which participants completed the same action but with no money available to be won or lost. The current study focused only on reward trials , as most prior research on ADHD symptomatology has focused on reward trials10. The SST consisted of serial presentations of leftward and rightward facing arrows. Participants were instructed to indicate the direction of the arrows using a two-button response box , except when the left or right arrow was followed by an arrow pointing upward . Participants were also instructed to respond as “quickly and accurately as possible”. Trials were then categorized based on the participant’s accuracy (“correct” and “incorrect”). The performance variable used for the SST was stop signal reaction time (SSRT), which represents the duration required to inhibit a “go” response after a “stop signal” has been presented and functions as an index for inhibitory speed.The tasks used in the current study have been described previously31. All sMRI and fMRI data were preprocessed by the DAIRC using pipelines that have been detailed in prior work27. Briefly, sMRI data were preprocessed using FreeSurfer version 5.327 to produce CT and CSA measures for each of the 74 Destrieux atlas36 regions of interest in each hemisphere  and GMV for nine subcortical regions in FreeSurfer’s ASEG parcellation in each hemisphere , plus the brainstem which was not split by hemisphere. All structural MRI data were visually examined by a trained ABCD technician, who rated them from zero to three on five dimensions: motion, intensity homogeneity, white matter underestimation, pial overestimation, and magnetic susceptibility artifact. From this an overall score was generated recommending inclusion or exclusion27. All subjects recommended for exclusion based on their Freesurfer data were excluded from all analyses in the current study, including fMRI analyses as the fMRI processing pipeline relies on the Freesurfer cortical reconstruction.Structural and functional MRI scans were acquired at sites across the United States using 26 different scanners from two vendors ; there were also three sites using Philips scanners that were excluded from analyses due to an error in processing prior to their release. MRI sequences are reported in incorrect stop – correct go and correct stop – correct go; for the EN-Back the only contrast was 2-Back vs. 0-Back; for the MID, contrasts were reward anticipation – neutral anticipation and positive reward outcome – negative reward outcome .fMRI data were preprocessed using a multi-program pipeline that yielded neural activation in these same cortical and subcortical regions for each fMRI contrast. The contrasts used for the SST were https://github.com/owensmax/ADHD. Covariates were participants’ age, sex, race, pubertal status, handedness, internalizing symptom score from the CBCL, parent’s highest education level, and family income. An additional analysis was also added that also used stimulant medication status (yes/no) as a covariate and so we examined stimulant medication status’ association with ADHD symptomatology. Additionally, framewise displacement from the relevant fMRI scan was used as a covariate and for structural MRI the average of framewise displacement from the fMRI scans was used. In structural MRI analyses, total intracranial volume was also used as covariate. To account for the large numbers of siblings and multiple data collection sites, family ID (used to denote sibling status) was modeled as a random effect nested inside a random effect of scanner in all mixed effects models37 and is standard on the ABCD Data Exploration and Analysis Portal (DEAP). This nested approach was used since all siblings in each family were collected at the same scanner site. In these analyses, the covariates were the independent variables and ADHD symptomatology was the dependent variable. Additionally, to investigate if working memory and inhibitory control were associated with ADHD symptomatology, we examined the association of behavioral performance on the EN-Back and Stop Signal tasks with attention symptoms. d′ (z(hit rate) − z) was used as the performance measure for the EN-Back tasks and stop signal reaction time was used as the performance metric for SST. In these analyses, the performance metrics were used as the independent variables, along with all fixed effect covariates, and ADHD symptomatology was used as the dependent variable.To investigate the relationship between covariates and ADHD symptomatology, we examined the association of each covariate with ADHD symptomatology in a separate mixed effect model for each covariate using R version 3.6.1. Code for all analyses is available at Elastic net regression was used to build predictive models for each of the imaging modalities  using the glmnet package in MATLAB R2018b. Separate models were built for each MRI paradigm , with all brain variables used as features  and ADHD symptomatology used as the target . Three versions of the analysis were run, one in which covariates were not accounted for, one in which the ADHD symptomatology score was residualized so that its shared variance with the covariates was removed, and one in which covariates including medication status were residualized from ADHD symptomatology.R2. For the internal cross-validation, each R2 represents the accuracy of predicting the internal validation set (the 5th fold) using the model built on the training set (folds 1–4); to confirm the model’s generalizability, another R2 was derived by predicting the external test set  using the most successful of the 5 models built in the 5-fold cross-validation. See Initially, data were divided in an 80%/20% split, with the 80% used as a training/validation set for model building and the 20% used as a final external test set. Then, elastic net regression model training was conducted in a 5-fold internal cross-validation framework with 80% of the data used for model training and 20% of the data used as an internal validation set to assess the model’s performance out-of-sample. Regularization hyperparameter tuning was conducted through a further nesting of a 20-fold cross-validation within the 5-fold cross validation  and on the SST .In the full sample, all demographic covariates but age were related to ADHD symptomatology Table , with thR2 = 0.8%; all model statistics in Table R2 = 0.2% for the best model in the 5-fold cross-validation which explained 0% of the variance in the external test set. Likewise, when medication was included as a covariate the best sMRI model found an R2 = 0% for the best model in the 5-fold cross-validation which explained 0.1% of the variance in the external test set. In non-covaried analyses, different regional patterns emerged for CSA and CT. ADHD symptomatology was predicted by lower CSA in the DLPFC, VLPFC, ACC, insula, lateral temporal cortex, and lateral occipital cortex. In contrast, ADHD symptomatology was predicted by lower CT in the ACC, left insula, medial temporal cortex, precentral gyrus, and postcentral sulcus, and greater CT in the VLPFC, right insula, and lateral occipital cortex. The only region in which ADHD symptomatology was predicted by subcortical gray matter volume was the caudate, for which less gray matter volume predicted greater ADHD symptomatology. Regions identified in elastic net regression and confirmed in univariate analyses are shown in Fig. When not residualizing for the effects of potentially confounding variables, the best model for sMRI data explained 1.1% of the variance in ADHD symptomatology in the internal validation set, with some shrinkage when tested on the external test set . When covariates were residualized, the best MID model had an R2 = 0% on the internal validation set and R2 = 0.1% on the external test set. When medication was added as a covariate, the best MID model had an R2 = 0% on the internal validation set and R2 = 0% on the external test set. Given the poor predictive ability of the SST and MID models, we did not investigate their features.The best model for SST predicted raw ADHD symptomatology with Results of the elastic net regression and mixed effects modeling for categorical ADHD symptomatology using a tertile split of the CBCL were quite similar to the primary analyses of the study that used the CBCL ADHD symptomatology measure continuously. In short, with the categorical version of the CBCL the EN-Back predicted categorical ADHD symptomatology beyond covariates, with models using similar regions as those predicting continuous ADHD symptomatology. sMRI predicted categorical ADHD symptomatology but not beyond covariates. SST and MID did not predict categorical ADHD symptomatology. In contrast, elastic net analyses were not able to derive a model that robustly predicted ADHD diagnosis from the K-SADS ADHD diagnosis using any of the three task fMRI paradigms or sMRI. These results are reported in Supplemental Results, Supplemental Tables 38, inhibitory control11, and reward processing10, we were surprised to see only working memory activation was able to predict ADHD symptomatology.The current study used elastic net regression with nested cross-validation to build models for predicting ADHD symptomatology out-of-sample using four sMRI and fMRI paradigms. Results indicate that the fMRI EN-Back working memory task was the most useful imaging paradigm to predict ADHD symptomatology even when accounting for numerous sociodemographic factors. Brain morphometry was able to predict ADHD symptomatology when sociodemographic factors were not accounted for, but not when covariates were accounted for. Even without accounting for sociodemographic factors, the best models for SST and MID were not effective at predicting ADHD symptomatology. Based on literature demonstrating individuals with ADHD symptomatology show poorer performance and different neural activation for working memory39 and increased activation in task negative regions40.The features used by the best EN-Back models suggest that as ADHD symptomatology increases, activation in task positive regions  decreases and activation in task negative regions  increases. This is highly consistent with the existing literature, which has shown that during working memory tasks, individuals with ADHD show reduced activation in task positive regions14. Regarding subcortical GMV, the caudate was the only region in which GMV appeared in the best elastic net regression model and was confirmed in univariate analysis to be associated with ADHD symptomatology. This is consistent with the largest examination of the correlates of ADHD for subcortical GMV in youths, which also found lower caudate volume in children with ADHD15. In the current study, ADHD symptomatology was predicted by lower CT in the caudal ACC, precentral and postcentral gyri, and medial temporal lobe, and higher CT in the VLPFC and medial and lateral occipital cortex, partially overlapping with the regions observed in the EN-Back model. Given that CT was not linked to ADHD symptomatology in the study by Bayard et al. and the literature on CT and ADHD symptomatology has not been consistent across small studies (see Lin and Roth11), we would describe the regional findings detailed here as preliminary.The CSA features identified by the best sMRI model overlapped considerably with those in the EN-Back models; ADHD symptomatology was predicted by less CSA in the DLPFC, caudal ACC, and lateral temporal cortex. These findings converge with the largest prior study of the association of ADHD symptomatology and CSA in adolescents, which also found that ADHD symptomatology were linked to less CSA in the DLPFC and caudal ACCR2 = 0.2% on internal validation set, 0.0% on external test set). Covariate use in the structural MRI literature is varied41 and it creates considerable ambiguities in interpreting findings; in the present findings, it is unclear if the factors proposed as covariates should be considered confounding third variables or meaningful and potentially causal factors. For example, it is very likely that growing up in impoverished circumstances affects the brain’s development and increases the risk of developing ADHD symptomatology43; consequently to remove variance in brain and ADHD symptomatology that is shared by socioeconomic status may serve to deflate the magnitude of the association between the two. While the field of cognitive neuroscience works towards a consensus on how best to handle covariates, we opted to report results both with and without covariates.While the relations of CSA and caudate GMV have been reproduced across studies when covariates are not accounted for , the question remains as to whether it is more appropriate to correct for demographic factors that likely are related to both ADHD symptomatology and brain structure and function and may play a causal role in their development. In the current study, accounting for age, sex, race, handedness, pubertal status, comorbid internalizing psychopathology, parental income, and parental education reduced the prediction accuracy of the elastic net regression considerably  that may prove better for investigating how inhibitory control and reward processing differences in those with ADHD symptomatology manifest in the brain. Alternately, it is also possible that prior findings linking ADHD symptomatology to SST and MID were spurious or that differences in the neural correlates of inhibitory control and reward processing are limited to other age groups, as most prior studies examined older adolescents and adults.44. However, it has been noted that these guidelines understate the importance of associations between 0.1 and 0.2, as many relationships in day-to-day life that most would consider meaningful fall within this range45, such as the relationship of antihistamine use to allergy symptoms (Pearson’s r = 0.11), ibuprofen to headache severity (Pearson’s r = 0.14), combat exposure in the Vietnam war to likelihood of developing PTSD (Pearson’s r = 0.11), college grades to job performance (Pearson’s r = 0.14), and the critical ratings to a film’s box office success (Pearson’s r = 0.17)46. As larger datasets become available, it is becoming more apparent that prior small studies showing “large” associations between brain and behavior were much too optimistic47. It is also worth noting that small effect sizes found in the current study are consistent with other large MRI studies on the neurobiological correlates of ADHD. For example, a recent ENIGMA ADHD study found small effect sizes for differences in gray matter volume in individuals with ADHD 15. Likewise, a recent IMAGEN study found small effect sizes for associations of cortical thickness to ADHD symptoms in adolescents . The largest and most thorough machine learning study to examine ADHD in children  found that their best model using sMRI predicted ADHD with an AUC = 0.67 17. This is slightly larger than the effects in the current study but is consistent when considering that these studies were comparing a clinical sample of individuals with an ADHD diagnosis and controls without ADHD symptomatology. There have not been any comparable and adequately powered studies with which to compare effect sizes to the current results for the EN-Back.A major consideration for the current study is the magnitude of the observed effect sizes. Even the best model predicting ADHD symptomatology explained just 2% of the variance out of sample – equivalent to a Pearson’s correlation of 0.14. According to Cohen’s heuristic, a correlation of 0.1 is considered smallAnother consideration is that of in-scanner motion. Children with ADHD symptomatology are known to be prone to fidgeting during MRI sessions and in the current study in-scanner motion explained 1–2% of the variance in ADHD symptomatology across fMRI scans. As a consequence, we made several attempts to account for in-scanner motion, such as using a stringent exclusion criteria for excess in-scanner motion  and covarying for in-scanner motion in all analyses. While this provides protection against the possibility that results are entirely a consequence of movement-induced scanner artifact, it also means that children with the most severe ADHD symptomatology were the most likely to be excluded, resulting in artificially truncated variance in ADHD symptomatology. This may contribute to the small effects seen in the current study and it is possible that effects may have been somewhat larger if these exclusions were not necessary to guard against artifact. As such, technical innovations in fMRI acquisition or processing that can reduce motion or its impacts on data would be tremendously helpful in the study of the neurobiology of ADHD symptomatology.49; it shows excellent concordance with clinical interviews done by mental health professionals and convergent and discriminant validity with numerous other indicators of psychopathology. Increasingly, research suggests that ADHD is a dimensional construct and levels of attention problems that do not meet the diagnostic threshold for ADHD can have negative effects on individuals’ quality of life21. Given that the current study used a non-clinical sample, we think measuring ADHD continuously was the most appropriate approach. Notably, when we re-analyzed the data using ADHD diagnosis from the K-SADS as the target variable our elastic net approach was not able to build a model that could robustly predict ADHD diagnosis. We suspect that this was a result of the loss of statistical power from artificially binarizing a continuous phenomenon into imbalanced groups. However, we do recognize this as a limitation of the study, as our results cannot be directly generalized to a formal ADHD diagnosis, which (despite its flaws) does represent the dominate approach in modern clinical psychiatry. It is also a limitation that our current results do not speak to specific ADHD subtypes, but rather focus on ADHD symptomatology in the aggregate.It is also worth considering the measure used to assess ADHD symptomatology. The CBCL is among the best validated parent-report measures of child ADHD symptomatology15. Several meta-analyses of task fMRI differences in children with ADHD have found similar patterns of activation for children on and off medication8.One further consideration is the medication status of the participants. Results were not affected substantially by including each participant’s medication status as a covariate, suggesting that medication was not the primary driver of differences in brain structure and function in individuals with ADHD symptomatology. This was expected based on prior literature, which suggested that medication effects would not represent a substantial confound to the current study. The largest previous study on this topic to date found no differences in morphometry between children with ADHD on and off stimulant medicationUsing elastic net regression with nested cross-validation, the current study found compelling evidence that ADHD symptomatology is associated with less activation during engagement of working memory in task positive regions of the brain and more activation in task negative regions, consistent with prior literature. The current study also confirmed prior work indicating that lower CSA and GMV of the caudate is associated with more ADHD symptomatology, though this was not the case after accounting for sociodemographic factors. Previously identified associations of activation during behavioral inhibition and reward processing were not confirmed in the current study.Supplemental Materials