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Objective: Executive functions (EF) are cognitive skills important for regulating behavior and achieving goals. Executive function deficits are common in children who struggle in school and are associated with multiple neurodevelopmental disorders. However, there is also considerable heterogeneity across children, even within diagnostic categories. This study took a data-driven approach to identify distinct clusters of children with common profiles of EF-related difficulties, and then identified patterns of brain organization that distinguish these data-driven groups. Method: The sample consisted of 442 children identified by health and educational professionals as having difficulties in attention, learning and/or memory. We applied community clustering, a data-driven clustering algorithm, to group children by similarities on a commonly used rating scale of EF-associated behavioral difficulties, the Conners-3 questionnaire. Furthermore, we then investigated whether the groups identified by the algorithm could be distinguished on white matter connectivity using a structural connectomics approach combined with partial least squares analysis. Results: The data-driven clustering yielded three distinct groups of children with symptoms of either: (1) elevated inattention and hyperactivity/impulsivity, and poor executive function, (2) learning problems, and (3) aggressive behavior and problems with peer relationships. These groups were associated with significant inter-individual variation in white matter connectivity of the prefrontal and anterior cingulate cortices. Conclusion: In sum, data-driven classification of EF-related behavioral difficulties identified stable groups of children, provided a good account of inter-individual differences, and aligned closely with underlying neurobiological substrates.
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NEW RESEARCH
Data-Driven Subtyping of Executive FunctionRelated
Behavioral Problems in Children
Joe Bathelt, PhD, Joni Holmes, PhD, Duncan E. Astle, PhD, on behalf of the Centre for Attention
Learning and Memory (CALM) Team
Objective: Executive functions (EF) are cognitive skills that are important for regulating behavior and for achieving goals. Executive function decits
are common in children who struggle in school and are associated with multiple neurodevelopmental disorders. However, there is also considerable
heterogeneity across children, even within diagnostic categories. This study took a data-driven approach to identify distinct clusters of children with
common proles of EF-related difculties, and then identied patterns of brain organization that distinguish these data-driven groups.
Method: The sample consisted of 442 children identied by health and educational professionals as having difculties in attention, learning, and/or
memory. We applied community clustering, a data-driven clustering algorithm, to group children by similarities on a commonly used rating scale of EF-
associated behavioral difculties, the Conners 3 questionnaire. We then investigated whether the groups identied by the algorithm could be distin-
guished on white matter connectivity using a structural connectomics approach combined with partial least squares analysis.
Results: The data-driven clustering yielded 3 distinct groups of children with symptoms of one of the following: (1) elevated inattention and
hyperactivity/impulsivity, and poor EF; (2) learning problems; or (3) aggressive behavior and problems with peer relationships. These groups were
associated with signicant interindividual variation in white matter connectivity of the prefrontal and anterior cingulate cortices.
Conclusion: In sum, data-driven classication of EF-related behavioral difculties identied stable groups of children, provided a good account of
interindividual differences, and aligned closely with underlying neurobiological substrates.
Key words: executive function, childhood, nosology, structural imaging
J Am Acad Child Adolesc Psychiatry 2018;57(4):252262.
xecutive functions (EFs) are a collection of cognitive pro-
cesses that help to regulate thoughts and behavior. They
are critically involved when we make plans, solve prob-
lems, and attain goals.
1
Better EF is linked to many positive outcomes
2
such as greater success in school,
3,4
better physical and mental
health,
5,6
and better overall quality of life.
7
In contrast, decits in EF
are associated with slow school progress,
8
difculties in peer relation-
ships,
9
and poor employment prospects.
10
Behaviorally, EF decits
may manifest as distractibility, dgetiness, poor concentration, chaotic
organization of materials, and trouble completing work. EFs comprise
multiple dissociable domains,
11
and children may show different pro-
les of strength and weaknesses across these domains. This is also the
case for diagnostic groups that are dened by behaviors that relate to
EF, for example, attention-decit/hyperactivity disorder (ADHD).
12
In
fact, difculties in EF have been associated with several common
neurodevelopmental disorders, including ADHD,
13
autism spectrum
disorder (ASD),
14
and dyslexia.
15
Despite the strong association be-
tween EF and outcomes highly relevant to childrensdevelopment,the
heterogeneity of EF difculties across children makes it difcult to
devise effective intervention strategies and to investigate etiological
mechanisms. The aim of the current study was to use a data-driven
approach to identify groups of children with similar proles of EF-
associated behavioral problems and to relate these proles to differ-
ences in white matter connectivity.
Data-driven subgrouping can provide the practical advantage of
clearly dened groups of children with highly similar behavioral prob-
lems. In turn, this may help with identifying the pathophysiological
mechanisms associated with those shared difculties. The current study
used a data-driven community clustering approach to group children by
the similarity of their behavioral problems. In contrast to widely used
factor-analytic approaches that aim to reduce measured variables to a
smaller set of latent factors (e.g., grouping questionnaire items that relate
to hyperactivity or inattentiveness), the clustering approach that we used
groups children by similarities in their behavioral ratings. This alternative
approach is made possible by recent advances in network science
methods. Most clustering algorithms necessitate a priori assumptions,
such as the geometrical properties of the cluster shape, the tuning of some
parameters, or setting the number of desired clusters. These assumptions
are difcult to make, but network science provides a possible solution.
Network science is the study of complex networks, which represent
relationships among data as a network of nodes connected by edges. This
methodological approach provides a mathematical tool for quantifying
the organization of networks and the relationships among the nodes
within them.
16
Dening subdivisions of highly connected nodes within a
network, so-called communities, is an area of network science that has
received considerable attention, as it applies to many real-world prob-
lems.
17
In the case of psychometric data, the network can represent the
similarity of scores between participants. Community detection makes it
E
252 www.jaacap.org Journal of the American Academy of Child & Adolescent Psychiatry
Volume 57 / Number 4 / April 2018
possible to dene subgroups of participants that are most similar while
being as distinct as possible from other subgroups. Our aim was to
identify clusters in a large sample of children, according to the similarity
of their EF-related behavioral problems, using a community detection
approach based on the Conners questionnaire. This scale is routinely
administered in health care and educational settings in many clinics in
the United Kingdom.
We applied the data-driven clustering approach in a large sample of
children (N ¼442) identied as having problems in attention, learning,
and/or memory by educational and clinical professionals working in
various specialist childrens services. This sample includes common,
complex, and comorbid cases of behavioral and cognitive difculties.
Many of these children would not be recruited by studies that use strict
exclusory criteria to identify rarer selective cases, but are routinely seen by
specialist clinicians and educators. This large heterogeneous group of
children provides a perfect dataset for testing data-driven grouping
methods. Moreover, understanding the proles of EF-associated behav-
ioral difculties in children currently receiving the attention of these
specialists may provide useful information for practitioners and may shift
research focus toward these relevant behavioral proles.
An additional aim was to relate the proles of EF-associated
behavioral problems to potential biological mechanisms. We explored
differences in white matter connectivity between the groups identied
through the community detection. White matter maturation is a crucial
process of brain development that extends into the third decade of life,
18
and which relates closely to cognitive development.
19-21
It is thought to
support cognitive development through better communication and
integration among brain regions, particularly over longer distances,
22
Accordingly, the brain can be modeled as a network of brain regions
connected by white matter, commonly referred to as a connectome. Brain
regions vary in the number of their connectionstheir node degree
which gives an indication of their importance for the network.
23
To
explore which brain regions were most closely linked to the behavioral
proles identied through community clustering, we used a multivariate
dimension-reduction technique called partial least squares (PLS).
24
In our
analysis, PLS dened brain components that maximally distinguished the
behaviorally dened groups.
METHODS
Participants
The sample consisted of ratings on 442 children (age: mean ¼110.51
months; SE ¼1.24; range ¼62215; 295 male). The proportion of
boys was higher in this referred sample, in line with prevalence estimates
of ADHD in the UK (ADHD: 4:1 male:female).
25
Behavioral difculties
associated with ADHD were assessed using the Conners Parent Rating
Short Form 3rd edition,
26
herein referred to as Conners 3.The ratings
were completed by parents or caregivers as part of a larger ongoing study
at the Centre for Attention, Learning and Memory (CALM) at the MRC
Cognition and Brain Sciences Unit, University of Cambridge. Children
were recruited to the CALM research clinic on the basis of having
problems in attention, learning, and/or memory that had come to the
attention of a professional working in schools (e.g., special needs teacher)
or specialist childrens community services (e.g., clinical or educational
psychologists, speech and language therapists, or pediatricians). During
the clinic visit, children completed a wide range of cognitive assessments,
and their parents/caregivers lled in questionnaires about their childs
behavior. Children were also invited for magnetic resonance imaging
(MRI) (see Figure 1 for attainment). The data reported here include
those from 3 questionnaires and the MRI data. Exclusion criteria for
referrals were signicant or severe known neurological disorders, prob-
lems in vision or hearing that were uncorrected, or a native language
other than English. This study was carried out in accordance with the
Declaration of Helsinki and was approved by the local NHS Ethics
committee (Reference: 13/EE/0157). Parents/caregivers provided written
consent, and children gave verbal assent.
Some children in the broad sample of children referred for problems
relating to attention, learning, and/or memory had received diagnoses
through standard community services (see Table 1 for a breakdown of
diagnoses). Among the children with a diagnosis, ADHD was the most
common. Other diagnostic labels were rare. Therefore, diagnostic labels
were grouped together. Primary diagnoses of dyslexia, dyscalculia, or
dysgraphia were summarized as learning decits.Primary diagnoses of
autism spectrum disorder, autism, or Asperger syndrome were summed as
ASD.Other labels, such as OCD, depression, anxiety, or develop-
mental delay occurred only in a few individuals and were grouped as
other.
Behavioral Analysis
Questionnaire Data. The Conners 3 scale
26
is a parent questionnaire
designed to assess behavioral difculties associated with ADHD and
related disorders. It is well validated, with good psychometric integrity
(internal consistency: Cronbachs
a
¼0.91 [range 0.850.94]; factorial
validity: root mean square error of approximation [RMSEA] ¼0.07
based on conrmatory factor analysis in a replication sample; for details,
see Conners
26
). Questionnaire items are summarized into 6 subscales
(Inattention, Hyperactivity/Inattention, Learning Problems, Executive
Function, Aggression, Peer Problems), and a total ADHD score is also
derived. T scores of 60 and above are indicative of clinical levels of
problems. A high proportion of children in the sample had scored in this
range on each of the subscales (Table 2).
FIGURE 1 Overview of Data Included in Behavioral and
Connectome Analysis
Note: MRI ¼magnetic resonance imaging.
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SUBTYPING EXECUTIVE FUNCTION BEHAVIORS
The Conners 3 also contains 2 validity scales to detect response bias
(that is, the rater tries to convey an overly positive or negative impression
to secure a certain outcome).
26
The validity scales indicated a possibly
overly negative response style for 80 responses. Highly negative scores
may indicate extreme problems in the rating domains or a negative bias of
the rater, which may overestimate the childs difculties. Analyses were
carried out including and excluding ratings with high negative impression
scores.
The Behavioral Rating Inventory of Executive Function (BRIEF) is
a questionnaire about behaviors associated with EF problems for parents
of children and adolescents 5 to 18 years of age.
27
There are 8 subscales
measuring behavior problems related to inhibition, shifting, emotional
control, initiation, working memory, planning/organizing, organization
of materials, and monitoring.
The Strengths and Difculties Questionnaire (SDQ) is a
parent-rated scale for children and adolescents 8 to 16 years of age. It
provides ratings for emotional symptoms and prosocial behavior as
well as scores for problems related to behavioral conduct, hyperactivity/
inattention, and peer relationships.
Community Detection
Community detection is an optimization clustering method. Networks in the
current analysis represented the child-by-child correlations across the 6 scales
of the Conners 3 questionnaire. Questionnaire scales were used because the 4-
point range of individual items was too limited to distinguish individuals. The
community algorithm starts with each network node, namely, child, in a
separate community and then iteratively parcellates the network into com-
munities to increase the quality index (Q), which represents the segregation
between communities with higher values indicating stronger segregation,
until a maximum is reached. The current study used the algorithm described
by Rubinov and Sporns
28
as implemented in the Brain Connectivity Toolbox
(https://sites.google.com/site/bctnet/) version of August 2016, which is an
extension of the method described by Blondel et al.
29
to networks with
positive and negative edges. This algorithm is not deterministic and may yield
different solutions at each run. To reach a stable community assignment, we
applied the consensus clustering method described by Lancichinetti and
Fortunato
30
(see Figure S1, available online, for a comparison with an alter-
native algorithm). In short, an average community assignment over more than
100 iterations was generated. The community assignment was then repeated
further until the community assignment did not change between successive
iterations. The robustness of the community detection was tested with
simulated networks with known community structure varying the probability
of within-module versus between-module connections and adding random
noise. The results indicated that the implementation of the algorithm could
detect the community structure reliably over a range of these parameters (see
Supplement 1 and Figure S2, available online). The analysis was implemented
in Python2.7.11. The code for the entire analysis is available online (https://
github.com/joebathelt/Conners_analysis). A comparison exploratory factor
analysis with principal component analysis is presented in the Supplement
(see Figure S3, available online).
Statistical Analysis
Groups dened by the community detection algorithm were compared
on scales of the Conners 3 questionnaire. ShapiroWilk tests indicated
that scores within groups deviated from normality assumptions.
31
Group
contrasts were therefore based on nonparametric MannWhitney U
tests. The Bonferroni method was used to account for multiple com-
parisons. Statistical tests were carried out using Scientic Python (SciPy)
version 0.17.0 implementation.
32
Structural Connectome. The aim of this analysis was to explore
whether the data-driven grouping was related to differences in brain
structure. To this end, white matter connectivity of brain regions was
estimated from diffusion-weighted images. Next, we used a multivariate,
dimension-reduction technique to relate the white matter connectivity of
brain regions to the group assignment.
Participant Sample for the Connectome Analyses. A subset of
191 families agreed to participate in the neuroimaging part of the study.
A total of 43 scans were excluded for their poor quality, that is,
incomplete scan data, visually identied movement artifact, maximum
displacement in the diffusion sequence of more than 3mm as determined
by FMRIB Software Library (FSL) eddy (see Figure 1 for an overview of
attrition). The nal sample consisted of 148 complete data sets (behavior,
T1, diffusion-weighted images). The MRI sample did not signicantly
differ in age from the behavioral sample (MRI sample [months]: mean ¼
117.05, SD ¼27.436, t(359) ¼1.34, p¼0.181). The ratio of groups
TABLE 1 Breakdown of Children by Pre-existing Diagnoses
and Referral Routes
Diagnosis Total %
None 302 76.7
ADHD 61 15.6
Learning decit 32 8.2
ASD 24 6.2
Other 23 5.9
Referrer Total %
SENCo 262 66.9
Pediatrician 82 21.0
Clinical psychologist 29 7.4
Speech and language Therapist 29 7.4
Specialist teacher 13 3.3
ADHD nurse practitioner 13 3.3
Educational psychologist 6 1.5
Family worker locality team 5 1.3
Child psychiatrist 2 0.5
Private tutor 1 0.3
Note: ADHD ¼attention-decit/hyperactivity disorder; ASD ¼autism spectrum
disorder; SENCo ¼special educational needs coordinator.
TABLE 2 Scores on Each Scale of the Conners 3
Questionnaire (Inattention, Hyperactivity/Impulsivity,
Learning Problems, Executive Function, Aggression, Peer
Relationships) for the Entire Sample
Scale Mean SD Min Max T>60 T>60%
Inattention 79.74 11.955 40 90 398 90.0
Hyperactivity/Impulsivity 72.87 16.338 40 90 315 71.3
Learning Problems 75.95 11.912 42 90 390 88.2
Executive Function 73.81 12.906 40 90 363 82.1
Aggression 62.95 17.268 34 90 205 46.4
Peer Relationships 71.94 17.973 44 90 290 65.6
Note: The last 2 columns indicate the total number and the percentage of children
in the sample with Tscores in the clinical range on each scale. Max ¼maximum;
Min ¼minimum.
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Volume 57 / Number 4 / April 2018
BATHELT et al.
dened in the analysis of the behavioral sample was similar in the MRI
subsample (MRI sample: C1: 0.36; C2: 0.33; C3: 0.30).
MRI Data Acquisition. Magnetic resonance imaging data were
acquired at the MRC Cognition and Brain Sciences Unit, University of
Cambridge. All scans were obtained on the Siemens 3 T Tim Trio system
(Siemens Healthcare, Erlangen, Germany), using a 32-channel quadra-
ture head coil. The imaging protocol relevant here consisted of 2 se-
quences: T1-weighted MRI and a diffusion-weighted sequence.
T1-weighted volume scans were acquired using a whole-brain
coverage 3D Magnetization Prepared Rapid Acquisition Gradient Echo
(MP RAGE) sequence acquired using 1-mm isometric image resolution.
Echo time was 2.98 milliseconds, and repetition time was 2,250
milliseconds.
Diffusion scans were acquired using echo-planar diffusion-weighted
images with an isotropic set of 60 noncollinear directions, using a
weighting factor of b ¼1,000 s 3mm
2
, interleaved with a T2-
weighted (b ¼0) volume. Whole-brain coverage was obtained with 60
contiguous axial slices and isometric image resolution of 2 mm. Echo
time was 90 milliseconds, and repetition time was 8,400 milliseconds.
Structural Connectome Construction. The white matter con-
nectome reconstruction followed the general procedure of estimating the
most probable white matter connections for each individual and then
obtaining measures of fractional anisotropy (FA) between regions
(Figure 2). White matter connectome reconstruction was carried out as
previously described.
33
Figure 2 provides an overview. The methodo-
logical details of the connectome construction are presented in
Supplement 1, available online.
Statistical Analysis of Connectome Data. For the analysis of the
connectome data, the node degree of each node in the network was
calculated for each participant. Partial least squares (PLS) regression was
used to identify the linear combination of brain areas that best explained
group membership for the groups identied through community clus-
tering. The PLS model was evaluated by tting the model to a random
FIGURE 2 Overview of Processing Steps for Structural Connectome Estimation
Note: ANTs ¼Advanced Normalization Tools; DiPy ¼Diffusion Imaging in Python; FSL ¼FMRIB Software Library; WM ¼working memory. Other abbreviations are names
of functions in the software packages mentioned.
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SUBTYPING EXECUTIVE FUNCTION BEHAVIORS
FIGURE 3 Overview of Community Clusters and Their Behavioral Proles
Note: (a) Prole of ratings on the Conners 3 questionnaire in the 3 clusters indicated by the community detection algorithm. The top of the gure shows the mean of scores
in each group with 2 standard errors. The scores represent residuals after regressing the effect of age. The bottom gure shows the results of groupwise contrasts on each
scale. Red indicates a signicant difference between groups after Bonferroni correction. (b) Comparison of the groups on scores standardized with reference to the norma-
tive data of the Conners 3 questionnaire. (c) Child-by-child correlation matrix of Conners 3 scores after ordering the matrix according to the cluster assignment indicated by
community clustering. The order matrix shows a clear separation between the clusters. (d) Correlation matrix in a spring layout color-coded according to the cluster assign-
ment indicated by community clustering. The spring layout representation shows clear spatial separation between the clusters. C1 ¼cluster 1 (inattention, hyperactivity/
impulsivity/executive function); C2 ¼cluster 2 (learning problems); C3 ¼cluster 3 (aggression, peer relations).
256 www.jaacap.org Journal of the American Academy of Child & Adolescent Psychiatry
Volume 57 / Number 4 / April 2018
BATHELT et al.
selection of 60% of the data and evaluating the model t in a test set of
40%. The root mean square error (RMSE) of a model based on the
training data was signicantly lower when assessed with the test data
compared to randomly shufed samples (10-fold cross-validated RMSE:
mean ¼0.35, SE ¼0.025; permuted sample: mean ¼0.81, SE ¼0.018;
permutation test: p¼0.002).
The contribution of brain regions to the PLS latent variables was
evaluated in a bootstrap procedure in which 60% of the sample was
randomly selected and the PLS model was tted (1,000 permutations).
The loading of brain regions onto PLS latent variables was expressed as
the mean loading divided by the standard error across permutations.
24
A
Procrustes rotation was applied to align the factor across iterations of the
permutation procedure. All procedures were implemented using sci-kit-
learn functions v0.18.1 under Python v2.7.12.
34
RESULTS
Community Detection Indicates 3 Subgroups
The current study used graph theory to derive clusters of children with
similar proles across ratings on the Conners 3 questionnaire. The
community detection algorithm in conjunction with consensus clustering
arrived at a stable solution with 3 clusters. The quality index (Q ¼0.55)
indicated a good separation of the clusters (see Blondel et al.
29
for quality
indices of reference networks). A highly similar, 3-cluster structure was
also detected when excluding participants with a high negative impres-
sion rating (Q ¼0.59) and when randomly selecting one-half (Q ¼0.6)
or one-fourth (Q ¼0.61) of the sample.
The cluster assignment resulted in roughly equal splits among the 3
clusters (cluster 1: 150 [33.93%]; cluster 2: 145 [32.80%]; cluster 3: 147
[33.25%]). There were signicant differences on all subscales of the
Conners 3 questionnaire between groups (Figure 3 and Table 3). Chil-
dren in the clusters were characterized either by problems associated with
cognitive control (C1: Inattention, Hyperactivity/Impulsivity/Executive
Function), learning difculties (C2: Learning Problems), or behavioral
conduct problems (C3: Aggression, Peer Relations). There was no dif-
ference in age or gender distribution among the clusters (Table 4).
Standardized scores indicated that the majority of children in the current
sample scored in the elevated to highly elevated range across all Conners 3
subscales relative to age norms. The proles based on scaled raw scores
were also apparent when using the age-standardized scores (Figure 3b).
Next, the prevalence of pre-existing diagnoses in each cluster was
evaluated. Children with a diagnosis of ADHD were overrepresented in
C1: Inattention, Hyperactivity/Impulsivity/Executive Function (see
Table 5 for a breakdown of diagnoses per cluster,
c
2
(3,354) ¼72.87, p
<.001). Other diagnoses were equally distributed between the clusters;
ASD:
c
2
(3,354) ¼0.06, p¼.971, Anxiety/Depression:
c
2
(3,354) ¼
0.54, p¼.764, Learning Decit:
c
2
(3,354) ¼3.88, p¼.144).
Subgroups Show Differences in Other Questionnaire
Measures of Executive Function and Everyday
Difculties
Next, the groups dened through community assignment based on
Conners 3 data were compared on other questionnaire measures of
behavioral problems linked to EF difculties (BRIEF) and everyday
behavioral problems (SDQ). A comparison of these measures indicated
signicant differences between the groups. For the BRIEF, children in
Cluster 1 (Inattention/hyperactivity/Executive Function) had more
problems with working memory. Children in Cluster 2 (Learning
Problems) were rated as having fewer difculties with inhibition and
monitoring. Children in Cluster 3 (Aggression/Peer Problems) were also
rated as having signicantly higher problems in emotional control
compared to the other groups (Figure 4a).
For the SDQ, children in Cluster 1 (Inattention/hyper-
activity/Executive Function) were characterized by high ratings for hy-
peractivity compared to Cluster 2 (Learning Problems), but lower
conduct and peer relationship problem ratings compared to Cluster 3
(Aggression/Peer Problems). Children in Cluster 2 (learning problems)
received signicantly lower ratings for problems related to hyperactivity.
Children in Cluster 3 (Aggression/Peer Problems) received signicantly
higher ratings for conduct and peer relationship problems (Figure 4b).
Data-Driven Grouping Leads to More Homogeneous
Behavioral Proles
The novel recruitment method of our sample, which includes children
with specic, multiple, and no diagnoses, enabled us to explore the
homogeneity of the behavioral proles within established diagnostic
categories by comparison with our data-driven groupings. For the sta-
tistical comparison, a random sample of 15 (65% of the smallest sample
size) was drawn from all participants within a group, and correlations
between their scales were calculated. This procedure was repeated 1,000
times to create a bootstrap sample of correlations. The correlations were
averaged over the 3 data-driven groups and over the 4 diagnostic cate-
gories (ADHD, ASD, Learning Decit, Other). The statistical
TABLE 3 Scales of the Conners 3 Questionnaire: Inattention, Hyperactivity/Impulsivity (HyperactImpuls), Learning Problems
(LearnProb), Executive Function (ExeFunc), Aggression, Peer Relationship Problems (PeerRel)
Scale
Inattention/
Hyperactivity/
Executive
Function (C1)
Learning
Problems (C2)
Aggression/
Peer
Problems (C3) 1 vs. 2 1 vs. 3 2 vs. 3
Median MAD Median MAD Median MAD Up U p U p
Inattention 0.11 0.810 0.71 0.404 0.01 0.959 4867 <.001 6487 <0.001 120.26 1.00
HyperactImpuls e0.76 0.682 0.63 0.636 0.38 0.886 3149 <.001 9294 0.133 7321 <.001
LearnProb 0.90 0.524 e0.15 0.642 e0.58 0.876 3269 <.001 9051 0.052 4137 <.001
ExeFunc e0.10 0.760 0.60 0.599 e0.13 0.953 5427 <.001 7027 <0.001 11782 1.00
Aggression e0.59 0.497 e0.53 0.452 0.26 1.048 7649 .843 6885 <0.001 6871 <.001
PeerRel e0.45 0.665 e0.56 0.571 0.67 0.938 8085 1.00 5.744 <0.001 7099 <.001
Note: All pvalues are Bonferroni corrected. MAD ¼median absolute deviance; U ¼Mann Whitney U statistic.
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SUBTYPING EXECUTIVE FUNCTION BEHAVIORS
comparison indicated that the difference between correlations in the data-
driven groups and the diagnostic groups was signicantly above 0,
indicating higher correlations in the data-driven grouping (n ¼1,000,
mean ¼0.23, SE ¼0.001, p¼0.001). Crucially, the similarity was also
signicantly higher when comparing the data-driven groups to diagnostic
groups on other questionnaires that were not used to inform the clus-
tering algorithm (BRIEF: mean ¼0.15, SE ¼0.001, p¼0.001; SDQ:
mean ¼0.07, SE ¼0.001, p¼0.026). This indicates that the data-
driven grouping identied groups of children with more common pro-
les of behavioral symptomatology than we would expect to nd in
children grouped on the basis of more traditional diagnostic criteria.
Subgroups Show Differences in the Structural
Connectome
Next, we investigated the relationship between white matter connectivity
and the groups dened through community clustering using partial least
squares (PLS) regression. The rst 3 PLS components explained 48% of
variance in group membership (component 1: 21.23% [SD: 4.302];
component 2: 16.28% [SD: 5.944]; component 3: 10.57% [SD: 4.277],
bootstrapped mean and standard deviation [SD] more than 1,000 per-
mutations). Further components explained less than 5% of the variance
and were therefore dropped from the analysis. Comparison of component
loadings per group indicated signicant lower loading of C1 (Inattention/
Hyperactivity/Executive Function) compared to the other groups for PLS
component 1, signicantly higher loading in C1 (Inattention/Hyperac-
tivity/Executive Function) compared to C3 (Aggression/Peer Problems)
for PLS component 2, and signicantly lower loading in C1 (Inattention/
Hyperactivity/Executive Function) compared to C2 (Learning Problems)
for PLS component 3.
There were differences in the brain areas that distinguished the
groups. PLS 1, which distinguished between C1 (Inattention/
Hyperactivity/Executive Function) and the other groups, loaded most
heavily on the rostral middle frontal, superior frontal, lateral orbito-
frontal, anterior cingulate, lateral occipital, and fusiform cortex
(Figure 5). The second PLS component, which distinguished between
C2 (Learning Problems) and C1 (Inattention/Hyperactivity/Executive
Function), loaded the most on the rostral middle frontal, lateral orbito-
frontal, anterior and posterior cingulate, and lateral occipital cortex. The
third PLS component, which distinguished C3 (Aggression/Peer Prob-
lems) from the other groups, loaded on the lateral orbitofrontal, anterior
cingulate, entorhinal and lateral occipital cortex, and also on connections
of the right pallidum and putamen (Table 6).
DISCUSSION
In this study, we used a data-driven clustering algorithm to group chil-
dren according to their similarity on ratings of executive function (EF)
related behavioral problems. Among a large sample of children with
common, complex, and comorbid behavioral problems, there exist
distinct behavioral proles. Three groups were identied: one with
problems related to EF, inattention and hyperactivity; a second group
with severe learning difculties; and a third group with behavioral
conduct problems. These groups were consistent in randomly selected
subsets of the sample, and were reliably reproduced in simulated data
with a known structure, even when adding considerable noise. The 3
behavioral proles identied were evident in 2 additional parent rating
scales that were not used to inform the original algorithm. Furthermore,
comparison of white matter connectivity indicated that the data-driven
groups were distinguished by connectivity of the lateral prefrontal and
cingulate cortex
One of the subgroups was characterized by elevated symptoms of
inattention, hyperactivity/impulsivity, and EF. This group was also rated
as having increased difculties with behaviors relating to working
memory, organization, planning, and hyperactivity on 2 other rating
scales that were not used as part of the clustering algorithm. This
behavioral prole captures core problems associated with the ADHD
diagnostic label, which is also marked by high levels of inattention and
hyperactivity and EF problems.
13,35-37
A disproportionate number of
children with an ADHD diagnosis were assigned to this cluster. How-
ever, this subtype was not synonymous with ADHD, as one-half of the
children with an ADHD diagnosis were split across the other 2 clusters
that were dened by markedly different behavioral proles.
A second subgroup had more severe learning decits relative to the
other 2 groups. On other questionnaires, they were rated as having fewer
problems with inhibition, attention, and other aspects of EF compared to
children in the other clusters. However, their scores on these scales were
in the elevated and clinical range when compared to age norms, indi-
cating that they fall below age expected levels for attention and EF, but
had less pronounced difculties in these areas than children in the other
TABLE 4 Characteristics of Each Cluster
Group N
Sex Age, y
Male/Female
c
2
p
a
Mean (SD) Tp
C1 150 110/40 0.01 .934 9.28 (2.427) 1 vs. 2 e0.02 .981
C2 145 80/65 0.08 .771 9.28 (2.143) 1 vs. 3 1.03 .304
C3 147 115/32 0.04 .842 9.01 (2.023) 2 vs. 3 1.12 .263
Note:
a
c
2
test in each group relative to the sex distribution in the whole sample. C1 ¼cluster 1 (inattention, hyperactivity/impulsivity/executive function); C2 ¼cluster 2
(learning problems); C3 ¼cluster 3 (aggression, peer relations).
a
c
2
test in each group relative to the sex distribution in the whole sample.
TABLE 5 Breakdown of Diagnoses in Each Cluster Identied
Through Data-Driven Clustering
Diagnosis C1 C2 C3 Total
ADHD 33 4 24 61
ASD 13 5 6 24
Learning decit 3 22 7 32
Other 7 8 8 23
None 94 106 102 302
Total 150 145 147 442
Note: ADHD ¼attention-decit/hyperactivity disorder; ASD ¼autism spectrum
disorder; C1 ¼cluster 1 (inattention, hyperactivity/impulsivity/executive function);
C2 ¼cluster 2 (learning problems); C3 ¼cluster 3 (aggression, peer relations).
258 www.jaacap.org Journal of the American Academy of Child & Adolescent Psychiatry
Volume 57 / Number 4 / April 2018
BATHELT et al.
clusters. Overall, this group displayed elevated symptoms of inattention
and EF difculties combined with fewer problems with hyperactivity/
impulsivity. This prole resembles that described for the inattentive
subtype of ADHD,
38
but it should be noted that the most distinguishing
feature of this group was pronounced learning difculties rather than
inattention.
A third subgroup was characterized by difculties with aggression
and peer relationships. Children in this group were also rated as having
increased problems with behaviors related to emotional control and
conduct on the 2 rating scales that were not used as part of the clustering
algorithm. The distinction between groups with problems associated with
either EF or behavioral conduct is reminiscent of the debate surrounding
the overlap between ADHD and oppositional deant disorder (ODD)/
conduct disorder (CD). Some authors have argued for a high degree of
overlap between these diagnostic groups,
14
but evidence from genetic and
imaging studies suggested distinct pathophysiological mechanisms.
39-41
Consistent with these results, the current study shows that behavioral
ratings of inattention/hyperactivity and aggression/peer relationship
problems form distinct clusters.
These results demonstrate that data-driven clustering using a com-
munity detection algorithm can be used to characterize common and
complex behavioral problems in children. The advantage of this approach
is that groups identied through the algorithm display maximally
homogeneous behavioral proles. Greater behavioral homogeneity is
likely to align more closely with potential biological mechanisms. Indeed,
attempts to characterize subgroups based on brain function using similar
community clustering techniques seem to converge on a similar
distinction between children showing decits with either cognitive con-
trol (C1, C2) or behavioral/emotional regulation (C3).
42
In the current
study, the exploratory analysis showed that our data-driven subgrouping
was associated with underlying differences in structural connectivity
between groups. The areas that distinguished the groups have been
suggested to play a role in relevant behaviors, making it possible to
formulate hypotheses about neurobiological mechanisms associated with
the different behavioral proles. For instance, the group characterized by
problems relating to attention and EF showed differences in connectivity
of the prefrontal, anterior cingulate cortex, and lateral occipital cortex.
These differences in white matter connections of circuits related to
inhibitory control,
43
goal-directed behavior,
44
and visual attention
45
may
play a role in the etiology of these behavioral problems. In contrast,
children with a prole of problems relating to emotional regulation and
peer relationships were distinguished from the other groups by differences
in white matter connectivity of the rostrolateral prefrontal cortex, anterior
cingulate cortex, pallidum, and putamen. These ndings may imply a
difference in integration between the prefrontal cortex and the basal
ganglia system.
46,47
Brain differences associated with learning problems
are more difcult to interpret because the majority of published studies
focuses on much rarer specic learning problems, for example, dyslexia,
dyscalculia, rather than general mechanisms of poor learning. Prefrontal
and cingulate areas implicated in the current analysis may suggest the
involvement of circuits involved in switching attention.
48
Furthermore,
ventral temporal areas have been implicated in both reading
49
and
mathematics,
50
and may be related to mental imagery.
51
It is important to be mindful of some caveats to our approach, and
to the utility of data-driven grouping more generally. First, the grouping
was based on parent-ratings, which have known limitations.
52
Second,
the grouping was based on just one behavioral checklist. We believe that
it is important that these machine-learning approaches produce gener-
alizable groups: that is, the groups must differ on other data not intro-
duced to the algorithm. If groups can only be distinguished on the
FIGURE 4 Prole of Ratings for Children in the Clusters
Dened by Community Module Assignment on (a) a
Questionnaire on Executive Function Difculties (BRIEF) and
(b) a Questionnaire on Strengths and Difculties (SDQ)
Note: The lines indicate the mean of each group across the questionnaire scales,
with error bars showing 2 standard errors around the mean. The bottom of each
gure shows the binary outcome of t tests comparing the groups. Red indicates
a signicant result (p
corrected
<.05). after Bonferroni correction. Note that higher
scores indicate a higher level of difculties on each scale, apart from the Prosocial
Behavior (Prosoc) scale, where high scores indicate more prosocial behavior. C1 ¼
cluster 1 (inattention, hyperactivity/impulsivity/executive function); C2 ¼cluster 2
(learning problems); C3 ¼cluster 3 (aggression, peer relations); Cond ¼Conduct
Problems; Emo ¼Emotional Problems; EmotCont ¼Emotional Control; Hyper ¼
Hyperactivity; Inh ¼Inhibition; Init ¼Initiate; Monit ¼Monitoring; Org ¼Organi-
zation of Materials; Peer ¼Peer Problems; Prosoc ¼Prosocial Behavior WM ¼
Working Memory.
Journal of the American Academy of Child & Adolescent Psychiatry www.jaacap.org 259
Volume 57 / Number 4 / April 2018
SUBTYPING EXECUTIVE FUNCTION BEHAVIORS
FIGURE 5 Relationship Between the Node Degree of Brain Regions in the Structural Connectome and Clusters Based on
Conners 3 Responses
Note: The brain maps show the score of partial least squares (PLS) components for brain regions that most strongly distinguished the group (top 25%). PLS scores above 2
are considered to be signicantly predictive. The graphs show the statistical comparison of groups on loadings for each component. *p<0.05; **p<0.01; ***p<0.001.
C1 ¼cluster 1 (inattention, hyperactivity/impulsivity/executive function); C2 ¼cluster 2 (learning problems); C3 ¼cluster 3 (aggression, peer relations).
260 www.jaacap.org Journal of the American Academy of Child & Adolescent Psychiatry
Volume 57 / Number 4 / April 2018
BATHELT et al.
measures introduced to the machine learning, this suggests that there is
not a genuine distinction between the groups, and instead the algorithm
is overtting. Our groupings differ on other questionnaires that were held
out of the clustering process, but that are designed to tap similar con-
structs. Third, the diagnostic information was based on community
practitioner assessments rather than diagnosis by a single evaluator within
the research team. This approach is common with cohort studies that
make use of community-reported diagnoses (e.g., Russell et al.
25
).
Consequently, the diagnoses are reective of children that typically
present at secondary and tertiary services, and may be more informative
about the children that these professionals routinely see. However, it is
important to note that we cannot guarantee that these diagnoses reect a
diagnostic gold standard, which is sometimes sought for research pur-
poses but which may not be reected in community clinical diagnoses.
Fourth, there were only a few cases with some diagnoses, for example,
anxiety or ASD. Therefore, the study was not adequately powered to
investigate homogeneity within these diagnostic groups.
In summary, clustering of similarities across behavioral problem
identied 3 groups with distinct proles of difculties that related to
inattention, learning, and peer relationships, respectively. These groups
were also distinguished by the connectivity of circuits previously impli-
cated in executive function and behavioral regulation, including the
prefrontal cortex, cingulate cortex, and their subcortical connections.
These ndings act as an important proof of principle: data-driven
proling provides a means of distinguishing common and complex
behavioral problems in children that relate closely to neurobiological
mechanisms.
Accepted January 31, 2018.
Drs. Bathelt, Holmes, and Astle are with the MRC Cognition and Brain Sciences
Unit, University of Cambridge, UK.
This work has been supported by Medical Research Council intramural
programs (MC-A0606-5PQ40 for J.H.; MC-A0606-5PQ41 to J.B. and D.A.).
The Centre for Attention Learning and Memory (CALM) research clinic is based
at and supported by funding from the MRC Cognition and Brain Sciences Unit,
University of Cambridge. Members of the CALM team have been involved in
the conceptualization of the study and have contributed important feedback
that informed the analysis. However, this was a collaborative contribution and
only the named authors meet all criteria for full authorship. The Principal
Investigators are Joni Holmes, PhD (Head of CALM), Susan Gathercole, PhD
(Chair of CALM Management Committee), Duncan Astle, PhD, Tom Manly,
PhD, and Rogier Kievit, PhD. Data collection is assisted by a team of
researchers and PhD students at the CBSU that includes Sarah Bishop, BSc,
Annie Bryant, BSc, Sally Buttereld, MPhil, MA, Erica Bottacin, MSc, Lara
Bridges, BSc, Gemma Crickmore, BSc, Fanchea Daly, MSc, Laura Forde, MSc,
Andrew Gadie, BSc, Sara Gharooni, MSc, Erin Hawkins, PhD, Agniezska Jar-
oslawska, PhD, Amy Johnson, PhD, Silvana Mareva, MA, Sinead OBrien, MSc,
Cliodhna OLeary, MSc, Joseph Rennie, BSc, Ivan Simpson-Kent, BSc, Fran-
cesca Woolgar, BSc, and Mengya Zhang, MSc.
The authors thank the many professionals working in childrens services in the
South-East and East of England for their support, and to the children and their
families for giving up their time to visit the clinic.
Disclosure: Drs. Bathelt, Holmes, and Astle report no biomedical nancial
interests or potential conicts of interest.
Correspondence to Joe Bathelt, PhD, MRC Cognition and Brain Sciences Unit,
University of Cambridge, 15 Chaucer Road, Cambridge CB2 7EF, UK; e-mail:
joe.bathelt@mrc-cbu.cam.ac.uk
0890-8567/$36.00/ª2018 American Academy of Child and Adolescent
Psychiatry. Published by Elsevier Inc. This is an open access article under the
CC BY license (http://creativecommons.org/licenses/by/4.0/).
https://doi.org/10.1016/j.jaac.2018.01.014
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TABLE 6 Loading of Partial Least Squares (PLS) Components
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Hemisphere Structure PLS 1 PLS 2 PLS 3
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Amygdala 0 0 0
Caudate 0 0 75
Hippocampus 0 0 92
Pallidum 0 0 0
Putamen 0 0 80
Thalamus 0 0 0
Right Accumbens 0 0 0
Amygdala 0 0 0
Caudate 0 0 0
Hippocampus 0 0 0
Pallidum 0 0 0
Putamen 0 0 0
Thalamus 0 0 0
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BATHELT et al.
SUPPLEMENT 1
METHOD
Formal Denition of the Quality Index Metric
We used a quality index that aims to maximise connections strength within
modules while minimizing connection strength between modules. The
metric described by Rubinov and Sporns
1
as implemented in the Brain
Connectivity Toolbox (https://sites.google.com/site/bctnet/) was used
that incorporates positive and negative weights. The formal denition of
the quality index from the original paper is as follows:
The connection between nodes iand jwith positive weight is
wþ
ij ˛ð0;1and with negative weight is w
ij ˛½ 1;0Þ. The total sum of
all positive connections is vþ¼P
ij
wþ
ij and all negative connections is
v¼P
ij
w
ij . The strength of the node iis s
i¼P
j
w
ij . The chance-
expected within-module connection weight is eþ
ij ¼sþ
isþ
j
vþfor positive
connections and e
ij ¼s
is
j
vfor negative connections.
d
MiMjis 1 when
iand jare in the same module and 0 otherwise. The quality index is
dened as Q¼1
vþP
ij
ðwþ
ij eþ
ij Þ
d
MiMj1
vþþvP
ij
ðw
ij e
ij Þ
d
MiMj
Comparison Analysis Using Principal Components
Typically, factor analysis is based on the correlation or covariance between
measures, for example, scales of the questionnaire. The correlation or
covariance matrix is then decomposed into matrices that explain the
maximum amount of variance (principal component analysis) or that are
statistically independent (independent component analysis) using singular
value decomposition. These methods provide insight into the relationship
between the measures, for example, scales loading onto a common factor
that is aligned with a theoretical construct. In contrast, the network science
approach used in the current study investigates correlations across scales
between individuals. It is concerned with the similarity between individuals
rather than questionnaire scales. One of the advantages of using the
community clustering approach is that individuals get assigned to groups.
In contrast, applying a factor analysis would distribute loading on the same
individual, which is difcult to interpret.
For comparison with the community clustering results, an exploratory
factor analysis using principal component analysis was carried out on the
scales of the Conners 3 questionnaire. This analysis was carried out using
the psych package v1.7.8 (http://www2.uaem.mx/r-mirror/web/packages/
psych/) under R v3.4.1. Varimax rotation was used to obtain orthogonal
factors. Inspection of the eigenvalues indicated that a 2-factor solution is
sufcient to explain a maximum amount of variance (see scree plot in
Figure S3, available online). Using 2 factors, the factor with high loading on
Hyperactivity/Impulsivity, Aggression, and Peer Relationships, and a fac-
tor with high loading on Inattention, Learning Problems, and Executive
Function was found. Using a 3-factor solution, the PCA solution was
similar to the dimensions identied using community clustering
(Figure S3). The 3-factor PCA showed a factor with high loading on
Inattention, Hyperactivity/Impulsivity, and Executive Function, a second
factor with high loading on Aggression and Peer Relationships, and a third
factor with high loading on Learning Problems. Although this approach is
helpful to understand how scales relate to each other and may be related to
theoretical constructs, it is difcult to group children based on these results.
Structural Connectome Construction
The white matter connectome reconstruction followed the general pro-
cedure of estimating the most probably white matter connections for each
individual, and then obtaining measures of fractional anisotropy (FA)
between regions (Figure 2). The details of the procedure are described in
the next paragraphs, and followed the same procedure as previously
used.
2
In the current study, MRI scans were converted from the native
DICOM to compressed NIfTI-1 format (dcm2nii). Subsequently, a
brain mask was derived from the b0-weighted volume of the diffusion-
weighted sequence, and the entire sequence was submitted for
correction for participant movement and eddy current distortions
through the FMRIB Software Library (FSL) eddy tool. Next, nonlocal
means that de-noising
3
was applied using the Diffusion Imaging in
Python (DiPy) v0.11 package
4
to boost signal-to-noise ratio. The
diffusion tensor model was tted to the pre-processed images to derive
maps of fractional anisotropy (FA) using dtitin FSL v.5.0.6.
5
A
constant solid angle (CSA) model was tted to the 60-gradient-
direction diffusion-weighted images using a maximum harmonic order
of 8 with DiPy. Next, probabilistic whole-brain tractography was
performed based on the CSA model with 8 seeds in any voxel with a
General FA value higher than 0.1. The step size was set to 0.5, and
the maximum number of crossing bers per voxel was set to 2.
For the region of interest (ROI) denition, T1-weighted images
were preprocessed by adjusting the eld of view using FSL robustfov;
nonlocal means denoising in DiPy, deriving a robust brain mask using
the brain extraction algorithm of the Advanced Normalization Tools
(ANTs) v1.9 (see Avants et al.),
6
and submitting the images to recon-
all pipeline in FreeSurfer v5.3 (http://surfer.nmr.mgh.harvard.edu).
Regions of interests (ROIs) were based on the Desikan-Killiany par-
cellation of the MNI template
7
with 34 cortical ROIs per hemisphere
and 17 subcortical ROIs (brainstem, and bilateral cerebellum, thal-
amus, caudate, putamen, pallidum, hippocampus, amygdala, and nu-
cleus accumbens). The surface parcellation of the cortex was
transformed to a volume using the aparc2aseg tool in FreeSurfer.
Furthermore, the cortical parcellation was expanded by 2 mm into the
subcortical white matter using in-house software. To move the par-
cellation into diffusion space, a transformation based on the T1-
weighted volume and the b0-weighted image of the diffusion
sequence was calculated using FreeSurfer bbregister and applied to the
volume parcellation. For each pairwise combination of ROIs, the
number of streamlines intersecting both ROIs was estimated and
transformed to a density map. A symmetric intersection was used; that
is, streamlines starting and ending in each ROI were averaged. The
weight of the connection matrices was based on fractional anisotropy
(FA). To obtain FA-weighted matrices, the streamline density maps
were binarized after thresholding, multiplied with the FA map, and
averaged over voxels to obtain the FA value corresponding to the
connection between the ROIs. This procedure was implemented in-
house based on DiPy v0.11 functions.
4
SUPPLEMENTARY ANALYSES
Comparison Analysis With an Alternative Community
Detection Algorithm
The results of the clustering using an alternative community detection
algorithm were tested. The KerighanLin algorithm was used for the
comparison,
8
which can incorporate signed edges like the algorithm used
in the main analysis. The results indicated that community clustering
used in the main analysis and the KernighanLin algorithm produced
identical results (Figure S1). This was reected in the partition distance
metrics for the community afliations produced by the algorithms
(normalized variance: 0; normalized mutual information: 1; calculated
using Brain Connectivity Toolbox functions).
Journal of the American Academy of Child & Adolescent Psychiatry www.jaacap.org 262.e1
Volume 57 / Number 4 / April 2018
SUBTYPING EXECUTIVE FUNCTION BEHAVIORS
Robustness of the Consensus Clustering Algorithm
To test the reliability of the community detection algorithm under
varying conditions, random networks with known community structure
were created. The networks consisted of 100 nodes with 4 modules. The
connection likelihood within and between clusters was systematically
varied between 0.1 and 0.9. The quality index of the community
structure was calculated at each combination of between- and within-
cluster connection likelihood. The results indicated a high-quality
index for network with higher within-cluster than outside-cluster
connection likelihood (Figure S2a). High connection density outside of
clusters had a large inuence, even when the connection likelihood
within modules was very high.
For comparison with the empirical network of Conners 3 score
correlations, the connection density within and between networks was
calculated. To this end, all connections were binarized so that any
connection with a Pearson correlation coefcient above 0 was set to 1.
The connection density was estimated as the ratio between existing
connections in the binarized empirical network and a fully connected
network of the same size. Connection density within modules based on
consensus clustering was 0.79 and connection density between modules
was 0.05. Together with the results of the simulated networks, these
connection densities indicate very high separation of the network
clusters.
We further tested the robustness of the community assignment by
adding increasing percentages of random Gaussian noise (
m
¼0,
s
¼1)
to the network matrix and repeated the consensus clustering procedure
(Figure S2a). The quality index indicated good separation of the clusters
between 5% and 30% noise (Q between 0.62 and 0.65). No stable
assignment could be reached at 35% of noise and above. These results
indicate that the community assignment is robust to a considerable
amount of noise.
Inuence of Connection Weight and Thresholding on
Structural Connectome Results
Different methods exist for the construction of structural networks from
diffusion-weighted data, and there is currently no scientic consensus on
the best approach.
9
Networks in the current analysis were weighted by
fractional anisotropy (FA), a commonly used measure of white matter
organization based on the diffusion tensor model. FA characterizes the
directedness of diffusion within a voxel, but may lead to misinterpreta-
tion in regions of crossing bers.
10
Therefore, the main analysis was
repeated with networks weighted by Generalized FA (GFA) based on a
constant solid angle (CSA) model, which is better able to take crossing
bers into account.
11
The node degree for each brain region was identical
for the GFA and FA model for density thresholds between 5% and 15%
(KolmogorovSmirnov test for 2 samples: p¼1.0 uncorrected for all
regions). It follows that the PLS analysis provides the same results for
networks weighted by FA and GFA, as this analysis was based on node
degrees, and the node degrees were identical for both models within the
relevant density range.
Another potential source of variation in the analysis is the density
threshold. Network analyses are sensitive to the number of connections.
Therefore, density thresholding is often applied, but the chosen threshold
may inuence the results of the analysis. For the current investigation,
the inuence of different density thresholds was systematically investi-
gated by repeating the analysis over a range of densities and comparing
the factor scores in a repeated-measures analysis of variance model with
factors for density and the interaction between density and component
(components loading density þcomponent þdensity component).
The results indicated no signicant effect of density or the interaction
between density and any component (model t: F(9, 14790) <0.001,
p¼1, adjusted R
2
¼0.001; density: t<0.001, p¼1, interactions:
t<0.001, p¼1).
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262.e2 www.jaacap.org Journal of the American Academy of Child & Adolescent Psychiatry
Volume 57 / Number 4 / April 2018
BATHELT et al.
FIGURE S2 Results of Robustness Testing
Note: (a) Quality indices of consensus clustering using simulated networks with varying levels of within (pin) and between (pout ) connections probabilities. High within-
cluster and low between-cluster connectivity led to high separation of clusters with consensus clustering, that is, high quality indices. (b) Consensus clustering using
the empirical child-by-child network of Conners 3 correlations with varying levels of added noise. The 3-cluster solution could be reconstructed up to 30% of added
Gaussian noise. At a higher level of noise, no clustering solution could be obtained.
FIGURE S1 (A) Community-Grouped Adjacency Matrix Based on the Community Clustering Algorithm Used in the Main
Analysis. (B) Community-Grouped Adjacency Matrix Based on the KernighanLin Algorithm
Journal of the American Academy of Child & Adolescent Psychiatry www.jaacap.org 262.e3
Volume 57 / Number 4 / April 2018
SUBTYPING EXECUTIVE FUNCTION BEHAVIORS
FIGURE S3 Principal Component Analysis (PCA) of the Conners 3 Scales
Note: The left panel shows the correlation matrix. The tables show the factor loadings and explained variance (prop. ¼proportional; cumul. ¼cumulative). The right gure
shows the eigenvalues of each component (scree plot).
262.e4 www.jaacap.org Journal of the American Academy of Child & Adolescent Psychiatry
Volume 57 / Number 4 / April 2018
BATHELT et al.
... Ongoing discussion centres on whether four [4][5][6] or five [7] groups exist, and what characterises each cluster. Other examples include the identification of protein communities involved in cancer metastasis [8], responder types to cancer treatment [9], Parkinson's disease subtypes [10], brain types [11], and behavioural phenotypes [12][13][14][15][16]. ...
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