Introduction

Autism spectrum disorder (ASD) is characterized by impairments in social communication and interactions, as well as restricted and repetitive behaviours and interests [1]. Studies have shown that up to 70% of children and adolescents with ASD have one comorbid psychopathology, while 40% have at least two [2]. Anxiety is the most prevalent comorbidity in children and adolescents with ASD, with 30 to 80% meeting the threshold for a clinical diagnosis [3, 4]. Clinically severe anxiety may include uncontrollable panic, an inability or limited capacity to engage in social activities, disrupted sleep, difficulty concentrating, somatic symptoms (e.g., chest pain, nausea, trouble breathing), and avoiding triggering places and people [5]. The likelihood of being diagnosed with anxiety while under the age of 18 is more than two-times higher in those with ASD, compared to typically developing (TD) children and adolescents [6]. ASD-specific anxiety refers to individuals diagnosed with ASD who also display atypical characteristics of anxiety, such as atypical phobias, extreme rigidity, sensory overload or anxiety in relation to changes in routines [3, 7, 8]. Among individuals with ASD, anxiety is associated with sleep problems, self-injurious behaviours, and parental stress, thereby highlighting the need to identify environmental factors that may contribute to its occurrence [9, 10]. Although academic interest in the biological mechanisms and symptoms that underly anxiety in ASD has peaked in recent years [3, 7, 11,12,13,14], the extent to which anxiety influences overt behaviours remains largely unknown.

Anxiety in children with ASD is also associated with family stress, mood disorders, and depression [15]. In the general population, up to 88% of individuals diagnosed with an anxiety disorder have also met the criteria for a depressive disorder [16]. Those diagnosed with co-occurring anxiety and depression report severe and chronic symptoms that significantly impair daily living when compared to those without comorbid diagnoses. The bidirectional relationship between anxiety and depression is, in part, accounted for by the neurophysiological response to stress [16, 17]. The fight or flight response is activated by an anxiety-inducing event notifying the amygdala, dorsal anterior cingulate cortex, hippocampus, hypothalamus, basal ganglia, and brainstem to release a surge of cortisol into the bloodstream [17]. As the body begins to settle and cortisol release diminishes, the drastic change from high to low stress can result in depression. The neurophysiological cycle of anxiety followed by depression is common among those diagnosed with anxiety, and makes it largely ineffective to treat anxiety without also treating depressive symptoms. Clearly, anxiety in children with ASD presents a serious safety risk, and improved understanding of factors that influence anxiety is needed [18].

The high prevalence of anxiety in children with ASD has encouraged the exploration into etiological and behavioural mechanisms [3, 12, 13, 19, 20]. Children and adolescents with ASD and anxiety report worse emotional functioning, mood regulation, and ability to form meaningful social relationships than TD children both with and without anxiety [6]. One study identified a distinction between common anxiety characteristics in the general population and “autism-related” anxiety symptoms [3]. For example, children and adolescents with ASD reported heightened auditory sensitivities, increased difficulty with change and specific phobias, such as changes in food or the sound of a hairdryer. A more recent imaging study examined children with ASD and no anxiety, ASD and typical anxiety, ASD-specific anxiety, and TD youth with and without anxiety [7]. Left and right amygdala volumes were compared at four time points between the ages of three and 13. Children with ASD and typical anxiety showed significantly larger right amygdala volumes than TD children. In contrast, children with ASD-specific anxiety demonstrated significantly slower right amygdala growth and reduced volume than all other groups. These behavioural and biological differences highlight the unique developmental trajectory of ASD-specific anxieties. In turn, further examination of the behavioural implications of these biological differences is needed to better characterize at-risk children.

It is challenging to tease apart symptoms of anxiety from ASD symptomatology, particularly among those children who display low cognitive functioning [21,22,23]. Children and adolescents with anxiety disorders often present with symptoms from different diagnostic categories. For example, a child may insist on sameness, but also struggle to connect socially with peers. In turn whether these behavioural characteristics are reflective of ASD, generalized anxiety, or social anxiety disorder is challenging to assess. Finally, nearly 40 different measures have been used to assess anxiety in children and adolescents with ASD. However, the majority of instruments have yet to be validated for use within the ASD population and may overlook a range of anxiety symptoms exclusive to or heightened within the ASD community [8].

A comprehensive understanding of the risk factors associated with anxiety in children and adolescents with ASD is needed [1, 3, 6, 8]. In order to investigate the presentation of anxiety in children and adolescents who have ASD compared to peers who do not have ASD, we applied an artificial neural network analysis to standardized assessments of anxiety, internalizing and externalizing behaviours, and emotional symptoms. An artificial neural network, in the form of a self-organizing map (SOM), was created to reflect unique anxiety profiles in children with and without ASD. We further extracted the unique features associated with each anxiety profile to identify characteristics that are unique to individuals with ASD who experience anxiety. It was hypothesized that children and adolescents with ASD that high levels of anxiety would be associated with features of ASD symptomatology, such as social communication deficits and peer problems, which will be identified using a recursive feature elimination (RFE) analysis.

Methods

Participants

Neurotypical (N = 151) and neurodiverse (N = 111) children and adolescents were recruited by the Healthy Brain Network (HBN), an initiative to create an inventory of biological markers of mental health disorders in the developing brain [24]. In order to meet inclusion criteria, one must identify as a male or female person between the ages of five and 21, with parents (or a caregiver) who are capable of providing verbal and written consent. Youth between five and 18 years of age must provide verbal assent, which is the clear expression of agreement to participate. Children with ASD were diagnosed by a clinician using the Autism Diagnostic Observation Schedule (ADOS-2) and the Kiddie Schedule for Affective Disorders and Schizophrenia-Children’s Version (K-SADS). Youth with no diagnosis resulting from the K-SADS were classified as TD. Exclusion parameters included acute safety concerns, cognitive or behavioural impairments that may interfere with the child’s participation (e.g., inability to fully understand or communicate responses to questionnaire items, as discerned by the examiner and informed by clinical expertise), or medical issues that may confound brain scan results. Additionally, all individuals taking stimulants were required to document the medication taken on the day of their participation given that stimulant use may influence one’s performance on cognitive and behavioural measures.

Both TD and children and adolescents with ASD completed testing over the course of two years. Measures of behaviour, family structure, stress and trauma, substance use, and language were collected, as well as physiological and diagnostic assessments. The data used in the present study were obtained from the Child and Mind Institute, Healthy Brain Network (https://data.healthybrainnetwork.org/main.php). The current work utilized 262 observations comprised of data from TD children and adolescents as well as those with a primary clinical diagnosis of ASD. Ethical approval was obtained by the Chesapeake Institutional Review Board (IRB). Written and verbal informed consent was collected from adults prior to data collection, as well as verbal assent in participants 17 and under. The research was conducted in accordance with the Declaration of Helsinki.

Materials and measures

Demographics

Through self and parent-report questionnaires, demographic information was collected including biological sex, age, and parental relationship status [24].

Socioeconomic status

The Barratt Simplified Measure of Social Status (BSMSS) was administered to measure socioeconomic status (SES) [25]. Marital and employment status, educational accomplishments, and occupational prestige are used to orient one’s SES. The BSMSS is strictly ordinal for the purpose of clustering participants into like-groups. It is important to note that the BSMSS does not indicate one’s social class (e.g., middle-class), and reliability statistics cannot be applied. For example, level of education choices are less than grade seven (score = 3), less than ninth grade (score = 6), less than 11th grade (score = 9), high school graduate (score = 12), at least one year of college (score = 15), college education (score = 18), and graduate degree (score = 21). Depending on the sample scores obtained, a mean value will be determined within the sample. This mean value will be used to group participants into similar educational attainment categories.

Diagnostic assessments

The K-SADS is a semi-structured interview used to measure current and past symptoms of anxiety, mood, psychotic, and disruptive behavioural disorders in children and adolescents ages six to 18 [26]. Questions such as “Have you been having any worries lately?” and “Did you look forward to doing the things you used to enjoy?” are asked by the examiner. Questions are designed to elicit responses that indicate the presence of depressive disorders, anxiety disorders, eating disorders, conduct disorders, substance use disorders, and other mental health concerns. Items are scored from zero (no information) to three (feels the queried symptom most of the day more days than not). Interviews were conducted with both participants and parents in order to determine or rule out a clinical diagnosis. Children and adolescents suspected of having ASD symptoms were referred for further diagnostic assessment using the Autism Spectrum Screening Questionnaire (ASSQ) and the ADOS-2.

The ASSQ is among the most widely used tools to identify children and adolescents ages six to 17 who may have an ASD [27]. In this instrument, 27 items are completed by parents and/or teachers of youth displaying symptoms that are characteristic of ASD [26]. Participants are asked to state no (0), somewhat (1), or yes (2) to each question with regard to their child or student. The ASSQ contains questions such as “this child has markedly unusual posture” and “this child accumulates facts on certain subjects but does not really understand the meaning” [27]. Parents and/or teachers are asked to report based on how this child differs from other children or adolescents of the same age [27]. Total scale scores range from zero to 54, with higher scores indicating the presence of more severe ASD symptoms. Research has demonstrated that there is a 90% positivity rate of an ASD diagnosis among those who score 13 or above [27, 28]. The ASSQ demonstrates excellent test–retest reliability (r = 0.90, p < 0.001) and good inter-rater reliability (r = 0.79, p < 0.001) between parents and teachers. Additionally, this assessment has been found to have 91% sensitivity, and 86% specificity, indicating that the ASSQ produces few false negatives (sensitivity) and few false positives (specificity).

Children and adolescents suspected of having an ASD were evaluated using the ADOS-2. The ADOS-2 is a play and activity-based assessment that allows for the real-time observation of ASD symptoms and behaviours [29]. The test is designed for youth ages 12 months into adulthood who do not have significant sensory or motor impairments. An appropriate module is selected based upon the participant’s age, language, and level of development. The ADOS-2 is comprised of various activities, including a construction task, make-believe play, joint interactive play, a demonstration task, a description of a picture, and understanding of friends, relationships, and marriage. Activities are completed and scored using a coding system that examines the presence or absence of abnormality on a given task. The ADOS-2 is considered the “gold standard” in the diagnosis of ASD.

Autism symptom severity

The Social Communication Questionnaire (SCQ) developed by Rutter and colleagues (2003) is used to assess communication skills among youth with and without ASD [30]. Forty items are completed by the primary caregiver of the child or adolescent aged four or older. Caregivers are asked questions such as “does she/he ever have any interests that preoccupy her/him and might seem off to other people (e.g., traffic lights, drainpipes, etc.)?” or “does she/he nod her/his head to indicate yes?”. Items are answered using a yes or no response system, whereby no = zero and yes = one. The first instrument item regarding the use of language is not scored, and is used to determine whether the abnormal language section is applicable to the specific child. As such, total scale scores range from zero to 39 (if the abnormal language section is completed) or zero to 32 (if not). A total score is obtained based upon the sum of all items, and a cut-off score of 15 is suggested to indicate those with more severe ASD symptoms who may need further clinical evaluation. Research has found the SCQ to have strong internal consistency (α = 0.80), and test–retest reliability ranging from r = 0.87 to 0.96 (p < 0.0001) [31].

The Social Responsiveness Scale (SRS-2)-School Age is comprised of 65 items to identify the presence and severity of social impairment related to ASD [32, 33]. The SRS-2 is completed by parents or teachers of youth ages four to 18, and asks responders to consider statements concerning social awareness, social cognition, social communication, restricted interests and repetitive behaviour, social motivation, and social interaction. The SRS-2 includes statements such as “expressions on his or her face don’t match what he or she is saying” and “my child knows when he or she is talking too loud or making too much noise”. Each item is scored on a Likert scale ranging from not true (0) to almost always true (3) and scores are summed for each subscale as well as a total scale score. Higher scores indicate greater severity of social skill deficits, with T scores of 76 or higher representing severe deficits and those under 60 falling within the typical range. The SRS-2 demonstrates strong rest-retest reliability (r = 0.80 to 0.95, p < 0.001) and interrater reliability (r = 0.75 to 0.77, p < 0.001). Total internal consistency is excellent, at α = 0.95.

The Repetitive Behaviors Scale-Revised (RBS-R) provides a quantitative, continuous measure of repetitive behaviours that are often attributed to ASD [34, 35]. Stereotypic behaviour, self-injurious behaviour, compulsive behaviour, ritualistic/sameness behaviour, and restricted interests are measured using 43 items. There is also an additional item that asks respondents to rate the overall severity of behaviours on a range of zero to 100. The RBS-R is completed by parents of participants ages six to 17, and includes items such as “my child flaps hands, wiggles or flicks fingers, claps hands, waves or shakes hands or arms” and “my child hits or bangs head or other body part on the table, floor or other surface”. Items are rated on a 4-point Likert scale (0 = behaviour does not occur, 1 = behaviour occurs and is a mild problem, 2 = behaviour occurs and is a moderate problem, and 3 = behaviour occurs and is a severe problem) and responses should be based upon behaviour within the past month [36]. Scores for each subscale are totaled to determine the area of greatest concern. Subscale internal consistency is good, ranging from r = 0.73 to 0.95 (P < 0.001) [36, 37]. Both participants with and without ASD completed ASD diagnostic assessments.

Anxiety symptoms

The Screen for Child Anxiety Related Disorders-Parent Report (SCARED-P) contains 41 items assessing a child’s (aged eight to 18) anxiety symptoms within the last three months [38] The SCARED-P uses a 3-point Likert scale (0 = not true, 1 = somewhat true, and 2 = very true) to examine five subcategories of anxiety including generalized, separation, social, panic/somatic, and school avoidance. A sample-item from the separation anxiety subscale is My child worries about sleeping alone. Possible scores range from zero to 82, with a total score of 25 or more indicating the likely presence of an anxiety disorder. The SCARED-P demonstrates high reliability across the literature (average α = .95), even among ASD populations [38].

Emotional and behavioural problems

The Strengths and Difficulties Questionnaire (SDQ) is a 25-question Likert assessment of behavioural and psychosocial concerns in children ages two to 17 [39]. This questionnaire is used to assess internalizing (e.g., internalizing, depression) and externalizing behaviours (e.g., aggression). Five subscales consisting of emotional symptoms, conduct problems, hyperactivity/inattention, peer relationship problems, and prosocial behaviour are included in the questionnaire. The SDQ-internalizing subscale (SDQ-I) consists of both the emotional and peer relationship problem subscales. The emotional problems subscale measures depression, worry, fear, nervousness, and somatic symptoms. In the present study, the SDQ-I was used to assess both anxiety and depressive symptoms. Example statements from the emotional problems subscale include I worry a lot and I am often unhappy, depressed or tearful. A sample statement from the peer relationship subscale is Other children or young people pick on me. Questions are answered using a 3-point system (0 = not true, 1 = somewhat true, and 2 = certainly true). Both children and parents completed this inventory. SDQ-I scores can be calculated by adding up the scores for the emotional and peer relationship problem subscales, resulting in a score range between zero and 20. An SDQ-I score of 20 indicates severe emotional and relational concerns. Each of the SDQ-I subsections, emotional and peer relationship problems, are scored from zero to 10. A score of six or higher on the emotional problems subscale indicates very high difficulties, while a score of four or higher on the peer relationship problems subscale indicates severe social deficits. The SDQ demonstrates good reliability (α = .75).

In addition to the SDQ, the Child Behavior Checklist (CBCL) was completed by the guardians or teachers of all participants to further assess specific behavioural and emotional concerns. Two versions of the CBCL were utilized in the present study, namely the preschool version and the version for youth ages six to 18 (CBCL/6-18) [40]. The CBCL-preschool version was completed by guardians of children up to five, and includes 99 items regarding aggressive behaviour, attention problems, somatic complaints, sleep issues, anxious and/or depressed behaviour, oppositional defiant problems, attention deficit/hyperactivity issues, and pervasive developmental concerns. Adults completing the CBCL-preschool version were asked questions such as whether or not this child “avoids looking others in the eye”, is “cruel to animals”, and “is disobedient”. Similarly, the CBCL/6-18 asks 113 questions such as whether or not this child or adolescent “can’t sit still, is restless or hyperactive”, “fears going to school”, and “screams a lot”. The subscales measured on the CBCL/6-18 are similar to the preschool version, including anxious, depressed, and/or withdrawn behaviour, somatic complaints, thought problems, attention issues, social concerns, rule breaking behaviour, aggressive behaviour, and other significant problems of note. Both versions of the CBCL are scored using a three-point Likert scale ranging from zero (not true) to two (very true). Subscale scores are totalled along with a total scale score online, where higher scores indicate more frequent and severe symptoms. All versions of the CBCL demonstrate excellent total scale internal consistency (α = .97), with strong reliability on internal (α = .90) and external (α = .94) subscales [41]. All subscales have shown strong reliability, ranging from α = .71 to .89 for both test versions [42].

Tolerance of stress

The Distress Tolerance Scale (DTS) measures one’s capacity to experience and withstand negative psychological states [43]. The DTS consists of 15-items that explore four subscales. First, the absorption subscale measures the amount of attention one shifts to negative emotions and includes items such as “when I feel distressed or upset, I cannot help but concentrate on how bad the distress actually feels”. The appraisal subscale uses statements such as “my feelings of distress or being upset are not acceptable” to measure one’s subjective appraisal of distress. Statements such as “I’ll do anything to avoid feeling distressed or upset” make up the regulation subscale, which assesses one’s efforts to alleviate distress. Finally, the tolerance scale measures one’s perceived ability to tolerate emotional distress and includes statements such as “I can’t handle feeling distressed or upset”. Items are rated on a five-point Likert scale ranging from one (strongly disagree) to five (strongly agree). In addition to subscale scores, a total scale score is calculated by averaging each subscale mean. Higher scores indicate a greater ability to tolerate distress. The DTS exhibits strong test-retest reliability (r = .82 to .85, p < .001) over a six month period and displays excellent internal consistency (α = .93) [43, 44].

ADHD symptoms

The Strengths and Weaknesses Assessment of Normal Behavior (SWAN) Rating Scale for ADHD consists of 18 items used to assess both the presence and severity of ADHD symptoms [45]. The SWAN is completed by a caregiver, teacher, and/or physician on behalf youth ages six to 17. Adults are asked to answer each item with respect to how the youth in question compares to their peers of the same age over the past month. Questions around sustained attention, ability to remain seated and focused, and turn-taking are included in the assessment. Items are scored on a 7-point Likert scale (-3 = far above average, -2 = above average, -1 = slightly above average, 0 = average, 1 = slightly below average, 2 = below average, and 3 = far below average), with weaknesses scored positively and strengths scored negatively. An inattention average and hyperactivity average score are calculated by totalling each item score and dividing by the number of items in each subscale. An additional SWAN total average score is calculated based on each of the two subscales. The more attention or activity problems displayed by the child, the lower their total SWAN score. The SWAN demonstrates excellent total scale internal consistency (α = .88 to .95) with subscale internal reliability ranging from r = .72 to .90 [4, 46].

Parental practices

Parents completed the Alabama Parenting Questionnaire (APQ) [47].

The APQ consists of 42-Likert scale items examining parental involvement, positive parenting, poor monitoring/supervision, inconsistent discipline, and corporal punishment. Additional discipline practices including reasoning, ignoring, loss of privileges, time-out, and extra work are also assessed. Participants answer each question on a scale system (1 = never, 2 = almost never, 3 = sometimes, 4 = often, and 5 = always) with regards to how often each scenario occurs in their household. An example scenario from the inconsistent discipline subscale is Your child is not punished when they have done something wrong. All items are summed to obtain a total scale score ranging from 42 to 210. Total scores that are one standard deviation or greater above or below the mean are considered concerning. For example, parents who score low on involvement and monitoring, and high on inconsistent discipline and corporal punishment would be flagged as concerning over parents who receive average scores on these measures (e.g., average total score = 126). Good reliability across the literature is demonstrated with the APQ (α = 0.82).

Parental stress

The Parenting Stress Index (PSI-IV) is composed of 36-items assessing stress levels in parents of children between one month and 12 years old [48]. There are three domains, including parent distress (PD), parent-child dysfunctional interaction (P-CDI), and difficult child (DC). Within the PD domain are seven subscales, including competence, isolation, attachment, health, role restriction, depression, and spouse/parenting partner relationship. An example from the PD is I feel trapped by my responsibilities as a parent. The P-CDI contains questions regarding the parent/child relationship, the parent’s perception of the child, and whether or not their expectations have been met in parenthood. A sample P-CDI statement is When I do things for my child I get the feeling that my efforts are not appreciated very much. The DC domain contains six subscales, examining distractibility/hyperactivity, adaptability, reinforces parent, demandingness, mood, and acceptability. A statement from the DC domain is My child makes more demands of me than most children. The PSI-IV is a Likert scale (1 = strongly disagree, 2 = disagree, 3 = not sure, 4 = agree, and 5 = strongly agree), and each value can be tallied to get the total-stress score for the scale. Total stress scores range from 36 to 180, with scores of 36 to 100 representing typical stress, and scores 100 or higher as clinically significant distress. The PSI-IV demonstrates excellent reliability (α = 98).

Cognitive ability

The Wechsler Intelligence Scale for Children-Fifth Edition (WISC-V) was used to assess cognitive ability in the children [49, 50]. Subtests covering a range of abilities, including verbal comprehension, visual spatial skills, and processing speed, were completed by all children and adolescents ages six to 16. Average scores range from 90 to 109, with exceptionally low scores falling below 79 and high above 120. The WISC-V is often used to identify intellectual exceptionalities among school-age children, such as giftedness or IDs. Test scores have been repeatedly validated as useful for identification, placement, and resource allocation. Furthermore, the WISC-V is supported by strong split-half reliability (r = 0.96, p < 0.001), subtest reliability (r = 0.80 to 0.94, p < 0.001), and test–retest reliability (r = 0.71 to 0.90, p < 001).

Procedure

Email and poster advertisements were distributed among community members, educators, care providers, and parents in the New York City area [51]. Data collection for the study began in 2015. Advertisements stressed the value of participation for families whose children could benefit from learning accommodations at school, such as an individualized education program (IEP). All participants were screened over the phone by HBN researchers prior to answering questionnaires to ensure inclusion criteria was met.(i.e., between the ages of five and 21, with parents (or a caregiver) who are capable of providing verbal and written consent). Information regarding psychiatric and medical history was collected during the screening call, including the use of stimulant medication. Those participants enrolled in the study following the screening call were administered a semi-structured diagnostic interview by an HBN licensed clinician. Appropriate follow-up measures were completed when necessary by participants and/or their parents depending on the child’s age. For example, if the diagnostic interview yielded a suspected language disorder, the Clinical Evaluation of Language Fundamentals (CELF) would be completed by the participant in question. Participants completed all language and intelligence testing with supervision from a qualified clinician. Self-administered questionnaires, such as the CBCL and the APQ, were completed using an online patient portal system called NextGen. All assessments were completed over the course of four visits. Participants were compensated for their time.

Analysis

Statistical analyses were performed using R (Version 4.2.0) software [52]. To address the first aim to identify anxiety profiles, an unsupervised machine learning algorithm was used to generate a self-organizing map (SOM) [53]. A SOM is an unsupervised artificial neural network used to map and cluster large data sets, and has been used previously to characterize children with ASD [54,55,56]. Importantly, the SOM’s algorithm attempts to learn about the underlying structure of data itself, rather than which data corresponds to predefined groups, thereby allowing for the development of unique data-driven subgroups. This approach may be used to tease apart different anxiety subtypes that are embedded within clinically-recognized NDDs, thereby accounting for the heterogeneity of anxiety symptom presentation among children and adolescents with ASD.

In the present study, the SOM contained a node (or neuron) representing the unique anxiety profile of each participant within a two dimensional plane. Initial data points, referred to as input data, were used to generate the first several nodes within the model. This served as the framework for the model, within which the remainder of the data points were statistically compared. The nodes with the closest weight vector to the input data were selected by the SOM as the best-matching unit. This process allowed for all data points (nodes) to be appropriately categorized in the model. The statistical model was trained using 262 observations and a learning rate of α = 0.05, which is a standard SOM value [53]. The number of resulting clusters was informed through visual inspection of elbow graphs prior to SOM development.

Scores from the ASSQ, SCQ, SRS, SWAN, APQ, SCARED-P, and SDQ were used to create a five-by-five hexagonal topology [53, 57] resulting in three clusters. A hexagonal method is used to preserve topographical distances between nodes and reduce distortions from mapping. Participant age, sex, family SES, intelligence, and parental age were statistically controlled for throughout all analysis procedures by including them as covariates in a separate linear regression model for each variable of interest (that is, the ASSQ, SCQ, SRS, SWAN, APQ, SCARED-P, and SDQ) and extracting the residuals from each model to carry forward as the adjusted values. In the final model, a node representing the unique anxiety profile of each participant was mapped in a two-dimensional framework. Each cluster was formulated irrespective of diagnosis. Nodes that fell within a similar location were representative of participants with a similar anxiety profile [53]. For example, if two participants with ASD both display high levels of social anxiety and low separation anxiety, it was expected that their respective nodes would fall in close proximity within the model. The goal was to determine if diagnosis was predictive of cluster (or group) membership, regardless of the broad spectrum of characteristics displayed within each group. For example, the anxiety profile of a child with high anxiety may be characteristically distinct from those with low anxiety.

To address the second aim of identifying anxiety factors that determined cluster membership, recursive feature elimination (RFE) was conducted using all measures of anxiety, consisting of the five subscale scores and the overall score from the SCARED-P, as well as the nine subscale scores from the SDQ. Using RFE, the anxiety measures that contributed the most to the differences between cluster membership were identified. RFE is a statistical process in which the key features that contribute to the SOM model are isolated [58]. RFE scores and ranks features by permutation importance and removes those features with limited input to the model. This process is repeated until one feature with the largest contribution to the model remains. Permutation importance considers a variable of great importance only with respect to improving the predictive accuracy of the model.

Results

Participants

Of the 262 children and adolescents who participated in the current study, 111 were diagnosed with ASD (42%), and the remaining participants were typically-developing (Table 1). Participants were between the ages of five and 17 and the mean age was 10.5 years. The majority of the participants with ASD were boys (n=86, 77.4%). Both ASD and TD participants reported similar SES scores on the BSMSS, with all other scale scores being significantly larger among participants with ASD (Table 1).

Table 1 Demographics by diagnosis
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Anxiety profiles

Three anxiety profiles were identified using the SOM, with the data forming three distinct clusters (Fig. 1a). Cluster 1 was comprised of participants who report moderate levels of anxiety (Fig. 1b), cluster 2 was composed of participants reporting high levels of anxiety, and cluster 3 was characterized by low levels of anxiety.

Fig. 1
figure 1

Anxiety profiles in children and adolescents with ASD and TD children and adolescents. A Anxiety profiles identified using Self Organizing Maps. B Cluster membership by diagnosis

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Those in the low anxiety cluster (cluster 3), consisting primarily of TD participants (80%), demonstrated low depressive (M = 5.69; SD = 4.35) and anxiety (M = 7.91; SD = 6.93) symptoms, and also had strong communication skills (M = 5.36; SD = 3.39, Table 2).

Table 2 Basic demographics by cluster
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In contrast, nearly all participants diagnosed with ASD (94%) fell within the moderate and high anxiety clusters (clusters 1 & 2). The high anxiety cluster (cluster 2) was composed primarily of male-identifying participants with ASD. This cohort was characterized by high ASSQ (M = 27.67; SD = 7.85), SRS (M = 116.31; SD = 14.47), and anxiety scores (SCARED-P) (M = 24.94; SD = 13.63), ADHD symptoms (M = 1.38; SD = 0.75), social communication challenges (M = 16.92; SD = 4.17), repetitive behaviours (M = 79.19; SD = 35.74), and emotional and behavioural problems (M = 19.98; SD = 4.83). Those participants in the high anxiety cluster also reported the most severe depressive symptoms (M = 9.63; SD = 3.03) on the SDQ-I, suggesting that depression is a critical indicator of anxiety in children and adolescents with ASD. As compared to participants in the low anxiety cluster, these results suggest that participants in the moderate and high anxiety clusters may require more intensive support and interventions to aid in the management of their symptoms, given the comprehensive nature of their impairments.

With respect to anxiety measures, peer problems (M = 5.49; SD = 2.03) were the most reliable factor in determining cluster membership. The majority of participants who reported having significant peer problems (e.g., difficulty engaging in conversations, trouble making friends, and/or victimization of bullying/harassment) occupied the high anxiety cluster. Secondary factors associated with the high anxiety group were SDQ impact supplements (M = 6.41: SD = 1.89), total difficulties (M = 19.98; SD = 4.83), and hyperactivity concerns (M = 7.57; SD = 2.11).

The moderate anxiety cluster (cluster 1) was comprised of both ASD and TD participants. Participants in this cluster had low ADHD (M = 0.16; SD = 1.20) and excellent social responsiveness skills (M = 58.34; SD = 39.04) along with average ASSQ (M = 11.50; SD = 7.92), RBS-R (M = 34.41; SD = 41.92), depressive (M = 13.57; SD = 4.60), and anxiety (M = 14.96; SD = 9.21) scores.

RFE results displayed in Table 3 and Fig. 2 demonstrate that depression (measured using the SDQ-I) was the most robust indicator of high anxiety among both ASD and TD participants (11.71). Therefore, severe and frequent depressive symptoms, such as social isolation and unhappiness, are characteristic of anxiety in the high anxiety group of whom the vast majority had an ASD diagnosis. Additionally, generating impact statements (11.15), anxiety related to peer problems (11.07), total difficulties (10.77), and hyperactivity (10.39) scores on the SDQ were also among the most prominent contributors to the SOM model. Anxiety assessments (SDQ-I, SCARED-P) accounted for the first 15 features within the RFE, and are therefore the only features included in Fig. 2.

Table 3 Recursive feature extraction by cluster
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Fig. 2
figure 2

Recursive Feature Elimination (RFE) Applied to Anxiety Measures. Feature ranking was performed using permutation importance. SDQ (black); SCARED-P (dark grey)

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On the other hand, RFE findings indicated that total (3.62), generalized (3.33), social (3.10), and separation (1.86) anxiety as well as school avoidance (2.44) and panic disorder (0.47) on the SCARED-P were the weakest distinguishing factors between high, moderate and low anxiety clusters, along with conduct problems (1.36) as measured with the SDQ.

Discussion

The current study sought to identify anxiety profiles in a heterogenous cohort of children with ASD and those who are typically-developing. By using a well-phenotyped cohort, we were able to apply an artificial neural network analytic method applied to anxiety measures in children with and without ASD. Using this analysis, we found distinct clusters of children who have high, moderate, or low anxiety. We found that children with ASD generally had moderate or high anxiety. Some TD children had moderate anxiety; however, most TD children had low anxiety, and depression was strongly associated with high anxiety in both groups. Peer problems were an additional reliable factor in determining cluster membership; most participants who reported having significant peer problems (e.g., difficulty engaging in conversations, trouble making friends, and/or victimization of bullying/harassment) occupied the high anxiety cluster. These findings may correspond with the social motivation theory, which suggests that anxiety underlies the relationship between autistic symptoms and low social moviation [59]. Given the diagnostic makeup of the high anxiety cluster, it can be theorized that children and adolescents with ASD and anxiety are more likely than their TD peers to experience serious and disruptive peer interactions. In our analysis, age, sex, SES, intelligence, and parental age were included as covariates in a linear regression model to control for their potential effects. The residuals associated with each variable of interest were extracted after being adjusted for these covariates and used in subsequent analyses. None of the covariates had a significant effect on the identification or interpretation of the anxiety profiles, indicating that the profiles remained distinct and were not confounded by these demographic and clinical factors.

Anxiety in children with ASD is extremely common and is associated with increased social impairment and isolation over time, commonly resulting in a reduced QoL compared to TD youth [1, 60, 61]. Previous reports have also noted that specific types of anxiety in older adolescents are particularly resistant to cognitive behavioural therapy (CBT) when early treatment is not sought [22]. Efforts by healthcare providers, therapists, parents, and educators are essential to the success and development of children and adolescents with anxiety, who may tailor interventions according to one’s anxiety profile. For instance, individuals in the high to moderate anxiety clusters may require a more intensive and consistent application of anxiety management strategies to ensure their success. Previous and ongoing investigations into the implementation of CBT modified for use among children with anxiety in children with ASD shows promising results [62,63,64,65]. CBT adapted to meet the unique needs and barriers of working in the ASD community includes greater flexibility in techniques, heavy familial involvement, frequent use of exposure tasks, and the establishment of a reward system to promote engagement and trying new skills. Early interventions that focus on exposure and social skill development should begin as early as three years of age, allowing for the greatest possible reduction in future challenges [20, 62, 66]. In addition to working with a therapist or other healthcare provider, parents can expect frequent and unique expressions of anxiety from their children with ASD. They should also focus on becoming directly involved in the therapeutic process, both in and outside of sessions. Educators should maintain an open line of communication with parents (and healthcare providers when appropriate) to ensure they are providing the best learning and social environment possible for each child. Hyperactivity, social isolation, rigid expectations, and differences in communication styles, which some children with ASD may express in school settings, may be an area of key focus for educators. It may also be helpful for educators to implement various therapeutic strategies in the classroom, such as creating a token economy, tailoring homework to fit the learning style of the child, and avoiding group projects that often further highlight social isolation and rejection.

Depression was far more common among participants with high anxiety (predominantly ASD) and was the most prominent factor in differentiating cluster membership. High depression among youth with ASD and anxiety is largely attributed to frequent experiences of social isolation, often stemming from impaired social communication and interaction skills inherent to ASD [67,68,69]. Peer problems were also strongly indicative of high anxiety cluster membership. Clearly, depression is a significant predictor of high anxiety in both ASD and TD populations. In addition to the cortisol-related stress cycle, depression among youth with ASD who have anxiety may be accounted for by more frequent challenges in seeking out and maintaining social relationships. Additionally, children and adolescents with ASD are more likely to report feeling ostracized from their TD peers, which may contribute to high levels of depression among this group.

Children and adolescents with ASD who have anxiety should be assessed for possible comorbid depression. Given the bidirectional relationship between anxiety and depression, it may be ineffective to treat one without consideration for the other. The current findings also point to early intervention to develop and strengthen social and communication skills as critical to preventing and managing depression among youth with ASD-specific anxiety. Improved social engagement and conversational skills may reduce the occurrence of peer problems, consequently decreasing symptoms of depression and anxiety.

Relative to previous work exploring the relationship between ASD and anxiety [15, 70,71,72], using the current approach we analyzed data from a small sample of children and adolescents with ASD (N = 111). Given that youth with ASD were the population of interest in the present study, the small sample is a significant limitation to generalizing findings to the ASD community as a whole. As well, just over 22% of those diagnosed with ASD identified as female, meaning results are predominantly reflective of the male perspective of ASD-specific anxiety symptoms. The underrepresentation of females in our sample could mean that the anxiety profiles identified may be more reflective of male characteristics. It is plausible that female-identifying participants may experience anxiety differently than their male counterparts. For example, previous literature indicates that females with ASD often experience more internalized anxiety (e.g., sleep disruption and/or fear of change) while males express more outward behavioural concerns (e.g., hyperactivity, relational issues, and/or learning difficulties) that create more noticeable challenges both at home and school [73].The notable importance of peer problems in the current analysis may be more representative of male-identifying youth with ASD than females, potentially overlooking therapeutic and social interventions that could benefit female youth with ASD. Several limitations related to the use of the existing dataset included: lack of details concerning the timing of the assessments, and whether environmental conditions were standardized across sessions. Another limitation of the current study is that the SOM clusters were extremely unbalanced with respect to participant distribution. This may be attributed to limitations of the SOM technique itself, as the continuous mapping process is not confined by clear boundaries, which makes the identification of unique clusters highly dependent on the parameters specified by investigators. For example, there are only six participants with ASD in cluster one, and two TD individuals in cluster two. In turn, we did have a cluster of that only contained TD or ASD children and adolescents, indicating the need for further refinement of the anxiety measures that were included in the artificial neural network. Potentially, had more ASD-specific anxiety measures been included in the artificial neural network model to develop the SOM this may have further identified the features and risk factors associated with anxiety in children with ASD. Finally, it is difficult to determine if the high anxiety cluster is a result of ASD symptoms worsening anxiety or anxiety exacerbating core ASD symptoms, however this was not within the scope of the current study.

Conclusion

The present study provides novel insights into ASD-specific anxiety profiles by using an unsupervised machine learning model, in combination with an RFE analysis. This unique methodological approach ensures that data-driven subgroups are formulated irrespective of diagnosis, and the unique features associated with each anxiety profile are readily identified. Depression and peer problems were prominent factors that distinguished children and adolescents with ASD with high anxiety from children with and without ASD and those who are TD with low to moderate anxiety. Additionally, peer relationship problems pose a notable challenge the youth with ASD, and exacerbate both depression and anxiety symptoms. Total emotional difficulties and hyperactive behaviour also predispose children and adolescents with ASD more frequent and pronounced experiences of anxiety. Specific types of anxiety, including generalized, social, and separation, do not account for a significant difference between high and low levels of anxiety in youth with ASD. Findings indicate that early interventions, focused on family-involvement, emotional regulation, and the development of social and communication skills, must be consistently implemented among children and adolescents with ASD who have anxiety. Exposure to various social interactions and education on emotion management has shown promising results in reducing depression and anxiety among children and adolescents with ASD, while simultaneously fostering a sense of belongingness. Future investigations should explore the influence of parental mental health on the development and maintenance of anxiety and depression in children and adolescents with ASD. Another avenue of inquiry would be to apply modified CBT principles into educational settings to support youth with ways of learning that differ from the traditional curriculum. Finally, consideration must be given to the bidirectional relationship between ASD and anxiety. Developmental researchers should attempt to isolate whether anxiety worsens core symptoms of ASD, or if ASD heightens one’s experience of anxiety. A clear understanding of strategies to improve mental health among children and adolescents with ASD will enhance social engagement, communication, adjustment, and overall fulfillment and satisfaction throughout the lifespan.