ABSTRACT Cognitive control deficits are a hallmark of attention deficit hyperactivity disorder (ADHD) in children. Theoretical models posit that cognitive control involves reactive and

proactive control processes but their distinct roles and inter-relations in ADHD are not known, and the contributions of proactive control remain vastly understudied. Here, we investigate

the dynamic dual cognitive control mechanisms associated with both proactive and reactive control in 50 children with ADHD (16F/34M) and 30 typically developing (TD) children (14F/16M) aged

9–12 years across two different cognitive controls tasks using a within-subject design. We found that while TD children were capable of proactively adapting their response strategies,

between the cognitive control mechanisms was not present in children with ADHD. Finally, both reactive and proactive control functions were associated with behavioral problems in ADHD, and

multi-dimensional features derived from the dynamic dual cognitive control framework predicted inattention and hyperactivity/impulsivity clinical symptoms. Our findings demonstrate that ADHD

in children is characterized by deficits in both proactive and reactive control, and suggest that multi-componential cognitive control measures can serve as robust predictors of clinical

symptoms. SIMILAR CONTENT BEING VIEWED BY OTHERS REDUCED TEMPORAL AND SPATIAL STABILITY OF NEURAL ACTIVITY PATTERNS PREDICT COGNITIVE CONTROL DEFICITS IN CHILDREN WITH ADHD Article Open

access 08 March 2025 EXECUTIVE FUNCTION DEFICITS IN ATTENTION-DEFICIT/HYPERACTIVITY DISORDER AND AUTISM SPECTRUM DISORDER Article 29 August 2024 NEUROPHYSIOLOGICAL MARKERS OF ADHD SYMPTOMS

IN TYPICALLY-DEVELOPING CHILDREN Article Open access 31 December 2020 INTRODUCTION Attention deficit hyperactivity disorder (ADHD) is a common neurodevelopment disorder with prevalence rates

ranging from 5% to 10% of school-aged children worldwide [1, 2]. Strikingly, diagnostic rates of ADHD have doubled in the last two decades in the United States [3], increasing the need and

urgency to better understand pathophysiological mechanisms of the disorder. ADHD is primarily characterized by deficits in attention and cognitive control functions [4, 5]. However,

conventional behavioral measures such as accuracy and reaction time (RT) do not capture the complete range of component processes associated with cognitive control, nor are they able to

effectively distinguish these processes. Moreover, overt behavioral measures typically have weak to moderate effects in differentiating children with ADHD from typically developing (TD)

children [6] and have limited associations with core symptoms of the disorder, such as inattention and hyperactivity/impulsivity [7,8,9,10]. Recent theories and behavioral models of

cognitive control have suggested that both reactive and proactive control processes [11], which are dynamically modulated by task context, error monitoring, and prior expectations, play an

important role in cognitive control [12,13,14]. However, few studies have systematically examined dynamic, reactive, and proactive cognitive control in childhood ADHD. As ADHD is

characterized by heterogeneous patterns of both cognitive impairment [15] and symptom profiles, isolating intermediate phenotypes that are superior to current nosology is critical for

improving clinical assessments and treatment response. Here we address this gap and characterize multi-componential processes associated with dynamic dual cognitive control (DCC) mechanisms

in children with ADHD and their relation to the cardinal clinical symptoms of the disorder. The DCC model posits that there are two distinct operating modes underlying cognitive control:

reactive and proactive control [11] (Fig. 1c). Reactive control refers to one’s ability to withhold or override an automatic, habitual, or prepotent process when interference or a

countermanding event is detected [11, 16]. For example, a driver who sees a pedestrian suddenly stepping onto the road must quickly inhibit the prepotent action of continuing driving forward

instead apply the brake to stop the vehicle. A common behavioral index for reactive control is the stop-signal reaction time (SSRT) in the stop-signal task (SST), which estimates how fast

one can cancel a prepotent response [8, 17] (Fig. 1a, d). SSRT is widely used to characterize cognitive control deficits in ADHD [18,19,20]. Proactive control refers to one’s ability to

deploy, in advance, strategies to control an automatic, habitual, or prepotent process given the foreknowledge of interference or a countermanding event [11, 16, 21] (Fig. 1e). For instance,

when driving in a busy street, a driver may exercise caution by gently pushing the gas pedal to gradually accelerate the vehicle because the car in the front may slow down or come to a

sudden stop and the driver needs to be prepared to respond quickly. Proactive control has primarily been examined using context-driven response strategy adjustments when participants are

cued in advance and are indexed in such contexts by longer RTs when a high cognitive load is anticipated [14, 21]. The ability to make adjustments based on performance history is another

index of proactive control [22]. Specifically, post-error slowing is a proactive control-related behavioral adaption effect that follows the negative consequence of previous decision-making

and is associated with an elongated response time in the following trial [23] (Fig. 1e). However, whether post-error slowing is mainly driven by individual differences in adjustments of

response threshold or attention interference remains unresolved [14, 24]. More broadly, proactive control is a dynamic behavioral adaptation process as individuals learn from event history

and continuously update their beliefs about the nature of the cognitive task (e.g., the probability of a stop signal in the SST) [12, 25]. Previous studies have found that adult participants

proactively adjust their response strategy based on time-varying expectations of task-relevant signals [26, 27] but it is unknown whether children use a similar dynamic proactive control

strategy and to what extent such dynamic mechanisms are related to ADHD. Isolating proactive control strategies in children and distinguishing how they impact ADHD has important implications

for understanding disorder etiology, mechanistic heterogeneity, developmental trajectories, and treatment response. Reactive control has been the mainstay of cognitive control studies in

ADHD [6, 28, 29]. The most commonly used behavioral measures to quantify reactive control deficits include SSRT in the SST along with errors of commission in continuous performance tasks

(e.g., Go/NoGo task) [6, 28, 29]. Both measures have moderate effect sizes in differentiating children with ADHD from TD children [6, 28, 29], with SSRT having a slightly larger effect size

than commission errors [6]. Several studies have suggested that SSRT is not a robust predictor of ADHD [18,19,20] given that many children with ADHD have demonstrated similar SSRTs as those

without ADHD [24]. A meta-analysis showed that the effect sizes of SSRT in differentiating children with ADHD from TD children were influenced by task complexity, sex, and comorbidity [30].

However, weak group differences in SSRT reported in early studies may have arisen from small sample sizes (_n_ < 20) [31, 32]. Because cognitive control deficits, often operationalized

through SST, remain a key component in etiological theories of ADHD [5], it is important to evaluate the reliability of SSRT with different task complexities in children with ADHD with a

substantial sample size. In contrast to reactive control, proactive control has been largely ignored in studies of ADHD despite its potential to uncover robust components of cognitive

control dysfunction associated with the disorder. The limited research on proactive control to date has yielded inconsistent findings. One study reported that incarcerated adolescents have

more difficulty using proactive control strategies compared to the control group and this difference was associated with a diagnosis of ADHD [33]. Yet another study reported that children

with ADHD and TD children have similar proactive control capacities, measured by varying the need for inhibitory control between task runs [34]. Similar findings were reported in a study of

boys wherein proactive control was measured by manipulating the probability of stop signals in the SST [35]. Yet the evidence is mixed as other studies have reported less behavioral

adaptation, e.g., attenuated post-error slowing, in children with ADHD relative to TD children [36], indicating that at least some children with ADHD have difficulty in proactively adjusting

their response strategy after receiving negative feedback. The limited research leaves unclear the extent and sources of proactive control deficits in ADHD. Crucially, to the best of our

knowledge, no study to date has examined dynamic DCC mechanisms associated with time-varying demands of proactive and reactive control in children with ADHD. Moreover, their links to

clinical symptoms of ADHD are also not known. Here we systematically investigate dynamic DCC mechanisms in children with ADHD, with a focus on proactive control mechanisms under different

conditions, and tested their associations with core ADHD symptoms. To address these critical gaps in the literature, we used two experiments involving a standard SST and a cue-based stop

signal task (CSST) [17, 37, 38] to probe dynamic DCC processes in children with ADHD and matched TD children. Reactive control was measured on both the SST and the CSST using standard SSRT

estimation procedures [17, 39]. The SST required participants to make an accurate and speedy button-press response corresponding to a left- or right-pointing arrow (Go signal) and to

withhold responses when the arrow changed color (Stop signal). SSRT was determined by the distribution of Go RT and response rate in Stop trials based on the Race Model [39]. SSRT is an

optimal measure for reactive control and it has a strong association with stopping-related neural activity in cortical–subcortical circuits [40, 41]. SSRT was also estimated in the CSST in

the second experiment, using similar procedures as in the SST. Together, SST and CSST allowed us to examine the reliability of SSRT under different task complexity conditions. Proactive

control, including context-, performance-, and anticipation-driven proactive control, were examined separately in the CSST and SST using both model-free and model-based approaches (Fig. 1e).

The CSST is designed to probe context-driven proactive control. The task consisted of Certain and Uncertain Go trials. In the Certain Go trials, a color cue was used to indicate that there

would be no stop signals. In Uncertain Go trials, a different color cue indicated that a Stop signal may follow a Go signal. The context-driven proactive control was measured by the extent

to which responses were slowed in the Uncertain, relative to Certain, Go trials in the CSST. Next, performance-driven proactive control, or post-error slowing, was measured by differences in

RT between Go trials after unsuccessful stop trials (GoPUS) and Go trials after successful Go trials (GoPSG) in the SST (Fig. 1e). To further determine latent cognitive components that may

undermine feedback-driven proactive control in children with ADHD, we used a drift-diffusion model (DDM) to estimate three key decision-making components associated with post-error slowing:

decision threshold, drift rate, and non-decision time [42, 43]. Last, anticipation-driven proactive control was determined by the extent to which Go RT was modulated by the trial-wise

expectation of stop signals in the SST. The dynamic belief model (DBM) [12] was used to estimate trial-wise anticipation of the likelihood of stop signal (pstop) and anticipation-driven

proactive control capacity was quantified by the correlation between trial-wise Go RT and pstop [12, 26, 27] (Fig. 1e). Here we investigated whether children with ADHD can dynamically and

effectively update their belief about the probability of a stop signal from event history and modulate their proactive control efforts accordingly. Finally, little is known about the

relationship between reactive and proactive control in children and to what extent the dual control mechanisms predict core symptoms of ADHD, such as inattention and

impulsivity/hyperactivity. Here we purposely examined whether children who have better reactive control also have greater proactive control function and tested whether component measures of

reactive and proactive control can predict core symptoms of ADHD. We hypothesized that children with ADHD would have longer SSRT relative to TD children. We also predicted that children with

ADHD would have smaller context-driven response slowing and less post-error slowing than TD children. The DDM allowed us to further determine the contribution of latent decision-making

components underlying post-error slowing [44]. We hypothesized that if weak post-error slowing was related to difficulty in the timely adjustment of the decision boundary, children with ADHD

would show smaller post-error-related changes in response threshold than TD children. In contrast, if weak post-error slowing was linked to less post-error interference, perhaps arising

from poor self-awareness of mistakes, children with ADHD would exhibit smaller post-error-related changes in drift rate than TD children. Moreover, we predicted that children with ADHD would

exhibit poorer anticipation-driven proactive control, evidenced by a smaller correlation between trial-wise Go RT and pstop, than TD children. We further predicted that TD children who have

better reactive control would also have better proactive control but this relation may be dampened in children with ADHD. We also hypothesized that behavioral measures from the dynamic DCC

model would predict ADHD clinical symptoms, such as inattention and hyperactivity/impulsivity. RESULTS PARTICIPANTS’ DEMOGRAPHICS One hundred and seven children (9–12 years old) were

recruited from the local community. 50 children with ADHD (16F/34M, 11 ± 1 years old) and 30 TD children (14F/16M, 11 ± 1 years old) who completed two runs of SST and two runs of CSST and

met task performance criteria (see the “Methods” section for details) were included in the analyses. Table 1 summarizes participants’ demographic information, ADHD symptoms, and behavioral

performance in both the SST and CSST. Children with ADHD and TD controls did not differ in age, sex, and verbal IQ (all _p_s > 0.2, two-sample two-tailed _t_-test). Children with ADHD had

severe inattention and hyperactivity and impulsivity symptoms relative to TD children (_p_s < 0.001, two-sample two-tailed _t_-test, Table 1). OVERALL BEHAVIORAL PERFORMANCE IN THE SST

Participants achieved good performance in the SST and with high accuracy and fast RT on Go trials and targeted accuracy (close to 50%) on Stop trials. RT on UnsuccStop trials was

significantly shorter than on Go trials (_t_79 = 18.96, _p_ < 2.2E−16, one sample two-tailed _t_-test), suggesting no violation of the Race Model [17, 39]. REACTIVE CONTROL IN CHILDREN

WITH ADHD IN THE SST We tested whether children with ADHD exhibited a reactive control deficit in the SST. Children with ADHD had worse Go accuracy and longer average RTs and greater RT

standard deviations in both Go and UnsuccStop trials than TD children (all _p_s < 0.01, two-sample two-tailed _t_-test, Table 1). No significant group difference was found on Stop

accuracy (_p_ = 0.77, two-sample two-tailed _t_-test). This pattern indicates that performance-based step-wise adjustments of SSD were implemented successfully in both groups. Children with

ADHD had significantly longer SSRT than TD children (_t_74.48 = 2.85, _p_ = 0.006, _Cohen’s_ _d_ = 0.61, two-sample two-tailed _t_-test, Fig. 2a). The 95% confidence interval of SSRTs was

from 266 to 298 ms in TD children and from 298 to 330 ms in children with ADHD. These findings suggest worse reactive control ability relative to TD children. OVERALL BEHAVIORAL PERFORMANCE

IN THE CSST Participants achieved good performance in the CSST with high accuracy and fast RT on Go trials and targeted accuracy (close to 50%) on Stop trials. RT on UnsuccStop trials was

significantly shorter than on Uncertain Go trials (_t_79 = 13.55, _p_ < 2.2E−16, one sample two-tailed _t_-test), suggesting no violation of the Race Model [17, 39]. REACTIVE CONTROL IN

CHILDREN WITH ADHD IN THE CSST We tested whether children with ADHD exhibited a reactive control deficit in the CSST. Children with ADHD had longer average RTs and greater RT standard

deviations in both Uncertain Go and UnsuccStop trials than TD children (all _p_s < 0.05, two-sample two-tailed _t_-test, Table 1). Again, we found a significant group difference in SSRT

with longer SSRT in children with ADHD than TD children (_t_65.73 = 3.31, _p_ = 0.001, _Cohen’s_ _d_ = 0.75, two-sample two-tailed _t_-test, Fig. 2a). The 95% confidence interval of SSRTs

was from 266 to 304 ms in TD children and from 310 to 341 ms in children with ADHD. Next, we examined intra-subject reliability of the SSRT estimation. Indeed, there was a strong correlation

between SST and CSST in SSRT (_r_78 = 0.76, _p_ = 3.3E−16, Pearson’s correlation, Fig. 2b). This finding suggests that the difference in SSRT between children with ADHD and TD children has

high test–retest stability across different tasks. PROACTIVE CONTROL IN CHILDREN WITH ADHD IN THE CSST: INFLUENCE OF TASK CONTEXT To further investigate whether children with ADHD have

difficulty in adjusting their response strategy we examined how task context cues influence response slowing. Proactive control, induced by task context, was measured using the RT difference

between Uncertain Go and Certain Go in the CSST. We found that there was a significant context-induced proactive control in children (28 ± 33 ms, _t_79 = 7.58, _p_ = 5.6e−11, one sample

two-tailed _t_-test, Table 1), but there was not a significant group difference between children with ADHD and TD children (_t_75.85 = 0.65, _p_ = 0.52, two-sample two-tailed _t_-test, Fig.

3a), suggesting that children with ADHD are capable of using prior knowledge to adjust their response strategies. PROACTIVE CONTROL IN CHILDREN WITH ADHD IN THE SST: INFLUENCE OF PERFORMANCE

MONITORING We next investigated whether children with ADHD have difficulty adjusting their response strategy based on performance monitoring in the SST. Although no explicit feedback was

given in each trial, subjects were fully aware of whether they had made a button press or not as their motor responses served as implicit feedback. This was demonstrated by a significant

post-error slowing effect in TD children (42 ± 44 ms, _t_29 = 5.17, _p_ < 0.001, one sample two-tailed _t_-test, Table 1). Post-error slowing was measured using the difference in RT

between Go trials after Unsuccessful Stop trials (GoPUS) and Go trials after Successful Go trials (GoPSG). We found that children with ADHD had significantly smaller post-error slowing than

TD children (_t_67.99 = 2.65, _p_ = 0.01, _Cohen’s_ _d_ = 0.60, two-sample two-tailed _t_-test, Fig. 3b). The 95% confidence interval of post-error slowing was from 25 to 58 ms in TD

children and from −1 to 27 ms in children with ADHD. This finding suggests that children with ADHD have poorer proactive control ability associated with response slowing triggered by

performance monitoring or errors. To further examine whether post-error slowing benefits stopping performance, we compared the accuracy of Stop trials after Unsuccessful Stop trials

(StopPUS) and Stop trials after Successful Go trials (StopPSG) and found a significant post-error effect on stop accuracy (14 ± 16%, _t_79 = 8.01, _p_ < 0.001, one sample two-tailed

_t_-test, Table 1) in all young participants. Moreover, post-error slowing was significantly correlated with the post-error effect on stop accuracy (_r_ = 0.23, _p_ = 0.04, _Pearson’s_

correlation), suggesting that individuals who made more adjustments on reaction time (slowing more) benefitted in stopping accuracy. We also found that TD children showed a greater

post-error effect on stop accuracy than children with ADHD (TD: 21 ± 14%, ADHD: 11 ± 17%, _t_71.14 = 2.72, _p_ = 0.008, _Cohen’s_ _d_ = 0.60, two-sample two-tailed _t_-test).). The 95%

confidence interval of post-error effect on stop accuracy was from 15% to 26% in TD children and from 6% to 16% in children with ADHD. To better understand why children with ADHD did not

slow down their responses after committing wrong responses as much as TD children do, we applied a drift-diffusion model to unveil decision-making components, including threshold, drift

rate, and non-decision time, for each GoPUS and GoPSG trial per participant. We then computed differences in each decision-making component between GoPUS and GoPSG, which was further used to

test whether performance monitoring-induced changes in decision-making components would differentiate children with ADHD from TD children. We found that performance monitoring-induced

changes in response threshold were not significantly different between children with ADHD and TD children (_t_56.91 = 0.69, _p_ = 0.50, two-sample two-tailed _t_-test, Fig. 4a).

Interestingly, negative-feedback induced changes in drift rate were significantly smaller in children with ADHD than TD children (_t_59.68 = 2.14, _p_ = 0.03, _Cohen’s_ _d_ = 0.50,

two-sample two-tailed _t_-test, Fig. 4b). Negative-feedback induced changes in non-decision time were marginally significantly smaller in children with ADHD than TD children (_t_59.35 = 

1.98, _p_ = 0.05, _Cohen’s_ _d_ = 0.46, two-sample _t_-test, Fig. 4c). The 95% confidence interval of post-error effect on drift rate was from 3.18 to 3.89 in TD children and from 3.21 to

3.78 in children with ADHD. These findings suggest that errors have less interference on information accumulation speed in children with ADHD than in TD children. PROACTIVE CONTROL IN

CHILDREN WITH ADHD IN THE CSST: INFLUENCE OF EVENT HISTORY AND ANTICIPATION Next, we examined proactive control associated with the anticipation of stop signals. We used DBM to measure

trial-wise anticipation of stop signals (pstop). We then computed the correlation between pstop and RT across Go trials for each child, with higher correlations indicating more response

slowing when participants believe that the stop signal is more likely to occur. We found that children with ADHD had significantly lower correlations than TD children (_t_49.14 = 3.12, _p_ =

 0.002, _Cohen’s_ _d_ = 0.77, two sample two-tailed _t_-test, Fig. 3c), suggesting that children with ADHD are not as effective as TD children on adjusting their response strategy based on

anticipation of stop signals. The 95% confidence interval of the correlation between pstop and Go RT was from 0.13 to 0.23 in TD children and from 0.06 to 0.12 in children with ADHD. Results

suggest that children with ADHD have poorer proactive control ability associated with anticipation-related response slowing. REACTIVE AND PROACTIVE CONTROL MEASURES ARE CORRELATED IN TD

CHILDREN BUT NOT IN CHILDREN WITH ADHD Next, we examined whether reactive control and proactive control functions are correlated in children as previously demonstrated in adults [37].

Proactive control induced by task context had no significant correlation with SSRT in the whole cohort (_r_78 = −0.11, _p_ = 0.31, _Pearson’s_ correlation). When examining each group

separately, however, we found a significant correlation in TD children (_r_28 = −0.45, _p_ = 0.01, _Cohen’s d_ = 1.01, _Pearson’s_ correlation, Fig. 5a) but not in children with ADHD (_r_48 

= 0.24, _p_ = 0.09, _Pearson’s_ correlation). A Fisher’s _Z_ test confirmed that the correlation coefficients are significantly different between the two groups (_z_ = 3.02, _p_ = 0.001,

_Fisher’s_ test). Proactive control induced by performance monitoring had no significant correlation with SSRT in the whole cohort (_r_78 = −0.09, _p_ = 0.38, _Pearson’s_ correlation). When

examining each group separately, however, we found a significant correlation in TD children (_r_28 = −0.46, _p_ = 0.01, _Cohen’s d_ = 1.03, _Pearson’s_ correlation, Fig. 5b) but not in

children with ADHD (_r_48 = 0.15, _p_ = 0.31, _Pearson’s_ correlation). A Fisher’s _Z_ test confirmed that the correlation coefficients are significantly different between the two groups

(_z_ = 2.69, _p_ = 0.004, _Fisher_’s test). Proactive control induced by anticipation of stop signals had a significant correlation with SSRT in the whole cohort (_r_78 = −0.24, _p_ = 0.03,

_Cohen’s_ _d_ = 0.49, Pearson’s correlation). When examining each group separately, however, we found a significant correlation in TD children (_r_28 = −0.38, _p_ = 0.04, _Cohen’s_ _d_ = 

0.82, _Pearson’s_ correlation, Fig. 5c) but not in children with ADHD (_r_48 = −0.02, _p_ = 0.85, _Pearson’s_ correlation). A Fisher’s _Z_ test demonstrated that the correlation coefficients

are marginally significantly different between the two groups (_z_ = 1.57, _p_ = 0.06, _Fisher’s_ test). Additional multiple linear region analysis using age, gender, and IQ as confounds

found that proactive control induced by task context is a significant predictor of SSRT (_p_ = 0.02), proactive control induced by performance monitoring is a marginally significant

predictor of SSRT (_p_ = 0.05), and anticipation of stop signals is a marginally significant predictor of SSRT (_p_ = 0.06) in TD children (Supplementary Table S1). Together, our finding

suggests that TD children who have good reactive control also have good proactive control, like adults [37], but this association is not observed in children with ADHD. DUAL CONTROL

MECHANISMS IN RELATION TO CORE SYMPTOMS OF ADHD We used the SWAN to examine core symptoms of ADHD in relation to reactive and proactive control ability because it is sensitive to variance in

both inattention and hyperactivity/impulsivity dimensions [45]. SSRT in the SST was significantly correlated with Inattention (_r_2 = 0.08, _p_ = 0.009, _Cohen’s_ _d_ = 0.60, _Pearson’s_

correlation, Supplementary Fig. S1a) and Hyperactivity/Impulsivity scores (_r_2 = 0.09, _p_ = 0.004, _Cohen’s_ _d_ = 0.65, _Pearson’s_ correlation, Supplementary Fig. S1b), and SSRT in the

CSST were also significantly correlated with Inattention (_r_2 = 0.13, _p_ = 0.001, _Cohen’s d_ = 0.77, _Pearson’s_ correlation, Supplementary Fig. S1c) and Hyperactivity/Impulsivity scores

(_r_2 = 0.10, _p_ = 0.003, _Cohen’s d_ = 0.68, _Pearson’s_ correlation, Supplementary Fig. S1d). Proactive control induced by task context cues was not significantly correlated with

Inattention and Hyperactivity/Impulsivity scores (all _p_s > 0.5, _Pearson’s_ correlation). Proactive control induced by performance monitoring was significantly correlated with

Hyperactivity/Impulsivity scores (_r_2 = 0.11, _p_ = 0.003, _Cohen’s d_ = 0.70, Pearson’s correlation, Supplementary Fig. S2b) and marginally with Inattention (_r_2 = 0.04, _p_ = 0.06,

_Cohen’s d_ = 0.41, _Pearson’s_ correlation, Supplementary Fig. S2a). Proactive control induced by anticipation of stop signals was significantly correlated with Inattention (_r_2 = 0.08,

_p_ = 0.01, _Cohen’s_ _d_ = 0.58, _Pearson’s_ correlation, Supplementary Fig. S2c) and Hyperactivity/Impulsivity scores (_r_2 = 0.10, _p_ = 0.004, _Cohen’s d_ = 0.65, _Pearson’s_

correlation, Supplementary Fig. S2d). Additional multiple linear region analysis using age, gender, and IQ as confounds confirmed that behavioral measures of dual control mechanisms are a

significant predictor of core symptoms of ADHD (Supplementary Table S2). Together, our findings suggest that dual control functions are associated with both inattention and

hyperactivity/impulsivity symptoms. DUAL CONTROL MECHANISMS PREDICT CORE SYMPTOMS OF ADHD We further examined whether dual control mechanisms can predict core symptoms of ADHD. Specifically,

we trained multiple linear regression models based on behavioral measures of reactive and proactive control (i.e., SSRT and context-, performance monitoring-, and anticipation-triggered

proactive control) to predict inattention and hyperactivity, and impulsivity scores. A leave-one-out cross-validation procedure was applied, and model performance was assessed by the

correlation between predicted and observed clinical scores. We found that behavioral measures indexing dual control mechanisms can significantly predict inattention (_r_ = 0.24, _p_ = 0.02,

_Pearson’s_ correlation) and hyperactivity/scores (_r_ = 0.36, _p_ = 0.001, _Pearson’s_ correlation). Then, we tested whether the inclusion of proactive control measures is important for

clinical symptom prediction. To examine this question, we trained the prediction model using only the reactive control measure, SSRT. We found that the predicted and observed inattention

scores were marginally significantly correlated (_r_ = 0.21, _p_ = 0.06, _Pearson’s_ correlation) and that the predicted and observed hyperactivity/impulsivity scores were significantly

correlated (_r_ = 0.24, _p_ = 0.02, _Pearson’s_ correlation). Furthermore, we determined that prediction models built on both reactive and proactive control measures are marginally more

robust than prediction models built on reactive control measures alone in predicting hyperactivity/impulsivity scores (_p_ = 0.09, _Pearson and Filon’s_ test). DISCUSSION ADHD is a

heterogeneous disorder with diverse clinical presentations, cognitive impairments, and symptom trajectories. Although cognitive control deficits are a defining feature of ADHD symptom

presentation, the specific component mechanisms remain underspecified and underexplored in understanding etiological contributions and phenotypic presentations. We systematically

investigated dynamic DCC mechanisms associated with reactive and proactive control in children with ADHD and their relation to clinical symptoms of ADHD. Going beyond previous studies, we

used two different experiments, SST and CSST, to quantify reactive and proactive control using both model-free and model-based approaches. Crucially, our analytic approach allowed us to

investigate the influence of task context, performance monitoring, and anticipation of stop signals on the implementation of cognitive control in children with ADHD. We found that relative

to TD children, children with ADHD displayed longer SSRT, indicating a weaker reactive control function. For proactive control, children with ADHD demonstrated suboptimal response strategy

modulation driven by performance monitoring and the anticipation of stop signals relative to TD children. Furthermore, in contrast to findings in TD children, reactive and proactive control

were not correlated in children with ADHD. These findings suggest that children with ADHD have weaker and less coordinated reactive and proactive control abilities than TD children. Finally,

reactive and proactive control weaknesses predicted core symptoms of childhood ADHD, suggesting that the relationship between symptom presentation and performance on behavioral inhibition

tasks is more complex than what one reaction time measure can capture. Taken together, our findings highlight specific proactive and reactive cognitive control mechanisms and their disrupted

dynamics that are associated with ADHD symptom presentation, advancing our understanding of diverse cognitive profiles. REACTIVE INHIBITORY CONTROL DEFICITS IN ADHD ARE REPLICABLE Prominent

cognitive theories of ADHD have argued that deficits in inhibitory control are a cardinal feature of behavioral problems in affected individuals [4]. As such, understanding cognitive

components associated with inhibitory control deficits is a major endeavor in ADHD research. Many studies have used response inhibition tasks, such as SST, to probe inhibitory control, and

the SSRT is typically conceptualized as reactive (inhibitory) control [11, 16]. Here we used the SST and CSST to probe the reactive inhibitory control function. Averaged SSRTs in children

(9–12 years old) were 302 ± 54 ms in the SST and 310 ± 57 ms in the CSST, consistent with SSRTs reported in previous studies using the same age group [46,47,48]. SSRTs from the SST and CSST

were highly correlated, suggesting high intra-individual reliability of SSRTs across cognitive tasks in children. We found that children with ADHD have longer SSRT than TD children.

Critically, this finding was replicated in the CSST. Our results are consistent with previous meta-analyses [6, 28, 29, 49] and suggest that relative to TD children, children with ADHD have

greater difficulty with and take longer when controlling context-inappropriate impulsive actions. This finding demonstrates that children with ADHD have poor reactive inhibitory control

ability relative to TD children. CONTEXT-DRIVEN PROACTIVE CONTROL IS NOT COMPROMISED IN ADHD Proactive control is an important and understudied aspect of cognitive control function in ADHD.

The DCC model [11] suggests that proactive control plays an important role in adaptive task-context-based adjustments to response strategy, although this cognitive control component has

rarely been tested in childhood ADHD. Proactive control is a common behavioral strategy used to resolve potential future conflicts [11]. Task context cues that indicate an increased

possibility of cognitive control demands (e.g., stop signals) are often followed by longer reaction time regardless of whether additional cognitive control is actually needed for a specific

trial (e.g., go trial) [14]. Proactive control that is driven by contextual cues has been shown to be accompanied by suppression of excitability in the motor system [21]. One study has

suggested that proactive control may recruit similar cortical–subcortical systems as reactive control [38]. In the present study, we used the CSST to probe context-driven proactive control

in children. We found that there was significant response slowing in Uncertain Go, relative to Certain Go, trials, confirming that 9–12-year-old children can successfully use task contextual

cues to adjust their response strategies [50]. Contrary to our hypothesis, we did not find significant differences in context-driven proactive control between children with ADHD and TD

children. Three previous studies have examined proactive control in ADHD [24, 34, 51]. These studies have reported similar findings. A weakness of previous studies is that proactive control

was tested in different experimental blocks so that participants knew whether stop signals might occur or not from the very beginning of each task block [24, 34, 51]. In contrast, in the

present study, Uncertain Go trials that required proactive control, and Certain Go trials that did not require proactive control, were randomly intermixed within each test administration so

that participants needed to dynamically adjust their response strategies based on task contextual cues presented at the beginning of each trial. Our experimental design overcomes the

weaknesses of prior studies and provides strong evidence that children with ADHD have preserved the ability in maintaining task-set rules and implementing a context-appropriate response

strategy when explicit task cues are provided. PROACTIVE CONTROL DEFICITS ASSOCIATED WITH PERFORMANCE MONITORING IN ADHD Post-error slowing is one of the most robust measures of adaptive

response control [36]. Dominant theories of cognitive control attribute post-error slowing to the implementation of cautious response strategies after an incorrect outcome [52, 53]. A recent

study found that corticospinal excitability of the motor cortex is dampened after incorrect responses, suggesting that proactive inhibitory control influences subsequent decision-making

[54]. Other studies have argued that an attentional shift or lapse in sustained attention can account for, at least partially, a post-error slowing effect [55]. In the present study, we

assessed post-error slowing using RT differences between Go trials after an Unsuccessful Stop trial (the subject mistakenly pressed a button when a stop signal occurred) and Go trials after

a Successful Go trial. Although negative feedback was not explicitly given after each trial in this study, participants were aware of the mistakes made as there was a significant post-error

slowing effect in children (24 ± 50 ms, Table 1). Consistent with prior work [56], we found that children with ADHD had significantly less post-error slowing than TD children. Although

diminished poster-error slowing is often attributed to weaker response caution, a formal process model is needed to isolate the specific cognitive processes that are responsible for the

effects demonstrated here. Specifically, diminished post-error slowing in ADHD could also be attributed to distraction of attention, and/or disrupted perceptual and motor processes. To

disentangle the latent cognitive components that contribute to weak post-error slowing in children with ADHD, we used DDM [44]. DDM quantifies latent decision-making processes by estimating

three latent components underlying the time to respond on each trial: (1) decision threshold, which indexes the distance to a decision boundary, (2) drift rate, which indexes how fast

evidence is accumulated to reach a decision, and (3) a non-decision time, which indexes perception time prior to decision-making and motor response time after decision-making [42, 43]. We

specifically modeled decision-making processes underlying Go trials after Unsuccessful Stop trials and Go trials after Successful Go trials, computing the difference to index performance

monitoring induced changes in each latent decision-making component. We hypothesized that if weak post-error slowing was due to an impaired or suboptimal ability to adjust their response

boundary (i.e., response caution), children with ADHD would show smaller performance monitoring-induced changes in decision threshold than TD children. If children with ADHD paid less

attention to errors, they would show smaller performance monitoring-induced changes in drift rate than TD children. Finally, if weak post-error slowing was due to difficulty in adjusting

perceptual and motor processes after perceiving the error, children with ADHD would show smaller performance monitoring-induced changes in non-decision time than TD children. DDM analyses

revealed a significant between-group difference in drift rate: children with ADHD demonstrated smaller, performance-monitoring-induced changes than TD children, but not in decision

threshold. Our findings support an attentional account, rather than an impaired response caution account, for a weaker post-error slowing effect in children with ADHD. One possible mechanism

underlying greater post-error slowing is that children with ADHD may be less aware of errors, leading to a small interference effect on the evidence accumulation. The net effect is that

they do not sufficiently alter their decision-making following errors. Interestingly, our previous neuroimaging study showed that children with ADHD have significantly weaker error-related

activation in the salience network than TD children [57]. The salience network is important for identifying behaviorally relevant stimuli and is particularly sensitive to errors [58]. Weak

engagement of the salience network in response to errors suggests that relative to TD children, children with ADHD may be less sensitive to detecting the saliency of their errors. Our study

revealed smaller, performance-monitoring-induced changes in drift rate in children with ADHD, consistent with prior reports of salience network dysfunction in error processing. PROACTIVE

CONTROL DEFICITS ASSOCIATED WITH ANTICIPATION IN ADHD We not only rely on external cues to adjust our response strategies but also make predictions about future events to maximize the

benefit-to-cost ratio [12]. In the SST, although the overall probability of stop signals across all trials is pre-defined, the local probability of stop signals varies from trial to trial

and individuals adjust their response strategies based on their belief regarding how likely a stop signal will occur in the incoming trial. We used the DBM to estimate individuals’

trial-wise anticipation of the likelihood of a stop signal in the SST based on event history [12, 59]. Previous studies have demonstrated that adult participants implement a more cautious

response strategy when they anticipate a high likelihood of stop signals in the coming trials [26, 27]. In the present study, we found that trial-wise anticipation of stop signals was

significantly correlated with RT. This finding suggests that, like adults [26, 27], children ages 9–12 years are capable of learning from trial history, updating their belief of incoming

signals, and efficiently adjusting their response strategy accordingly. Crucially, this relation was stronger in TD children compared to children with ADHD, suggesting that learning-based

behavioral adaptation is less developed in children with ADHD. Children with ADHD may be less effective in updating their belief about the local probability of stop signals arising from a

poor ability to track event history. Furthermore, children with ADHD may be less motivated to make effortful, trial-wise response strategy adjustments. Several theories have proposed that

ADHD is associated with altered sensitivity to reinforcement, with behavioral and neuroimaging work suggesting that motivational disturbances represent a distinct subcomponent of ADHD [60].

Although we cannot rule out motivational influences, it is likely that deficits in decision-making strategies emerge from the interactive effects of disrupted learning mechanisms such as

belief updating and alterations in feedback sensitivity. PROACTIVE CONTROL IN RELATION TO REACTIVE CONTROL IN CHILDREN: DISRUPTED DYNAMICS IN ADHD The question of whether proactive control

processes influence reactive control has not been investigated in the context of childhood ADHD. Addressing this question has the potential to inform the integrity of dynamic DCC mechanisms

underlying cognitive control in ADHD. In neurotypical adults, one previous study has suggested that better proactive control function is correlated with greater reactive control [37]. Here

we tested this hypothesis in children and extended prior findings by examining proactive control triggered under different conditions. We found that SSRT was significantly correlated with

proactive control in TD children, suggesting that a close relationship between reactive and proactive control exists in children. Beyond the previous finding [37], we further demonstrated

that reactive control is not only correlated with context-driven proactive control but also with performance monitoring-driven and anticipation-driven proactive control. More importantly, we

determined that in children with ADHD, reactive and proactive control performances were not significantly correlated for all forms of proactive control. One previous study examined

post-error slowing in relation to SSRT in children with ADHD and TD children and found no significant relationship between reactive and feedback-driven proactive control [36]. However,

clinical and control groups were not evaluated separately. In short, unlike TD children, children with ADHD do not efficiently use reactive and proactive control in conjunction with each to

facilitate task performance. DISRUPTIONS IN PROACTIVE AND REACTIVE CONTROL PREDICT CORE SYMPTOMS OF ADHD Prominent cognitive models of ADHD suggest that deficits in inhibitory control

underlie behavioral problems in children with ADHD [4, 5]. Although many studies have highlighted deficits in inhibitory control as a cognitive phenotype of the disorder, these studies have

predominantly been based on measures of reactive control, and the differential contribution of proactive and reactive control is poorly understood. Furthermore, meta-analytic studies have

pointed out that SSRT measures have medium effect sizes in differentiating children with ADHD from TD children [6]. We used multiple model-free and model-based measures from the SST and

CSST, including different forms of proactive control induced by task context, performance monitoring, and anticipation, to predict behavioral problems associated with ADHD. These

multi-dimensional behavioral features characterize different components of dynamic DCC mechanisms as discussed above. Our analysis revealed three new results. First, we found a significant

relation between multiple measures of reactive and proactive control functions and inattention and hyperactivity/impulsivity scores in children. Importantly, behavioral measures of reactive

and proactive control remained robust predictors of clinical symptoms even when adjusting for potential confounds, such as age, sex, and verbal IQ. Second, we trained multiple linear

regression models and used a cross-validation procedure to demonstrate that behavioral measures of dynamic DCC mechanisms can predict clinical scores of ADHD in the unseen data. Third, we

found that behavioral measures from the dynamic DCC model have better predictive utility of clinical symptoms than behavioral measures from reactive control alone. These findings demonstrate

that the DCC model is a robust cognitive framework for uncovering latent cognitive deficits underlying behavioral problems in ADHD. CLINICAL IMPLICATIONS Both proactive and reactive control

are important skills for children to develop. For example, children who have difficulty in paying attention in the classroom can use proactive strategies to better control themselves and

resist potential distractors, e.g. turning off personal electronic devices. However, when an unexpected situation arises, reactive control is important to help children to inhibit

inappropriate behavior and make the more appropriate choice. Problematic cognitive control is fundamental to several etiological theories of ADHD, yet no reliable cognitive profiles have

emerged. As children and adolescents with ADHD are at an increased risk for a variety of poor health and social outcomes, identifying clinically meaningful intermediate phenotypes, their

neurobiological correlates and pathophysiology, and developmental trajectories is essential to improve prevention and intervention efforts. To render the heterogeneity problem in ADHD more

tractable, comprehensive approaches that go beyond reactive control are needed. Here, we synthesized cognitive control task-based performance into proactive and reactive control components,

demonstrating that children with ADHD have weaknesses in both and that, unlike the case for their TD peers, proactive and reactive control components were not significantly correlated.

Further, dual cognitive control measures demonstrated the better predictive utility of core ADHD symptoms than reactive control measures alone. Importantly, what might appear as a reactive

control problem, may be the result of dysfunctional proactive and reactive control dynamics. Such distinctions and precision may be extremely valuable in developing a better nosology for

ADHD, as well as improving clinical treatments and prediction. For instance, investigating dual control mechanisms can help determine deficits in proactive and/or reactive control domains,

which can allow for further examination of specific treatment responsiveness. This knowledge can help clinicians and researchers develop more targeted and effective treatments for children

with ADHD. Finally, our results broadly suggest that children with ADHD may have altered implicit learning as ineffective belief updating and information accumulation speed were observed

during conditions in which making errors could have occurred (anticipation) or did occur (performance monitoring). CONCLUSION We conducted a systematic investigation of cognitive control

deficits in children with ADHD in a dynamic framework of a dual cognitive control model. Our findings suggest that relative to their TD peers, children with ADHD suffer from weak reactive

control functions. They also have a diminished capacity to learn from trial history and performance and adjust their behavioral strategy accordingly, highlighting deficits in reactive

control. The dual cognitive control model is a robust cognitive framework for predicting behavioral problems in ADHD. Our findings thus provide novel insights into understanding the dynamic

and multi-componential mechanisms underlying cognitive control deficits in children with ADHD. METHODS PARTICIPANTS One hundred and seven children (9–12 years old) were recruited from the

local community. Informed written consent was obtained from legal guardians of the children and all the study protocols were approved by the Institutional Review Board of Stanford

University. Participants who completed two runs of each of SST and CCST and met task performance criteria (Go accuracy is above 50% and Stop accuracy is between 25% and 75%) were included in

the final analysis, resulting in 50 children with ADHD (16F/34M, 11 ± 1 years old) and 30 TD children (14F/16M, 11 ± 1 years old). See Table 1 for participant demographic information. The

sample size was chosen to maintain a predicted power of 0.8 with a significance level of 0.05 using the effect size of the SSRT difference between children with ADHD and TD children, which

is reported in a previous meta-analysis study [6]. Participants who do not meet task performance criteria were not different with respect to clinical symptoms from those included in the data

analysis (see Supplementary Results for details). CLINICAL AND NEUROPSYCHOLOGICAL ASSESSMENTS Children and their guardians completed a clinical and neuropsychological assessment session.

ADHD diagnosis was informed by the children’s guardians and further confirmed using the _Conners_ 3rd Edition. ADHD with conduct disorder and oppositional defiant disorder were not excluded

as they are common comorbidities [61, 62] (see Supplementary Methods and Results for details). Additional inclusion criterion for both children with ADHD and TD children were the following:

no history of claustrophobia, head injury, serious neurological or medical illness, autism, psychosis, mania/bipolar, major depression, learning disability, substance abuse, sensory

impairment such as vision or hearing loss, birth weight <2000 g and/or gestational ages of <34 weeks. All children were right-handed with an IQ >80. For all children, inattention

and hyperactivity/impulsivity symptoms were assessed using the _Conners_ 3rd Edition and Strengths and Weaknesses of Attention-Deficit/Hyperactivity-symptoms and Normal-behavior (SWAN)

rating scale. We used the SWAN to investigate the relation between cognitive task performance and clinical symptoms because the SWAN can capture variance between average behavior and far

above average range, which is well suited for dimensional analyses [45, 63]. Participants who were under stimulant treatment had gone through a washout period of at least 5 half-lives of the

medicine before testing. Details of the medication status of ADHD participants can be found in Supplementary Methods. INHIBITORY CONTROL TASKS SST In the stop-signal task (SST), each trial

started with a white cross in the center of the screen for 200 ms and was followed by a green arrow. Participants were told to make a left or right button press response if a left- or

right-pointing green arrow (Go signal) was presented, correspondingly. Occasionally (33% chance), the green arrow quickly turned to red (Stop signal) and participants needed to withhold

button press responses when the color change was detected. The interval between the onsets of the Go and Stop signals was the stop-signal delay (SSD). The SSD was initiated at 200 ms and its

value was adapted based on trial-by-trial performance in a staircase fashion. The SSD increased by 50 ms if a participant successfully withheld a response in the last stop trial; and the

SSD decreased by 50 ms if a participant failed withholding a response in the last stop trial. When there was no Stop signal, the Go signal was presented for 500 ms and the response window

was 1.5 s. Participants completed two runs of the SST in the scanner and each run included 96 trials (64 Go trials and 32 Stop trials) with jittered inter-trial intervals between 1 and 4 s.

CSST In the cued stop-signal task (CSST), each trial started with a white or green cross (Cue) in the center of the screen for 200 ms and followed by a green arrow. The white cross

represented the Uncertain Go trial, such that the green arrow could change to red (33% chance) and participants would need to withhold their response when the green arrow turned to red. In

the trials with the white cross, all the parameters were the same as the SST. The green cross represented the Certain Go trial, wherein the green arrow never changed color so no response

withholding was needed. Therefore, the white and green crosses represented two different task rules: one with the possibility to stop and the other with no stopping requirement at all.

Participants completed two runs of the CSST in the scanner and each run included 80 trials (32 Certain Go, 32 Uncertain Go, and 16 Stop trials) with jittered inter-trial intervals between 1

and 4 s. BEHAVIORAL MEASURES _Reactive control_ is measured by SSRT in the SST and CSST. First, we examined whether the behavioral data violated a main assumption of the Race Model, that the

mean RT in UnsuccStop trials should be shorter than the mean RT in Go trials [39]. Then, SSRT was computed using the integration method based on the Race model [39]: SSRT = _T_−mean SSD,

where _T_ is the point when the integral of the observed distribution of Go RT in the SST or Uncertain Go RT in the CSST equals the probability of unsuccessful stopping. For each individual,

we computed SSRT in the SST and CSST and evaluated the intra-subject reliability of SSRT estimation using _Pearson’s_ correlation. _Context-driven proactive control_ is quantified by

response slowing modulated by task cues in the CSST, which is Uncertain Go RT relative to Certain Go RT. _Feedback-driven proactive control_ is measured using post-error slowing in the SST,

which is the RT difference between GoPUS and GoPSG. Next, DDM was used to further investigate the decision-making processes underlying post-error slow (see below). _Anticipation-driven

proactive control_ is measured by the correlation between Go RT and pstop in the SST. Shapiro-Wilk test was used to test the normal distribution of data. Levene’s test was used to confirm

similar variance in behavioral measures between groups (_p_s > 0.05) DRIFT DIFFUSION MODEL: MODEL AND PARAMETERS The DDM has been extensively used to estimate two-choice decision-making

processes [44]. In this framework, decisions are modeled as a combination of three parameters: threshold (_a_) describing the distance between two decision boundaries, drift rate (_v_)

describing the rate at which evidence is accumulated for a given decision, and non-decision time (_t_) which is representative of those aspects of response time not included in decision

making (e.g., stimulus encoding, movement execution). Here we used the DDM to disentangle latent decision-making processes underlying post-error slowing. Specifically, the DDM was applied on

GoPUS and GoPSG trials to estimate condition-specific decision boundary, drift rate, and non-decision time for each subject. Changes in decision boundary, drift rate, and non-decision time

induced by errors were calculated by the differences between GoPUS and GoPSG conditions. Then, between-group differences were tested using two-sample _t_-tests. DDM estimation was conducted

using _fast-dm_ [43]. DRIFT DIFFUSION MODEL: MODEL DIAGNOSIS We carried out model diagnosis analyses to evaluate the goodness-of-fit of the DDM with the behavioral data. The model diagnosis

analyses indicated a good model fit of the DDM in the post-error slowing effect. See Supplementary Method and Supplementary Results for details. DYNAMIC BELIEF MODEL: MODEL AND PARAMETERS We

used a well-validated DBM [12, 27] to estimate trial-wise anticipation of stop signals in the SST for each participant. Here we provide a brief introduction to the DBM. More detailed

information and its validation can be found in previous studies [12, 27]. The DBM estimates the belief about the chance of an inhibitory cue occurring in the coming trial based on trial

history [59]. On an incoming trial _k_, subjects believe that the chance that an inhibitory cue will occur (Stop trial) is _r__k_ and the chance that no inhibitory cue will occur is

1−_r__k_. The model assumes that subjects believe that _r__k_ has a probability _α_ of being the same as _r__k_−1 (the chance that an inhibitory cue occurs in the previous trial) and a

probability 1−_α_ of being re-sampled from the prior distribution _π_(_r__k_): $$p\left( {{{{r}}}_{{{k}}}|{{{s}}}_{{{{k}}} - 1}} \right) = \alpha \ast p\left( {{{{r}}}_{{{{k}}} -

1}|{{{s}}}_{{{{k}}} - 1}} \right) + \left( {1 - \alpha } \right) \ast \pi \left( {{{{r}}}_{{{k}}}} \right)$$ where _s__k_ refers to the true trial type of trial _k_ (_s__k_ = 1 for Stop

trial, _s__k_ = 0 for Go trial); _p_(_r__k_−1|_s__k_−1) refers to the posterior distribution conditional on the last observed trial _k_−1; _π_(_r__k_) is assumed to be a _β_ distribution

with prior mean pm and shape parameter _scale_. The model also assumes that subjects update their prior belief using Bayesian inference, and therefore the posterior distribution is computed

based on Bayes’ rule: $$p\left( {{{{r}}}_{{{k}}}|{{{s}}}_{{{k}}}} \right) \propto p\left( {{{{s}}}_{{{k}}}|{{{r}}}_{{{k}}}} \right) \ast p\left( {{{{r}}}_{{{k}}}|{{{s}}}_{{{{k}}} - 1}}

\right)$$ The probability of trial _k_ being a Stop trial is determined by $$P\left( {{{{s}}}_{{{k}}} = 1|{{{s}}}_{{{{k}}} - 1}} \right) = {\int} {P\left( {{{{s}}}_{{{k}}} =

1|{{{r}}}_{{{k}}}} \right) \ast p\left( {{{{r}}}_{{{k}}}|{{{s}}}_{{{{k}}} - 1}} \right){{{dr}}}_{{{\mathrm{k}}}}} = {\int} {{{{r}}}_{{{k}}} \ast p\left( {{{{r}}}_{{{k}}}|{{{s}}}_{{{{k}}} -

1}} \right){{{dr}}}_{{{k}}} = \left( {{{{r}}}_{{{k}}}|{{{s}}}_{{{{k}}} - 1}} \right)}$$ In sum, the model allows us to estimate trial-by-trial anticipation of inhibitory cues pstop based on

subjects’ trial history (Go or Stop trials). We used the same model parameters {pm and scale}, which define the _β_ distribution, as in the previous study since they have been well validated

in the stop-signal task [27]. We optimized the model parameter _α_, which defines the re-sampling rate from the prior distribution, using an independent dataset (see below). DYNAMIC BELIEF

MODEL: OPTIMIZING MODEL PARAMETERS Because the parameters in the DBM were tuned based on behavioral data from adult participants [12, 27], we optimized the model parameters to better fit

performance in children. Specifically, we used an independent dataset involving 38 children (9–12 years old, 12F/26M, no history of neurological and psychiatric disorders, Supplementary

Methods) [46]. Legal guardians of the young participants provided written consent. Each child completed two runs of the same stop signal task, including 96 trials per run. To find out the

optimal α for the young participants, we gradually changed _α_ from 0.2 to 0.7 with increments of 0.05 and determine the saturation value of _α_ by how well the model fits the data. To test

model fitting, we examined the correlation between go RT and pstop on aggregate trial-wise data across participants. The assumption is that participants will adjust their response strategy

(i.e., be more cautious in making responses or wait for the stop signal) when they have high expectations for the occurrence of a stop signal in the coming trial. Specifically, for each _α_,

we binned the data for each small range of pstop, computed averaged pstop and go RT within each bin, and calculated the correlation between binned pstop and go RT. The optimal α for the

young participant is 0.3. Details of this analysis can be found in the Supplementary Results and Supplementary Figs. S3 and S4. To further examine the robustness of our finding with respect

to the choice of the model parameter, we repeated the same analyses with _α_ varying from 0.2 to 0.7 and replicated all the main findings (see details in Supplementary Results and

Supplementary Table S3). DYNAMIC BELIEF MODEL: MODEL DIAGNOSIS We carried out model diagnosis analyses to evaluate the goodness-of-fit of the DBM with the behavioral data. The model

diagnosis analyses indicated good model fit of the DBM. See Supplementary Method and Supplementary Results for details. DUAL CONTROL MEASURES PREDICT CORE SYMPTOMS OF ADHD To examine whether

behavioral measures of dual control mechanisms (i.e., SSRT, context, performance monitoring, and anticipation-triggered proactive control), can predict core symptoms of ADHD (inattention

and hyperactivity/impulsivity), we conducted multiple linear regression analysis and evaluated the model performance using leave-one-out cross-validation (LOOCV). Each time, one data point

was selected as a test set and the rest of the data were used as a training set. The training set was then used to train a multiple linear regression model, which was then applied to the

test set for classification. This procedure was repeated _N_ times with each data point used exactly once as a test set. _Pearson’s_ correlations were used to evaluate the correspondence

between predicted values and observed values. To further examine whether proactive control components play an important role in predicting core symptoms of ADHD, we trained a multiple linear

regression model based on a reactive control measure alone, i.e., SSRT, and then compared model performance with the model trained on dual control measures. CODE AVAILABILITY Code is

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2007;48:1080–7. Article  PubMed  Google Scholar  Download references ACKNOWLEDGEMENTS This research was supported by National Institutes of Health MH105625 (WC), MH124816 (WC), MH121069

(VM), EB022907(VM) and NS086085 (VM), NARSAD Young Investigator Award (WC), Stanford Maternal and Child Health Research Institute Grant (WC), and Stanford University Department of Psychiatry

Innovator Grant (WC). We thank Rachel Rehert and Ahmad Belai AI-Zughoul for their assistance with data collection and Elizabeth Kammer and Helena Chi Huynh for their assistance with the

data recording. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Psychiatry & Behavioral Sciences, Stanford University School of Medicine, Stanford, CA, USA Weidong Cai, 

Katherine Duberg & Vinod Menon * Wu Tsai Neuroscience Institute, Stanford University, Stanford, CA, USA Weidong Cai & Vinod Menon * Department of Psychology, School of Behavioral and

Brain Sciences, The University of Texas at Dallas, Richardson, TX, USA Stacie L. Warren * Department of Cognitive Science, University of California, San Diego, CA, USA Angela Yu *

Department of Psychology, University of California, Berkeley, CA, USA Stephen P. Hinshaw * Department of Psychiatry and Behavioral Sciences, University of California, San Francisco, USA

Stephen P. Hinshaw * Department of Neurology & Neurological Sciences, Stanford University School of Medicine, Stanford, CA, USA Vinod Menon Authors * Weidong Cai View author publications

You can also search for this author inPubMed Google Scholar * Stacie L. Warren View author publications You can also search for this author inPubMed Google Scholar * Katherine Duberg View

author publications You can also search for this author inPubMed Google Scholar * Angela Yu View author publications You can also search for this author inPubMed Google Scholar * Stephen P.

Hinshaw View author publications You can also search for this author inPubMed Google Scholar * Vinod Menon View author publications You can also search for this author inPubMed Google

Scholar CONTRIBUTIONS Conceptualization: WC, VM; Data acquisition: WC, KD, SLW; Methodology: WC, AY; Data analysis: WC, Writing: WC, SLW, VM; Review & editing: WC, SLW, AY, SPH, VM.

CORRESPONDING AUTHORS Correspondence to Weidong Cai or Vinod Menon. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S

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S.L., Duberg, K. _et al._ Both reactive and proactive control are deficient in children with ADHD and predictive of clinical symptoms. _Transl Psychiatry_ 13, 179 (2023).

https://doi.org/10.1038/s41398-023-02471-w Download citation * Received: 27 December 2022 * Revised: 02 May 2023 * Accepted: 12 May 2023 * Published: 26 May 2023 * DOI:

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