Brain and molecular mechanisms underlying the nonlinear association between close friendships, mental health, and cognition in children

  1. Chun Shen
  2. Edmund T Rolls
  3. Shitong Xiang
  4. Christelle Langley
  5. Barbara J Sahakian
  6. Wei Cheng  Is a corresponding author
  7. Jianfeng Feng  Is a corresponding author
  1. Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, China
  2. Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, China
  3. State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science (Fudan University), Ministry of Education, China
  4. Department of Computer Science, University of Warwick, United Kingdom
  5. Oxford Centre for Computational Neuroscience, United Kingdom
  6. Department of Psychiatry, University of Cambridge, United Kingdom
  7. Behavioural and Clinical Neuroscience Institute, University of Cambridge, United Kingdom
  8. Fudan ISTBI—ZJNU Algorithm Centre for Brain-Inspired Intelligence, Zhejiang Normal University, China
  9. Shanghai Medical College and Zhongshan Hospital Immunotherapy Technology Transfer Center, China
  10. Department of Neurology, Huashan Hospital, Fudan University, China
  11. Zhangjiang Fudan International Innovation Center, China

Abstract

Close friendships are important for mental health and cognition in late childhood. However, whether the more close friends the better, and the underlying neurobiological mechanisms are unknown. Using the Adolescent Brain Cognitive Developmental study, we identified nonlinear associations between the number of close friends, mental health, cognition, and brain structure. Although few close friends were associated with poor mental health, low cognitive functions, and small areas of the social brain (e.g., the orbitofrontal cortex, the anterior cingulate cortex, the anterior insula, and the temporoparietal junction), increasing the number of close friends beyond a level (around 5) was no longer associated with better mental health and larger cortical areas, and was even related to lower cognition. In children having no more than five close friends, the cortical areas related to the number of close friends revealed correlations with the density of μ-opioid receptors and the expression of OPRM1 and OPRK1 genes, and could partly mediate the association between the number of close friends, attention-deficit/hyperactivity disorder (ADHD) symptoms, and crystalized intelligence. Longitudinal analyses showed that both too few and too many close friends at baseline were associated with more ADHD symptoms and lower crystalized intelligence 2 y later. Additionally, we found that friendship network size was nonlinearly associated with well-being and academic performance in an independent social network dataset of middle-school students. These findings challenge the traditional idea of ‘the more, the better,’ and provide insights into potential brain and molecular mechanisms.

Editor's evaluation

The findings of this study yield important new insights into the relationship between the number of close friends and mental health, cognition, and brain structure. Due to the large sample sizes, the evidence is solid but would have been improved if both of the analysed datasets contained more closely matched measures. This work advances our understanding of how the friendship network relates to young adolescents' mental well-being and cognitive functioning and their underlying neural mechanisms.

https://doi.org/10.7554/eLife.84072.sa0

eLife digest

Close friendships are crucial during the transition from late childhood to adolescence as children become more independent from their parents and influenced by their peers. The brain undergoes a tremendous amount of development during this period, and it is also a time when mental health disorders often begin to emerge.

Scientists are still learning about how friendships shape brain development and mental health during this transition. Maintaining friendships takes time and mental resources so there may be limits on how many friends are beneficial. Here, Shen, Rolls et al. show that the having more friends is not always directly related to better mental health and cognitive abilities.

In the study, Shen, Rolls et al. analyzed data from nearly 7,500 young people between around 10 to 12 years old: this included, their number of close friends, their mental health and cognitive abilities such as working memory, attention and processing speed, and images of their brains. Data from a second set of about 16,000 young people were then analyzed to confirm the results.

Shen, Rolls et al. found having a higher number of close friends was associated with improved mental health and cognitive ability. However, this association stopped once around five friends had been reached, after which having more friends was no longer linked to better mental health and was even correlated with lower cognition. Additionally, individuals with too few or too many friends had more symptoms of Attention-deficit/hyperactivity disorder (ADHD) and were less able to learn from their experiences.

This non-linear relationship between number of friends and mental health and cognitive abilities can be partly explained by the structure of the brain. Shen, Rolls et al. found that brain regions associated with friendship were larger in individuals with more close friends, but did not increase any further once the number of friends a person had exceeded five individuals with around five close friends also had more of a receptor that is part of the opioid system, which may make them more responsive to laughter, friendly touch, or other positive social interactions.

These findings challenge the idea that having more friends is always better. It also provides insights into how friendships affect brain health during the transition from late childhood to adolescence. Insights from this study may aid the development of interventions to support healthy brain development during youth.

Introduction

Late childhood and its transition toward adolescence is a period marked by decreasing parental influence alongside increasing peer influence. It is a period critical for social interaction, during which friendships are especially important (Blakemore and Mills, 2014). During this period, the social brain is still undergoing significant development, in parallel with changes in social cognition (Mills et al., 2014). Meanwhile, evidence suggests that psychiatric disorders often have an onset in adolescence (Kessler et al., 2005), which may be partly influenced by the concurrent changes in the social environment and brain (Paus et al., 2008). Therefore, understanding the relationship between friendship, mental health, and cognition during this period, and the underlying brain mechanisms, is of considerable clinical and public health importance.

It has been well established that positive social relationships such as close friendships are essential for mental health and cognition in children and adolescents (Marion et al., 2013; Narr et al., 2019; Wentzel et al., 2018). However, it remains unclear whether having more close friends is necessarily better. Cognitive constraints and time resources limit the number of close social ties that an individual can maintain simultaneously (Dunbar, 2018). The innermost layer of the friendship group with the highest emotional closeness is around five close friends (the so-called Dunbar’s number) (Zhou et al., 2005). For now, only a few empirical studies have examined the nonlinear association between social relationships, mental health, and cognition in children and adolescents. For instance, a large study of a nationally representative sample in the United States reported that adolescents with either too many or too few friends had higher levels of depressive symptoms (Falci and McNeely, 2009). Two large-scale studies reported that the benefits of social interactions for well-being were nearly negligible once the quantity reached a moderate level (Kushlev et al., 2018; Ren et al., 2022). Additionally, a significant U-shaped effect was detected between positive relations with others and cognitive performance (Brown et al., 2021). Overall, the assumption of linearity still dominates studies of social relationships, and the effect of the friendship network size at the high end remains largely unexplored.

Despite a large body of evidence linking friendships to mental health and cognition, we know relatively little about the underlying mechanisms involved (Pfeifer and Allen, 2021). The social brain hypothesis proposes that the evolution of brain size is driven by complex social selection pressures (Dunbar and Shultz, 2007). Animal studies have shown that social network size can predict the volume of the mid-superior temporal sulcus (Sallet et al., 2011; Testard et al., 2022), a region in which neurons respond to socially relevant stimuli such as face expression and head movement to make or break social contact (Hasselmo et al., 1989a; Hasselmo et al., 1989b). In human neuroimaging studies, several key brain regions, including the medial prefrontal cortex (mPFC, i.e. orbitofrontal [OFC] and anterior cingulate cortex [ACC]), the cortex in the superior temporal sulcus (STS), the temporoparietal junction (TPJ), amygdala, and the anterior insula, have been implicated in social cognitive processes (Frith and Frith, 2007). Moreover, there has been an increasing number of studies dedicated to investigating the social brain in children and adolescents over the past decade (Andrews et al., 2021; Burnett et al., 2011).

At the molecular level, the μ-opioid receptor is widely distributed in the brain, particularly in regions associated with social pain such as the ACC and anterior insula (Baumgärtner et al., 2006). Recent studies have identified the crucial role of μ-opioid receptors in forming and maintaining friendships (Dunbar, 2018), and variations in the μ-opioid receptor gene have been related to individual differences in rejection sensitivity (Way et al., 2009). In addition, other neurotransmitters, including dopamine, serotonin, GABA, and noradrenaline, may interact with the opioids, and are involved in social affiliation and social behavior (Machin and Dunbar, 2011). Dysregulation of the social brain and neurotransmitter systems is also implicated in the pathophysiology of major psychiatric disorders (Porcelli et al., 2019). Taken together, it is suggested that changes in the social brain might explain the relationship between social connections and mental health (Lamblin et al., 2017). However, the empirical evidence on this topic is limited in late childhood and adolescence.

In this study, we aimed to investigate the relationship between the number of close friends, mental health, and cognitive outcomes, with a focus on potential nonlinear associations. We used data from the Adolescent Brain Cognitive Developmental (ABCD) study (Karcher and Barch, 2021) and an independent social network dataset (Paluck et al., 2016). These datasets provided reliable measures of close friend quantity, mental health, and cognition, and included a combined total of more than 23,000 participants (Figure 1a). To evaluate the potential nonlinear relation between friendship quantity (predictor) and mental health and cognition (outcome), two different analytic approaches were utilized. Specifically, we examined the presence of a significant quadratic term as an indicator of nonlinearity, and subsequently conducted a two-lines test (Simonsohn, 2018) to estimate an interrupted regression and identify the breakpoint (Figure 1b). To explore the underlying neurobiological mechanisms, we further tested the nonlinear association between the number of close friends and brain structure. We then correlated the related brain differences with the density of eight neurotransmitter systems, as well as the expression of the μ-opioid receptor gene (OPRM1) and the κ-opioid receptor gene (OPRK1) (Figure 1c). Finally, longitudinal and mediation analyses were conducted to uncover the direction and direct association between the number of close friends, mental health, cognition, and brain structure (Figure 1d). Based on the existing literature, we hypothesized that the number of close friends was nonlinearly related to mental health, cognition, and the social brain; and that this relationship could potentially be explained by brain differences and molecular mechanisms.

The study workflow.

(a) Study datasets and key measures used in the present study. (b) A two-step approach to evaluate the nonlinear association. The number of close friends is used as the independent variable in quadratic regression models. Once a significant squared term (‘b’) is found, a two-lines test is conducted to estimate the breakpoint. Then participants are classified into two groups according to the breakpoint. (c) Correlation of brain differences related to the number of close friends with neurotransmitter density and gene expression level. (d) Longitudinal and mediation analysis of the number of close friends, ADHD symptoms, crystalized intelligence, and the significant surface areas.

Results

Demographic characteristics

In the ABCD study, 7512 participants (3625 [48.3%] females, aged 9.91 ± 0.62 y) provided self-reported number of close friends, a broad range of mental health and cognitive measures, and quality-controlled MRI data at baseline (Table 1), and 4290 of them (2044 [47.7%] females, aged 11.49 ± 0.66 y) had 2-year follow-up data available (Table 2). In the social network dataset, 16,065 subjects from 48 middle schools (8065 [50.3%] female, aged 12.00 ± 1.03 y) who had complete key variables were included (Table 3).

Table 1
Characteristics of the study population in the Adolescent Brain Cognitive Developmental (ABCD) study at baseline*.
≤5 close friends(N = 4863)>5 close friends(N = 2649)p-value
Age9.91 ± 0.619.93 ± 0.630.08
Sex0.02
 Female2299 (47.3%)1326 (50.1%)
 Male2564 (52.7%)1323 (49.9%)
Race0.001
 White2672 (54,9%)1497 (56.5%)
 Black561 (11,5%)370 (14.0%)
 Hispanic1015 (20.9%)485 (18.3%)
 Asian109 (2.2%)45 (1.7%)
 Other506 (10.4%)252 (9.5%)
Family size 4.69 ± 1.824.58 ± 1.840.01
Family income7.28 ± 2.347.4 ± 2.350.03
Parental education16.82 ± 2.6216.97 ± 2.530.02
Body mass index18.71 ± 4.1118.73 ± 4.110.77
Puberty1.73 ± 0.861.78 ± 0.880.02
Urbanization §0.12
 Rural395 (8.5%)220 (8.7%)
 Urban clusters167 (3.6%)68 (2.7%)
 Urbanized area4,074 (87.9%)2,229 (88.6%)
Total close friends3.04 ± 1.3612.19 ± 13.14<0.001
Same-sex close friends2.41 ± 1.229.13 ± 9.82<0.001
Opposite-sex close friends0.63 ± 0.793.05 ± 5.79<0.001
  1. *

    Values are mean ± SDor N (%).

  2. For continuous data, t-test was performed; for categorical data, chi-square test was performed.

  3. 4780 and 2624 participants in ≤5 and >5 close friends groups have family size data, respectively.

  4. §

    4636 and 2517 participants in ≤5 and >5 close friends groups have urbanization data, respectively.

Table 2
Characteristics of the study population in the Adolescent Brain Cognitive Developmental (ABCD) study at 2-year follow-up (N = 4290).
Value*
Age11.49 ± 0.66
Sex
 Female2044 (47.7%)
 Male2246 (52.4%)
Race
 White2612 (60.9%)
 Black385 (9.0%)
 Hispanic791 (18.4%)
 Asian89 (2.1%)
 Other413 (9.6%)
Family income7.83 ± 2.04
Parental education17.11 ± 2.44
Body mass index20.35 ± 4.63
Puberty2.53 ± 1.05
Total close friends6.82 ± 8.37
Same-sex close friends4.99 ± 5.92
Opposite-sex close friends1.83 ± 3.66
  1. *

    Values are mean ± SDor N (%).

Table 3
Characteristics of the study population in the social network dataset (N = 16,056).
VariableValue *
Age12.00 ± 1.03
Sex
 Female8068 (50.3%)
 Male7988 (49.8%)
Grade
 5th grade1107 (6.9%)
 6th grade4190 (26.1%)
 7th grade5279 (32.9%)
 8th grade5480 (34.1%)
New to the school
 New to school4315 (26.9%)
 Returning to school11,741 (73.1%)
Most friends go to this school
 Yes14,429 (89.9%)
 No1627 (10.1%)
Outdegree8.08 ± 2.43
Indegree7.83 ± 4.42
Reciprocal degree3.82 ± 2.14
Well-being0.86 ± 0.24
Grade point average3.17 ± 0.61
  1. *

    Values are mean ± SD or N (%).

Nonlinear association between the number of close friends, mental health, and cognition

The number of close friends was significantly associated with 12 out of 20 mental health measures, and 7 out of 10 cognitive scores at baseline (the total F-value of the linear and quadratic terms, p<0.05/30; Figure 2a–g). For these 18 outcomes except the withdrawn/depressed, all quadratic terms reached significance after Bonferroni corrections (p<0.05/60), and all quadratic models provided a significantly better fit than the corresponding linear models (F = [13.25, 55.53], all p<0.001). For mental health, the greatest effect sizes of the quadratic terms were observed for social problems (β = 0.08, t = 5.92, p=3.3 × 10–9, ΔR2 = 0.43%) and attention problems (β = 0.12, t = 5.83, p = 5.8 × 10–9, ΔR2 = 0.42%), suggesting that the quadratic term of close friend quantity additionally explained 0.43 and 0.50% of the variability compared with the corresponding linear model. For cognition, the greatest effect sizes of the quadratic terms were observed for total intelligence (β = –0.35, t = –7.45, p=1.0 × 10–13, ΔR2 = 0.50%) and crystalized intelligence (β = –0.26, t = –6.87, p=6.7 × 10–12, ΔR2 = 0.43%) (Figure 2—figure supplement 1). The findings were robust with respect to random choice of the siblings (Figure 2—figure supplement 2).

Figure 2 with 5 supplements see all
Results of behavior-level nonlinear association analyses in the Adolescent Brain Cognitive Developmental (ABCD) study at baseline.

(a) Results of quadratic regression models. The total F values of quadratic and linear terms, and the t values of linear and quadratic terms are reported. An asterisk indicates statistical significance after Bonferroni correction (i.e., p<0.05/30 for F value, and p<0.05/60 for t value). Relationship between the number of close friends and the total problems (b), attention problems (c), withdrawn/depressed (d), social problems (e), fluid intelligence (f), and crystalized intelligence (g). The number of close friends is classified into 13 bins, sample sizes of which are 107, 585, 1104, 1196, 957, 914, 631, 399, 463, 363, 416 and 477. In each bin, the mean (i.e., black dot) and standard error (i.e., error bar) of the dependent variable are shown. The x-axis is in log scale, and the median of the number of close friends in each bin was labeled in the x-axis. The red line is the fitted quadratic model. (h) Results of the two-lines tests. The breakpoint and the estimated coefficients with 95% confidence intervals of linear regressions in each group separated by the breakpoint are reported. cbcl-scr-syn-anxdep, Anxious/Depressed Syndrome Scale; cbcl-scr-syn-withdep, Withdrawn/Depressed Syndrome Scale; cbcl-scr-syn-somatic, Somatic Complaints Syndrome Scale; cbcl-scr-syn-social, Social Problems Syndrome Scale; cbcl-scr-syn-thought, Thought Problems Syndrome Scale; cbcl-scr-syn-attention, Attention Problems Syndrome Scale; cbcl-scr-syn-rulebreak, Rule-Breaking Behavior Syndrome Scale; cbcl-scr-syn-aggressive, Aggressive Behavior Syndrome Scale; cbcl-scr-syn-internal, Internalizing Problems Syndrome Scale; cbcl-scr-syn-external, Externalizing Problems Syndrome Scale; cbcl-scr-syn-totprob, Total Problems Syndrome Scale; cbcl-scr-dsm5-depress, Depressive Problems DSM-5 Scale; cbcl-scr-dsm5-anxdisord, Anxiety Problems DSM-5 Scale; cbcl-scr-dsm5-somaticpr, Somatic Problems DSM-5 Scale; cbcl-scr-dsm5-adhd, ADHD DSM-5 Scale; cbcl-scr-dsm5-opposite, Oppositional Defiant Problems DSM-5 Scale; cbcl-scr-dsm5-conduct, Conduct Problems DSM-5 Scale; cbcl-scr-07-sct, Sluggish Cognitive Tempo Scale2007 Scale; cbcl-scr-07-ocd, Obsessive-Compulsive Problems Scale2007 Scale; cbcl-scr-07-stress, Stress Problems Scale2007 Scale; nihtbx-picvocab, Picture Vocabulary Test; nihtbx-flanker, Flanker Inhibitory Control and Attention Test; nihtbx-list, List Sorting Working Memory Test; nihtbx-cardsort, Dimensional Change Card Sort Test; nihtbx-pattern, Pattern Comparison Processing Speed Test; nihtbx-picture, Picture Sequence Memory Test; nihtbx-reading, Oral Reading Recognition Test; nihtbx-fluidcomp, Fluid Composite Score; nihtbx-cryst, Crystallized Composite Score; nihtbx-totalcomp, Total Composite Score.

Figure 2—source data 1

Results of behavior-level nonlinear association analyses in the Adolescent Brain Cognitive Developmental (ABCD) study at baseline.

https://cdn.elifesciences.org/articles/84072/elife-84072-fig2-data1-v1.xlsx

The average breakpoint of the number of close friends for the mental health and cognitive outcomes with significant quadratic terms was 4.89 ± 0.68 (Figure 2h). Both mental health and cognition were positively associated with close friend quantity, with an ideal number of around 5. These nonlinear associations were consistent in males and females (Figure 2—figure supplement 3). However, the number of same-sex close friends, but not of opposite-sex close friends, was significantly related to mental health and cognition (26 out of 30 measures with a significant F value after Bonferroni correction), and children with 4.05 ± 0.59 same-sex close friends had the best mental health and cognitive functions (Figure 2—figure supplement 4).

Finally, the same analyses were performed using the cross-sectional data collected at 2 y later (Figure 2—figure supplement 5). The number of close friends was significantly associated with 10 out of 20 mental health measures, and 3 out of 6 cognitive scores. Significant nonlinear associations were observed between close friend quantity and five measures, with an average breakpoint of 4.60 ± 0.55 close friends. The greatest effect sizes of the quadratic terms were observed for attention problems (β = 0.10, t = 3.63, p=2.9 × 10–4, ΔR2 = 0.27%) and crystalized intelligence (β = –0.24, t = –4.70, p=2.7 × 10–6, ΔR2 = 0.36%) for mental health and cognition, respectively.

The number of close friends was quadratically associated with brain structure

In the ABCD study, the number of close friends was significantly associated with the total cortical area (F = 6.29, p=1.0 × 10–3; Figure 3d), and the total cortical volume (F = 5.80, p=3.1 × 10–3). No significant relationship between the number of close friends and mean cortical thickness (F = 0.62, p=0.54) and total subcortical volume (F = 3.94, p=0.02) was found.

Figure 3 with 5 supplements see all
Nonlinear association between the number of close friends and cortical area in the Adolescent Brain Cognitive Developmental (ABCD) study at baseline.

(a) Cortical areas significantly associated with the number of close friends after FDR correction (i.e., 360 regions) based on the total F values of linear and quadratic terms. (b) Cortical areas with a significant linear or quadratic term. FDR correction was performed within the significant regions obtained in (a). (c) Top 10 regions with the strongest effect sizes of linear and quadratic terms, respectively. Relationship between the number of close friends and the total cortical area (d), left STGa (e), right TGd (f), left p32pr (g), left 13l (h), and left 47m (i). The number of close friends is classified into 13 bins, sample sizes of which are 107, 585, 1104, 1196, 957, 914, 631, 399, 463, 363, 416 and 377. In each bin, the mean (i.e., black dot) and standard error (i.e., error bar) of the dependent variable are shown. The x-axis is in log scale, and the median of the number of close friends in each bin was labeled in the x-axis. The red line is the fitted quadratic model. The names of the brain regions are from the HCP-MMP atlas.

Figure 3—source data 1

Results of nonlinear association analyses between the number of close friends and cortical area in the Adolescent Brain Cognitive Developmental (ABCD) study at baseline.

https://cdn.elifesciences.org/articles/84072/elife-84072-fig3-data1-v1.xlsx

After false discovery rate (FDR) correction (q < 0.05), the significant cortical areas associated with the number of close friends were mainly located in the OFC, insula, the ACC, the anterior temporal cortex, and the TPJ (Figure 3a). The brain region with the largest effect size for the linear term was the OFC (left medial OFC [area 11l and 13l] and lateral OFC [area 47m and 47s]). The quadratic terms of the number of close friends for all these regions were significant (Figure 3b), and the greatest effect sizes were observed in the temporal pole (left STGa: β = –0.58, t = –4.20, p=2.8 × 10–5, ΔR2 = 0.18%, Figure 3e; right TGd: β = –3.32, t = –4.11, p=4.0 × 10–5, ΔR2 = 0.18%, Figure 3f). These findings were robust for random choice of the siblings (Figure 3—figure supplement 1). Similar findings were found for cortical volumes (Figure 3—figure supplement 2). As the correlation of cortical area and cortical volume with the number of close friends is high (r = 0.78, p=3.3 × 10–76) and cortical area and volume themselves are highly correlated (r = 0.92, p=9.0 × 10–151; Figure 3—figure supplement 3), we focused on cortical area in the following analyses.

Further, two-lines tests suggested that participants with around five close friends (breakpoint = 5.30 ± 0.85) had the largest areas in these cortical regions (Figure 3—figure supplement 4). To illustrate the patterns of nonlinear relationships, we performed linear regression models in participants with ≤5 and >5 close friends, respectively. Similar regions to those found with quadratic models including the OFC, insula, the ACC, and temporal cortex were significant after FDR correction in the ≤5 group (Figure 3—figure supplement 5a and b), and the largest effect size was observed in the OFC (Figure 3—figure supplement 5c). However, the number of close friends was not related to cortical area in the >5 group (Figure 3—figure supplement 5d). Moreover, the cortical area associative patterns of close friend quantity in the two groups were not correlated (r = –0.02, p=0.78; Figure 3—figure supplement 5e).

Relationship to molecular architecture

As the number of close friends was nonlinearly associated with cortical area and the significant regions were only found in participants with no more than five close friends, we focused on the brain associative pattern for the number of close friends in the ≤5 group. We found that the correlations between the spatial pattern of cortical area related to the number of close friends and densities of neurotransmitters were not significant except for the μ-opioid receptor (Spearman’s rho = 0.44, Bonferroni corrected pperm = 0.02; Figure 4a and b). Transcriptomic analyses showed that OPRM1 (Spearman’s rho = 0.45, pperm = 0.001; Figure 4c) and OPRK1 (Spearman’s rho = 0.46, pperm = 0.002; Figure 4d) were highly expressed in regions related to the number of close friends.

Spatial correlation between cortical area differences related to the number of close friends in children with ≤5 close friends and density of neurotransmitters and gene expression level.

(a) Bootstrapped Spearman correlations (10,000 times) between t-statistics of close friendship quantity and densities of 14 neurotransmitter receptors or transporters. In each box, the line indicates the median and the whiskers indicate the 5th and 95th percentiles. p-Values were estimated by 5000 times permutation. *: Bonferroni corrected pperm < 0.05. MOR: μ-opioid receptor. (b) The scatter map of t-statistics of close friendship quantity and the density of the μ-opioid receptor. (c) The scatter map of t-statistics of close friendship quantity and the expression level of OPRM1 gene. (d) The scatter map of t-statistics of close friendship quantity and the expression level of OPRK1 gene.

Longitudinal and mediation results

As the nonlinear association between the number of close friends and ADHD symptoms is relatively strong and robust, and for cognitive outcomes, only crystalized intelligence was collected at 2-year follow-up in the ABCD study, we focused on these two measures in longitudinal and mediation analyses. The cross-lagged panel model (CLPM) revealed that participants having closer to five close friends had fewer ADHD symptoms 2 y later (β = 0.04, p<0.001; Figure 5a). CLPMs in separate groups confirmed that more close friends contributed to fewer ADHD symptoms in ≤5 group (β = –0.04, p=0.003; Figure 5—figure supplement 1a), but the effect reversed in the >5 group (β = 0.05, p=0.019; Figure 5—figure supplement 1b). The relationship between the absolute difference of close friend number to five and crystalized intelligence was bidirectional (Figure 5b). Only in the ≤5 group was a significant negative correlation found between crystalized intelligence at baseline and the number of close friends at 2-year follow-up (β = –0.06, p=0.001; Figure 5—figure supplement 1c and d).

Figure 5 with 1 supplement see all
Results of longitudinal and mediation analysis in the Adolescent Brain Cognitive Developmental (ABCD) study.

(a) Cross-lagged panel model (CLPM) of the absolute value of close friendship quantity to 5 and ADHD symptoms (N = 6013). Comparative fit index (CFI) = 0.996, Tucker–Lewis index (TFI) = 0.97, standardized root mean squared residual (SRMR) = 0.002, root mean square error of approximation (RMSEA) = 0.015. (b) CLPM of the absolute value of close friendship quantity to 5 and crystalized intelligence (N = 6013). CFI = 0.994, TFI = 0.96, SRMR = 0.003, RMSEA = 0.025. (c) Mediation analysis of close friendship quantity, the total area of significant regions, and ADHD symptoms. (d) The effect of individual significant cortical areas that mediated the association between close friendship quantity and ADHD symptoms after FDR correction. (e) Mediation analysis of close friendship quantity, the total area of significant regions and crystalized intelligence. (f) The effect of individual significant cortical areas that mediated the association between close friendship quantity and crystalized intelligence after FDR correction.

Mediation analyses were used to determine whether and the extent to which the association between the number of close friends, ADHD symptoms, and crystalized intelligence could be explained by the identified cortical areas in the ≤5 group. The total identified cortical area partly mediated the association between the number of close friends and ADHD symptoms (6.5%, 95% CI [3.4%, 14%]; path a*b: –0.005, 95% CI [-0.008,–0.003]; Figure 5c), and the mediation effects of individual significant regions ranged from 1.52 to 4.68% (Figure 5d). Similarly, the association between the number of close friends and crystalized intelligence was partly mediated by the total identified cortical area (13.5%, 95% CI [8.1%, 27%]; path a*b: 0.008, 95% CI [0.005, 0.01]; Figure 5e), ranging from 2.58 to 8.52% for each significant region (Figure 5f).

Findings in an independent social network dataset

Utilizing the social network dataset allowed us to extend findings in the ABCD study, as it is an independent and large dataset, a directed friendship network was generated by nomination, and different measures of mental health and cognition were collected (i.e., well-being and grade point average [GPA]). Three indicators of friendship network size (i.e., outdegree, indegree, and reciprocal degree; Figure 6) were significantly related to well-being (indegree: F = 38.63, p=1.8 × 10–17; outdegree: F = 33.55, p=2.9 × 10–15; reciprocal degree: F = 53.87, p=4.8 × 10–24; Figure 6—figure supplement 1a) and GPA (indegree: F = 28.08, p=6.7×10–13; outdegree: F = 46.66, p=6.2 × 10–21; reciprocal degree: F = 192.65, p=2.1 × 10–83; Figure 6—figure supplement 1b). Specifically, for well-being, all linear terms were significant, but only the quadratic term of outdegree was significant after Bonferroni correction (β = –2.9 × 10–4, t = –3.67, p=2.4 × 10–4, ΔR2 = 0.07%; Figure 6—figure supplement 1c). For GPA, the quadratic terms of all three indicators were significant, and the greatest effect size was observed in the outdegree (β = –0.001, t = –6.02, p=1.8 × 10–9, ΔR2 = 0.17%; Figure 6—figure supplement 1d). The two-lines tests revealed that the positive association of outdegree with well-being and GPA diminished once the outward nomination reached 7 or 8 (Figure 6—figure supplement 1d). The results confirmed that friendship network size especially outdegree was nonlinearly related to mental health and cognitive outcomes.

Figure 6 with 1 supplement see all
Distribution of outdegree, indegree, and reciprocal degree in the social network dataset.

(a) Distribution of outdegree which is the number of outward nominations. (b) Distribution of indegree which is the number of inward nominations. (c) Distribution of reciprocal degree which is the number of reciprocal nominations. Relationship of well-being with outdegree (d), indegree (e), and reciprocal degree (f). Relationship of grade point average (GPA) with outdegree (g), indegree (h), and reciprocal degree (i). In each bin, the mean (i.e., black dot) and standard error (i.e., error bar) of the dependent variable are shown. The red line is the fitted quadratic model. For outdegree, sample sizes of bins 1-11 are 92, 87, 208, 519, 803, 1230, 1326, 1286, 1235, 1151 and 8119. For indegree, sample sizes of bins 1-14 are 617, 728, 1116, 1341, 1526, 1563, 1532, 1462, 1273, 1095, 870, 1281, 716 and 936. For reciprocal degree, sample sizes of bins 1-11 are 797, 1561, 2356, 2774, 2765, 2260, 1685, 1039, 524, 220 and 75.

Discussion

The present study showed that close friendship quantity was associated with better mental health and higher cognitive functions in late childhood, and that the beneficial association diminished or reversed when increasing the number of close friends beyond a moderate level. The results also support the hypothesis that a quadratic association exists between the number of close friends and the areas of social brain regions such as the OFC, the ACC, insula, the anterior temporal cortex, and the TPJ. These regions mediated the nonlinear association between close friendship quantity and behavior. Furthermore, the brain differences related to the number of close friends were correlated with measures of the endogenous opioid involvement of the brain regions.

Social relationships play a double-edged role for mental health. Previous research has primarily focused on the positive aspects of social relationships, while the negative effects have received comparatively less attention (Song et al., 2021). In our study, we identified a robust nonlinear association of close friend quantity with various mental health and cognitive outcomes in the ABCD study at baseline and 2-year follow-up, and an independent social network dataset. This result demonstrates the persistence of the findings. The findings are in line with past studies, which showed that too large a social network size or too frequent social contacts were not positively correlated with well-being in adults (Kushlev et al., 2018; Ren et al., 2022; Stavrova and Ren, 2021) and were even negatively correlated with mental health in adolescents (Falci and McNeely, 2009). One explanation is that an individual’s cognitive capacity and time limit the size of the social network that an individual can effectively maintain (Dunbar, 2018). People devote about 40% of their total social efforts (e.g., time and emotional capital) to just their five most important people (Bzdok and Dunbar, 2020). In a phone-call dataset of almost 35 million users and 6 billion calls, a layered structure was found with the innermost layer having an average of 4.1 people (Mac Carron et al., 2016). There is a trade-off between the quantity and quality of friendships, with an increased number of close friends potentially leading to less intimacy. Meanwhile, spending too much time on social activities may lead to insufficient time for study and thereby to lower academic performance. Second, adolescents are particularly susceptible to peer influence (Berndt, 1979). Researchers have found that the presence of a peer may increase risk-taking behaviors that can be detrimental to mental health (Chein et al., 2011) and reduce cognitive performance (Wolf et al., 2015). Having more close friends may increase the possibility of this kind of influence.

Our study revealed a significant link between the number of close friends and the cortical areas of social brain regions in the largest sample of children to date. Studies suggest that two major systems in the brain related to social behavior include the affective system of the ACC, the anterior insula, and the OFC, and the mentalizing system typically involving the TPJ (Güroğlu, 2022; Schmälzle et al., 2017). The dorsal ACC and anterior insula play an important role in social pain (i.e., painful feelings associated with social disconnection) (Eisenberger, 2012). The OFC receives information about socially relevant stimuli such as face expression and gesture from the cortex in the superior temporal sulcus (Hasselmo et al., 1989a; Pitcher and Ungerleider, 2021), and is involved in social behavior by representing social stimuli in terms of their reward value (Rolls, 2019b; Rolls, 2019a; Rolls et al., 2006). The volume of the OFC is associated with social network size, partly mediated by mentalizing competence (Powell et al., 2012). Previous meta-analysis studies report an overlap in brain activation between all mentalizing tasks in the mPFC and posterior TPJ (Schurz et al., 2014). Notably, in our study, the positive relationship at the brain level only held for the children with no more than approximately five close friends, which is consistent with the behavioral findings. Furthermore, in these children, the areas of social brain regions partly mediated the relationship of the close friend quantity with ADHD symptoms and crystalized intelligence. Research also indicates that the brain regions regulating social behavior undergo structural development during adolescence (Blakemore, 2008; Lamblin et al., 2017; Mills et al., 2014). Animal studies provide evidence for the causal effect of social relationships on brain development. For instance, adolescent rodents with deprivation of peer contacts showed brain level changes including reduced synaptic pruning in the prefrontal cortex (Orben et al., 2020).

Moreover, the brain associative pattern of close friend quantity in children with no more than five close friends was correlated with the density of the μ-opioid receptor, as well as the expression of OPRM1 and OPRK1 genes. It is known that the endogenous opioid system has a vital role in social affiliative processes (Machin and Dunbar, 2011). Positron emission tomography studies in human revealed that μ-opioid receptor regulation in brain regions such as the amygdala, anterior insula, and the ACC may preserve and promote emotional well-being in the social environment (Hsu et al., 2013). Variation in the OPRM1 gene was associated with individual differences in rejection sensitivity, which was mediated by dorsal ACC activity in social rejection (Way et al., 2009). OPRM1 variation was also related to social hedonic capacity (Troisi et al., 2011). Pain tolerance, which is associated with activation of the μ-opioid receptor, was correlated with social network size in humans (Johnson and Dunbar, 2016). Social behaviors like social laughter and social touch increase pleasurable sensations and triggered endogenous opioid release to maintain social relationships (Dunbar, 2010; Manninen et al., 2017; Nummenmaa et al., 2016). Additionally, the opioid system has found to be associated with major psychiatric disorders especially depression (Peciña et al., 2019), which may help explain the association between social relationships and mental health problems.

Several issues should be taken into account when considering our findings. First, as an association study, no causal conclusion should be made in this study. It is unclear whether the number of close friends drives the social brain development or whether children with larger social brains tend to have more close friends. A bidirectional relationship has been reported in the literature (Dunbar and Shultz, 2007). Second, it is worth noting that the measures used in the ABCD study and the social network dataset differed, and the breakpoints identified in each dataset were not equivalent. However, relative to the optimal number of close friends, the primary objective of the current study was to examine the nonlinear relationship between the number of close friend and different behavioral outcomes and brain structure. In this sense, the findings from both datasets were similar, and the social network dataset provided valuable information regarding friendship measures and objective cognitive index that extended the results obtained from the ABCD study. Third, the quality of close friendships was not considered in the ABCD study. However, reciprocal degree is an indirect measure of friendship quality, which was found to be linearly associated with well-being and nonlinearly related to the GPA in the social network dataset. It has been reported that the relationship between having more friends and fewer depressive symptoms in adolescence is mediated by a sense of belonging (Ueno, 2005). Although current findings on the relative importance of friendship quantity and quality are inconsistent (Bruine de Bruin et al., 2020; Platt et al., 2014), it is essential for future studies to incorporate measures of close friendship quality and to test the potential interaction between quantity and quality. Finally, the interpretation of this study should be limited to the particular age range of late childhood and early adolescence, as well as Western culture. Further research is needed to explore whether the nonlinear relationship between the number of close friends and mental health and cognition, and the idea of having around five close friends as a breakpoint, can be generalized to other age ranges and cultures.

In conclusion, this study provides new evidence going beyond previous research that a larger number of close friends up to a moderate level in late childhood is associated with better mental health and higher cognitive functions, and that this can be partly explained by the size of the social brain including the OFC and TPJ, and the endogenous opioid system. This study may have implications for targeted friendship interventions in the transition from late childhood to early adolescence.

Materials and methods

Participants and behavioral measures

The ABCD study

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The ABCD study is tracking the brain development and health of a nationally representative sample of children aged 9–11 y from 21 centers throughout the United States (https://abcdstudy.org). Parents’ full written informed consent and all children’s assent were obtained by each center. Research protocols were approved by the institutional review board of the University of California, San Diego (no. 160091), and the institutional review boards of the 21 data collection sites (Auchter et al., 2018). The current study was conducted on the ABCD Data Release 4.0. At baseline, 8835 individuals from 7512 families (6225 [82.9%] with a child, 1252 [16.7%] with two children, 34 [0.5%] with three children, and 1 [0.01%] with four children) had complete behavioral and structural MRI data. To avoid the influence of family relatedness, we randomly picked only one child in each family, finally resulting in 7512 children, of whom 4290 had 2-year follow-up data.

Close friendships are characterized by enjoying spending time together, having fun, and trust. Participants were asked how many close friends that are boys and girls they have, respectively. Mental health problems were rated by the parent using the Child Behavior Checklist (CBCL), which contains 20 empirically based subscales spanning emotional, social and behavioral domains in subjects aged 6–18 (Achenbach and Rescorla, 2001). The CBCL has high inter-interviewer reliability, test–retest reliability, internal consistency, and criterion validity, and therefore is widely utilized by child psychiatrists, developmental psychologists, and other mental health professionals for clinical and research purposes (Achenbach et al., 1987). Raw scores were used in analyses, higher scores indicating more severe problems. Cognitive functions were assessed by the NIH Toolbox (Luciana et al., 2018), which has good reliability and validity in children (Akshoomoff et al., 2013). The toolbox consists of seven different tasks covering episodic memory, executive function, attention, working memory, processing speed, and language abilities, and also provides three composites of crystalized, fluid, and total intelligence (Weintraub et al., 2013). Uncorrected standard scores were used in analyses. All 10 cognitive scores were available at baseline, but only crystalized intelligence was collected 2 y later.

Social network dataset

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In order to extend the findings in the ABCD study, we utilized a publicly available dataset of a social network experiment, conducted among students in 56 middle schools in New Jersey, USA (Paluck et al., 2016) (https://www.icpsr.umich.edu/web/civicleads/studies/37070). All parents and students provided informed consent for the survey, and the research protocol was approved by the Princeton University Institutional Review Board. Participants were asked to report which other students (up to 10) in their school they chose to spend time with in the last few weeks, allowing us to generate a directed friendship network. Three kinds of network measures were created for each participant: (1) outdegree is a measure of sociability and refers to the number of friendship nominations that a participant made to other participants, (2) indegree is a measure of popularity and refers to the number of friendship nominations received from others, and (3) reciprocal degree refers to the number of outward nominations that are reciprocated by an inward nomination from the same person and to some extent reflects the quality of friendship. Well-being was assessed by three questions: ‘I feel like I belong at this school,’ ‘I have stayed home from school because of problems with other students,’ and ‘During the past month, I have often been bothered by feeling sad and down’ (Ren et al., 2022). Cognitive function was indirectly measured by the GPA on a 4.0 scale, obtained from school administrative records.

Structural MRI data

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In the ABCD study, 3D T1- and T2-weighted structural images were collected using 3T scanners at 21 data collecting sites (Casey et al., 2018). The detailed preprocessing pipeline has been described elsewhere (Gong et al., 2021). In brief, we used FreeSurfer v6.0 to preprocess the minimal preprocessed T1- and T2-weighted images downloaded from the ABCD study, including cortical surface reconstruction, subcortical segmentation, smoothed by a Gaussian kernel (FWHM = 10 mm), and estimation of morphometric measures (i.e., cortical area, thickness, and volume). Then, the cortical surface of each subject was registered to a standard fsaverage space and parcellated into 180 cortical regions per hemisphere as defined in the Human Connectome Project multimodal parcellation (HCP-MMP) atlas (Glasser et al., 2016). Volumetric reconstructions of subcortical structures were also obtained based on the Aseg atlas (Fischl et al., 2002).

Neurochemical data

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Fourteen receptors and transporters across eight different neurotransmitter systems (serotonin: 5HT1a, 5HT1b, 5HT2a, 5HT4, and 5HTT; dopamine: D1, D2, and DAT; GABA: GABAa; glutamate: mGluR5; norepinephrine: NAT; cannabinoid: CB1; opioid: MOR; acetylcholine: VAChT) were investigated. Density estimates were derived from average group maps of healthy volunteers scanned in prior PET and SPECT studies (Supplementary file 1). All density maps were downloaded online (https://github.com/juryxy/JuSpace/tree/JuSpace_v1.3/JuSpace_v1.3/PETatlas; Dukart et al., 2021), which had been registered and normalized into the Montreal Neurological Institute (MNI) space, and linearly rescaled to 0–100 (Dukart et al., 2021). For comparability, the HCP atlas in fsaverage space was converted to individual surface space (‘mri_surf2surf’) of the MNI brain template ch2 (Rorden and Brett, 2000) which was preprocessed by Freesurfer (‘recon-all’), and then was projected to volume (‘mri_label2vol’). The density maps were parcellated into the 360 cortical regions as the structural MRI data according to the volume-based HCP-MMP atlas. Specifically, for the μ-opioid receptor, occipital cortex served as the reference region (Kantonen et al., 2020) and was therefore excluded in analysis.

Transcriptomic data

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Gene expression data was from six neurotypical adult brains in the Allen Human Brain Atlas (Hawrylycz et al., 2012). We focused on the opioid receptor genes (i.e., OPRM1 and OPRK1). The preprocessed transcriptomic data were imported from Arnatkeviciute et al., 2019 (https://doi.org/10.6084/m9.figshare.6852911), including probe-to-gene re-annotation, intensity-based data filtering, and probe selection using RNA-seq data as a reference. Then, samples were assigned to brain regions according to the volume-based HCP-MMP atlas, and expression values were averaged within each region. Since right hemisphere data were only available for two donors, analyses were conducted on the left hemisphere only, finally resulting in 177 brain regions.

Statistical analysis

Nonlinear association analysis

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The nonlinear associations of close friendship quantity with mental health, cognition, and brain structure were investigated. The quantity of close friendship was log-transformed [log10(x + 1)] in analyses as it has a skewed distribution (Hobbs et al., 2016). Two different analytic approaches were used to robustly evaluate the nonlinear relationships. First, we fitted a quadratic regression model (y = bx2+ ax + c) with close friendship quantity as the independent variable. Close friendship quantity was mean-centered to ensure that the linear (a) and quadratic (b) terms were orthogonal. Three statistical parameters were of interest: a total F-value of linear and quadratic terms, reflecting the association between close friendship quantity and the measure of interest (Li et al., 2022); the quadratic term, indicating the presence of a nonlinear association; and the linear term. The effect size of the quadratic term was calculated by the change in the overall proportion of variance (adjusted R2) between the quadratic model and the corresponding linear model, and the effect size of the linear term was the ΔR2 between the linear model and the model with only covariates. The model fits of quadratic and linear models were compared by ANOVA. Although quadratic regression is widely used in psychosocial studies to detect the presence of nonlinearity (Nook et al., 2018; Ren et al., 2022), simulation studies showed that this approach for testing a U-shaped effect has a high false positive rate (Simonsohn, 2018). Therefore, we conducted a two-lines test (Simonsohn, 2018) once a significant quadratic term was found, which could estimate a data-driven breakpoint. We then split the data accordingly to fit two linear models, respectively. If the segment slopes have opposite signs and both of them are significant, a U-shaped relation exists. Same analytic approaches were used in behavioral and neuroimaging analyses. In the ABCD study, sex, age, parent education level, household income, ethnicity, puberty, body mass index (BMI), and site were used as covariates of no interest for the behavioral analyses. For the neuroimaging analyses, we additionally controlled for handedness, head motion, and MRI manufacturer. In the social network dataset, we controlled for sex, age, grade, whether the subject was or was not new to the school, and whether or not most friends went to this school. Bonferroni correction was used in behavioral analyses, and FDR correction was used in neuroimaging analyses.

Several sensitivity analyses were performed. To examine the potential sex influence, we conducted nonlinear association analyses in male and female, respectively. The effect of the sex of close friends was tested by separating close friends into same-sex and opposite-sex ones. To validate the findings from data at baseline and to test the hypothesis of stationarity for cross-lagged panel models (CLPM), we replicated the same analyses using the cross-sectional data collected at 2 y later. For neuroimaging analyses, if significant nonlinear associations were detected, we also conducted linear regression models in two groups split by the average breakpoint, respectively.

Spatial correlation with neurotransmitter density and gene expression

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Unthresholded t-statistic maps of brain structure associated with close friendship quantity in two groups (i.e., split by the average breakpoint) were used to correlate with neurotransmitter density and gene expression level by Spearman’s rank correlation. Bootstrapping was performed to ensure the robustness, and the significance was tested by 5000 times permutation, in which the correlation was re-computed using null t-statistic maps obtained by label shuffling for close friendship quantity (Chen et al., 2021).

Cross-lagged panel analysis

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Longitudinal relationships of close friendship quantity with ADHD symptoms (i.e., cbcl_scr_syn_attention) and crystalized intelligence were investigated using classic two-wave CLPMs implemented by Mplus 7.0. Firstly, we conducted CLPMs using the absolute value of the difference between close friendship quantity and the breakpoint, and then established CLPMs for participants with the quantity of close friendship ≤breakpoint and >breakpoint at baseline, respectively. We controlled for several stable (i.e., sex, parent education level, ethnicity, and site) and time-variant variables (i.e., age, household income, and puberty) in these models. The CLPMs met important assumptions such as synchronicity and stationarity (Baribeau et al., 2022; Kenny, 1975). The model parameters were estimated by the full information maximum likelihood method (Muthén et al., 1987). The model fit was evaluated by the Tucker–Lewis index (TLI), comparative fit index (CFI), root mean square error of approximation (RMSEA), and standardized root mean squared residual (SRMR), and interpreted using common thresholds of good fit (Hu and Bentler, 1999). All CLPMs reported in the current study have a good model fit.

Mediation analysis

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We used the baseline data in the ABCD study to test the associations between close friendship quantity, ADHD symptoms, crystalized intelligence, and brain structure. The total area of the significant brain regions was used as the mediator. Variables were normalized and then entered into the model. Sex, age, parent education level, household income, ethnicity, pubertal status, BMI, handedness, head motion, MRI manufacturer, and site were used as covariates of no interest. In addition to the total area, the mediation effect of individual significant regions was also evaluated, the p-values of the mediation effect corrected by FDR correction. Total, direct, and indirect associations were estimated by bootstrapping 10,000 times, and the 95% bias-corrected and accelerated confidence interval (CI) was reported. Analyses were performed using the R mediation package.

Data availability

The ABCD dataset is administered by the National Institutes of Mental Health Data Archive and is freely available to all qualified researchers upon submission of an access request (https://nda.nih.gov/abcd). All relevant instructions to obtain the data can be found in https://nda.nih.gov/abcd/request-access. The request is valid for one year. Data use should be in line with the NDA Data Use Certification. The social network dataset is openly available (https://www.icpsr.umich.edu/web/civicleads/studies/37070). Neurochemical data used in analysis are openly available (https://github.com/juryxy/JuSpace/tree/JuSpace_v1.3/JuSpace_v1.3/PETatlas). Gene expression data are openly available (https://figshare.com/articles/dataset/AHBAdata/6852911). The code used for this study is publicly available at https://github.com/chunshen617/friendship (copy archived at Shen, 2023).

The following previously published data sets were used
    1. Paluck EL
    2. Shepherd HR
    3. Aronow P
    (2020) CivicLEADS
    Changing Climates of Conflict: A Social Network Experiment in 56 Schools, New Jersey, 2012-2013.
    https://doi.org/10.3886/ICPSR37070.v2
    1. Arnatkevic̆iūtė A
    2. Fulcher BD
    3. Fornito A
    (2019) figshare
    A practical guide to linking brain-wide gene expression and neuroimaging data.
    https://doi.org/10.6084/m9.figshare.6852911

References

  1. Book
    1. Achenbach T
    2. Rescorla L
    (2001)
    Manual for the ASEBA School-Age Forms & Profiles: An Integrated System of Multi-Informant Assessment
    Burlington, VT: ASEBA.
    1. Baribeau DA
    2. Vigod S
    3. Brittain H
    4. Vaillancourt T
    5. Szatmari P
    6. Pullenayegum E
    (2022)
    Application of transactional (cross-lagged panel) models in mental health research: an introduction and review of methodological considerations
    Journal of the Canadian Academy of Child and Adolescent Psychiatry = Journal de l’Academie Canadienne de Psychiatrie de l’enfant et de l’adolescent 31:124–134.

Decision letter

  1. Robert Whelan
    Reviewing Editor; Trinity College Dublin, Ireland
  2. Christian Büchel
    Senior Editor; University Medical Center Hamburg-Eppendorf, Germany
  3. Robert Whelan
    Reviewer; Trinity College Dublin, Ireland
  4. Lisa Schreuders
    Reviewer; Leiden University, Netherlands

Our editorial process produces two outputs: i) public reviews designed to be posted alongside the preprint for the benefit of readers; ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.

Decision letter after peer review:

Thank you for submitting your article "Brain and molecular mechanisms underlying the nonlinear association between close friendships, mental health, and cognition in children" for consideration by eLife. Your article has been reviewed by 2 peer reviewers, including Robert Whelan as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Christian Büchel as the Senior Editor. The following individual involved in the review of your submission has agreed to reveal their identity: Lisa Schreuders (Reviewer #2).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential revisions:

1. Confirm that the statistical assumptions needed for CLPMs have been met?

2. In places, the phrasing is such that the reader could infer a direction of the effect in the cross-sectional results (e.g., line 173: "The ideal number of close friends was 5 and the closer to that number, the better *for* participants' mental health." [my emphasis]). Any such phrasing should be amended.

3. Can you put effect sizes more into context for the reader (i.e., what do results of these magnitudes mean in the real world)?

4. Provide a rationale for 5 friends as the breakpoint when the curve appears u-shaped. Looking at Figure 2, there is a grouping of close friend size between ~2 to ~10 (i.e., the bottom of the u is quite flat there). Although the breakpoint is 5 close friends, could one argue that poorer outcomes tend to occur at a higher number of close friends? That is, problems start when the slope of the upward curve starts to steepen (this would also suggest a result more closely aligned with the social network dataset, albeit the measures are different)?

5. Include some more information on the specific age-range that you are interested in for the study in the introduction/discussion.

6. In lines 181-184 it is stated that "Finally, same analyses were performed using the cross-sectional data collected at 2 years later, and the nonlinear associations of the number of close friends with ADHD symptoms and crystalized intelligence remained significant, with an average breakpoint of 4.83 {plus minus} 0.75 close friends (Figure S5)."

6a: So, all other found relations were not significant at follow up two years later? Please state this explicitly.

6b: In the discussion the authors do not elaborate on this result. What do the authors make from this?

7. Re. Figure S10e (explained in lines 230-232). Could the authors please explain how a correlation can be estimated between "the differences in cortical area related to the number of close friends in the two groups". This reads as if a correlation has been performed to test for between-subject differences.

8. It is unclear what the authors mean with the three indicators of friendship network size from the independent social network dataset (indegree, outdegree, reciprocal degree). This makes it hard to interpret the results. Please explicitly explain these terms.

9. Were the independent behavioral variables collected in the ABCD and independent dataset reliable?

Reviewer #1 (Recommendations for the authors):

Table 1 in the main manuscript described several characteristics of the ABCD dataset. More information would be helpful for the reader. Could you give a breakdown on all variables for the 2 groups (on the breakpoint of over and under 5 friends)? Are other, potentially relevant, variables available for the two groups? For example, position in family, family size, urban vs. rural dwelling etc. Perhaps rural dwellers have fewer opportunities to have a large circle of close friends, and perhaps rural dwellers are systematically different in other ways (e.g., diet, mental health).

I have little expertise with cross-lagged panel models; can you confirm that the statistical assumptions needed for CLPMs have been met?

I didn't find the inclusion of the second dataset especially convincing. I appreciate that ABCD is unique (and therefore finding a replication sample is very challenging), but the social network dataset was quite different in the measures used. After reading the manuscript I was left with the impression that calling the social network dataset results a 'validation' was somewhat of a stretch. The results of two datasets were broadly similar (breakpoint at 5 in ABCD, ~8 outward nomination in the social network dataset) rather than a validation per se.

In places, the phrasing is such that the reader could infer a direction of the effect in the cross-sectional results (e.g., line 173: "The ideal number of close friends was 5 and the closer to that number, the better *for* participants' mental health." [my emphasis]).

This is not a limitation of your study but, as I mentioned in the public review, the effect sizes are very small. For example, in the social network dataset the β for GPA was 0.001. I would rather read a paper with a huge sample size and small effect sizes than vice-versa but could you put the effect sizes into context for the reader?

Looking at Figure 2, there is a grouping of close friend size between ~2 to ~10 (i.e., the bottom of the u is quite flat there). Although the breakpoint is 5 close friends, could one argue that poorer outcomes tend to occur at a higher number of close friends? That is, problems start when the slope of the upward curve starts to steepen (this would also suggest a result more closely aligned with the social network dataset, albeit the measures are different)? The discussion of 5 as the breakpoint is more appropriate when the curve is v-shaped rather than u-shaped.

Reviewer #2 (Recommendations for the authors):

I am excited about this paper and believe it is of added value to the existing literature, but I would appreciate a clearer theoretical framework with regards to why certain biological constructs were assessed in this study (introduction) and interpretation of the results in the context of the existing literature (discussion) (see public review). I outline my remaining questions in more detail below.

The authors do not specify anything about the specific age-range they were interested in for the study in the introduction/discussion.

In lines 181-184 it is stated that "Finally, same analyses were performed using the cross-sectional data collected at 2 years later, and the nonlinear associations of the number of close friends with ADHD symptoms and crystalized intelligence remained significant, with an average breakpoint of 4.83 {plus minus} 0.75 close friends (Figure S5)."

(a) So, all other found relations were not significant at follow up two years later? Please state this explicitly.

(b) Furthermore, I believe in the discussion the authors do not elaborate on this result. What do the authors make from this?

I do not follow what is exactly being tested in Figure S10e (explained in lines 230-232). Could the authors please explain how a correlation can be estimated between "the differences in cortical area related to the number of close friends in the two groups". This reads as if a correlation has been performed to test for between-subject differences.

It is unclear what the authors mean with the three indicators of friendship network size from the independent social network dataset (indegree, outdegree, reciprocal degree). This makes it hard to interpret the results. Please explicitly explain these terms.

Were the independent behavioral variables collected in the ABCD and independent dataset reliable?

https://doi.org/10.7554/eLife.84072.sa1

Author response

Essential revisions:

1. Confirm that the statistical assumptions needed for CLPMs have been met?

Cross-lagged panel model (CLPM) is a method to examine the directional effects between two variables over time, simultaneously considering the synchronous and autoregressive relations. In the present study, we used the most basic CLPM which includes two constructs measured at two time points. Several important assumptions need to be met for CLPM (Baribeau et al., 2022; Kenny, 1975).

1) The synchronicity assumption requires that all measurements at each time point occurred at the same time, which is met for the data collection in the ABCD study.

2) Stationarity requires variables and relationships stay the same across time. We have confirmed that ADHD symptoms and crystalized intelligence were nonlinearly related to the number of close friends, with a breakpoint of around 5 close friends, at both baseline and 2-year follow-up (see the Results section).

3) Measurement error: The variables are assumed to be measured without error. However, it is difficult to assess measurement error directly. The assessments of ADHD symptoms and crystalized intelligence in the ABCD study are reliable and valid, which is helpful to minimize the measurement error.

4) Linearity: Relations between variables of interest are linear. We fitted CLPMs using the absolute difference of close friend quantity and the breakpoint, and CLPMs in participants with ≤5 and >5 close friends, respectively. Although we found nonlinear relationships of the number of close friends with ADHD symptoms and crystalized intelligence, the associations within groups by the breakpoint is linear.

5) A sufficient sample size of 200 participants has been proposed for CLPMs with two waves. Indeed, our study exceeds this, our sample size was in the thousands.

Finally, we used the Tucker-Lewis Index (TLI), Comparative Fit Index (CFI), root mean square error of approximation (RMSEA) and standardized root mean squared residual (SRMR) to assess the model fit. For the maximum likelihood method, a cutoff value close to 0.95 for TFI and CFI, a cutoff value close to 0.06 for RMSEA and 0.08 for SRMR indicate a good fit (Hu & Bentler, 1999). All CLPMs conducted in the present study have a good model fit.

We have now stated the assumptions and model fit criteria in the Statistical analysis, and reported the values of the model fit indices in the caption of Figure 5.

“The CLPMs met important assumptions such as synchronicity and stationarity (Baribeau et al., 2022; Kenny, 1975). The model parameters were estimated by the full information maximum likelihood method (Muthén et al., 1987). The model fit was evaluated by the Tucker-Lewis Index (TLI), Comparative Fit Index (CFI), root mean square error of approximation (RMSEA) and standardized root mean squared residual (SRMR), and interpreted using common thresholds of good fit (Hu & Bentler, 1999). All CLPMs reported in the current study have a good model fit.” (Lines 552-559, Page 27)

“a. CLPM of the absolute value of close friendship quantity to 5 and ADHD symptoms (N=6,013). CFI = 0.996, TFI = 0.97, SRMR = 0.002, RMSEA = 0.015. b. CLPM of the absolute value of close friendship quantity to 5 and crystalized intelligence (N=6,013). CFI = 0.994, TFI = 0.96, SRMR = 0.003, RMSEA = 0.025.”

2. In places, the phrasing is such that the reader could infer a direction of the effect in the cross-sectional results (e.g., line 173: "The ideal number of close friends was 5 and the closer to that number, the better *for* participants' mental health." [my emphasis]). Any such phrasing should be amended.

Thank you for pointing out this. Indeed, it is impossible to infer a direction of the effect from cross-sectional data, as such data do not allow for the assessment of temporal precedence between variables. Further revisions shown in the paper:

“Both mental health and cognition were positively associated with close friend quantity, with an ideal number of around 5.” (see Lines 171-173, Page 9)

3. Can you put effect sizes more into context for the reader (i.e., what do results of these magnitudes mean in the real world)?

We agree with the Reviewer that the large sample size derives low P-values for even small effect sizes. Therefore, we reported effect sizes of the quadratic and linear terms calculated by the change in the adjusted R2. For example, at baseline, the greatest effect sizes of quadratic terms were observed for social problems and total intelligence. The results showed that the quadratic term of close friend quantity additionally explained 0.43% and 0.50% of the variability, respectively, compared with the corresponding linear models. Complex psychological factors are typically determined by a multitude of causes, and any individual cause is likely to have only a small effect (Götz et al., 2022). Although the effect size is small, our primary aim is to investigate the nonlinear links between the number of close friend, mental health, and cognition, as the effect of the friendship network size at the high end remains largely unexplored in children and adolescent. We utilized two independent datasets of large sample sizes and different statistical approaches to show that the nonlinear associations are reliable and solid to various confounders. As the friendship quantity is a modifiable factor, a small but reliable effect size can be valuable.

To further contextualize the effect sizes, we have included the following in the Results:

“For mental health, the greatest effect sizes of the quadratic terms were observed for social problems (β = 0.08, t = 5.92, p = 3.3⨉10-9, ΔR2 = 0.43%) and attention problems (β = 0.12, t = 5.83, p = 5.8⨉10-9, ΔR2 = 0.42%), suggesting that the quadratic term of close friend quantity additionally explained 0.43% and 0.50% of the variability compared with the corresponding linear model.” (Lines 159-164, Pages 8-9).

4. Provide a rationale for 5 friends as the breakpoint when the curve appears u-shaped. Looking at Figure 2, there is a grouping of close friend size between ~2 to ~10 (i.e., the bottom of the u is quite flat there). Although the breakpoint is 5 close friends, could one argue that poorer outcomes tend to occur at a higher number of close friends? That is, problems start when the slope of the upward curve starts to steepen (this would also suggest a result more closely aligned with the social network dataset, albeit the measures are different)?

In our study, we conducted two-lines tests to detect U-shaped relationships, which involves a sign change, to complement the estimation of quadratic regression models. The Robin Hood algorithm is used to set a breakpoint to maximize the statistical power for U-shape testing instead of fitting the data as well as possible. Thus, the algorithm determines a breakpoint that will increase the statistical strength of the weaker of the two lines by allocating more observations to that segment without overly attenuating its slope (Simonsohn, 2018). We found the breakpoints for mental health and cognition ranged from 4 to 6 close friends, with an average of 4.89 ± 0.68 (Figure 2h).

However, we acknowledge the Reviewer's concern that poorer outcomes may occur at higher numbers of close friends. As we have clarified, the primary objective of our study is to examine the nonlinear relationships between the number of close friends, mental health, and cognition rather than determining the optimal number of close friends. Therefore, we have now revised our statement of the breakpoint to "around 5" or “approximately 5” in the manuscript, and provided additional explanations in the Discussion.

“Second, it is worth noting that the measures used in the ABCD study and the social network dataset differed, and the breakpoints identified in each dataset were not equivalent. However, relative to the optimal number of close friends, the primary objective of the current study was to examine the nonlinear relationship between the number of close friend and different behavioral outcomes and brain structure.” (Lines 364-369, Page 18)

5. Include some more information on the specific age-range that you are interested in for the study in the introduction/discussion.

Thank you for your constructive comment. We have revised the Introduction to make it more focused on the specific age-range of interest by updating the reference and adding the specific age-range when citing it. Additionally, we have clarified the theoretical framework by explaining the rationale behind assessing the social brain.

“For now, only a few empirical studies have examined the nonlinear association between social relationships, mental health, and cognition in children and adolescents. For instance, a large study of a nationally representative sample in the United States reported that adolescents with either too many or too few friends had higher levels of depressive symptoms (Falci & McNeely, 2009).” (Lines 77-81, Pages 4-5)

“Despite a large body of evidence linking friendships to mental health and cognition, we know relatively little about the underlying mechanisms involved (Pfeifer & Allen, 2021). The social brain hypothesis proposes that the evolution of brain size is driven by complex social selection pressures (Dunbar & Shultz, 2007). Animal studies have shown that social network size can predict the volume of the mid-superior temporal sulcus (Sallet et al., 2011; Testard et al., 2022), a region in which neurons respond to socially relevant stimuli such as face expression and head movement to make or break social contact (Hasselmo, Rolls, & Baylis, 1989; Hasselmo, Rolls, Baylis, et al., 1989). In human neuroimaging studies, several key brain regions, including the medial prefrontal cortex (mPFC, i.e. orbitofrontal [OFC] and anterior cingulate cortex [ACC]), the cortex in the superior temporal sulcus (STS), the temporo-parietal junction (TPJ), amygdala, and the anterior insula, have been implicated in social cognitive processes (Frith & Frith, 2007). Moreover, there has been an increasing number of studies dedicated to investigating the social brain in children and adolescents over the past decade (Andrews et al., 2021; Burnett et al., 2011).

At the molecular level, the μ-opioid receptor is widely distributed in the brain, particularly in regions associated with social pain such as the ACC and anterior insula (Baumgärtner et al., 2006). Recent studies have identified the crucial role of μ-opioid receptors in forming and maintaining friendships (Dunbar, 2018), and variations in the μ-opioid receptor gene have been related to individual differences in rejection sensitivity (Way et al., 2009). In addition, other neurotransmitters including dopamine, serotonin, GABA, and noradrenaline may interact with the opioids, and are involved in social affiliation and social behavior (Machin & Dunbar, 2011). Dysregulation of the social brain and neurotransmitter systems is also implicated in the pathophysiology of major psychiatric disorders (Porcelli et al., 2019). Taken together, it is suggested that changes in the social brain might explain the relationship between social connections and mental health (Lamblin et al., 2017). However, the empirical evidence on this topic is limited in late childhood and adolescence.” (Lines 89-117, Pages 5-6)

We have also rewritten the Discussion to make the main messages in each paragraph clear.

“Social relationships play a double-edged role for mental health. Previous research has primarily focused on the positive aspects of social relationships, while the negative effects have received comparatively less attention (Song et al., 2021). In our study, we identified a robust nonlinear association of close friend quantity with various mental health and cognitive outcomes in the ABCD study at baseline and 2-year follow-up, and an independent social network dataset. This result demonstrates the persistence of the findings. The findings are in line with past studies, which showed that too large a social network size or too frequent social contacts were not positively correlated with well-being in adults (Kushlev et al., 2018; Ren et al., 2022; Stavrova & Ren, 2021) and were even negatively correlated with mental health in adolescents (Falci & McNeely, 2009). One explanation is that an individual’s cognitive capacity and time limit the size of the social network that an individual can effectively maintain (Dunbar, 2018). People devote about 40% of their total social efforts (e.g., time and emotional capital) to just their 5 most important people (Bzdok & Dunbar, 2020). In a phone-call dataset of almost 35 million users and 6 billion calls, a layered structure was found with the innermost layer having an average of 4.1 people (Mac Carron et al., 2016). There is a trade-off between the quantity and quality of friendships, with an increased number of close friends potentially leading to less intimacy. Meanwhile, spending too much time on social activities may lead to insufficient time for study and thereby to lower academic performance. Second, adolescents are particularly susceptible to peer influence (Berndt, 1979). Researchers have found that the presence of a peer may increase risk-taking behaviors which can be detrimental to mental health (Chein et al., 2011), and reduce cognitive performance (Wolf et al., 2015). Having more close friends may increase the possibility of this kind of influence.

Our study revealed a significant link between the number of close friends and the cortical areas of social brain regions in the largest sample of children to date. Studies suggest that two major systems in the brain related to social behavior include the affective system of the ACC, the anterior insula, and the OFC, and the mentalizing system typically involving the TPJ (Güroğlu, 2022; Schmälzle et al., 2017). The dorsal ACC and anterior insula play an important role in social pain (i.e., painful feelings associated with social disconnection) (Eisenberger, 2012). The OFC receives information about socially relevant stimuli such as face expression and gesture from the cortex in the superior temporal sulcus (Hasselmo, Rolls, & Baylis, 1989; Pitcher & Ungerleider, 2021), and is involved in social behavior by representing social stimuli in terms of their reward value (Rolls, 2019a, 2019b; Rolls et al., 2006). The volume of the OFC is associated with social network size, partly mediated by mentalizing competence (Powell et al., 2012). Previous meta-analysis studies report an overlap in brain activation between all mentalizing tasks in the mPFC and posterior TPJ (Schurz et al., 2014). Notably, in our study, the positive relationship at the brain level only held for the children with no more than approximately 5 close friends, which is consistent with the behavioral findings. Furthermore, in these children, the areas of social brain regions partly mediated the relationship of the close friend quantity with ADHD symptoms and crystalized intelligence. Research also indicates that the brain regions regulating social behavior undergo structural development during adolescence (Blakemore, 2008; Lamblin et al., 2017; Mills et al., 2014). Animal studies provide evidence for the causal effect of social relationships on brain development. For instance, adolescent rodents with deprivation of peer contacts showed brain level changes including reduced synaptic pruning in the prefrontal cortex (Orben et al., 2020).

Moreover, the brain associative pattern of close friend quantity in children with no more than five close friends was correlated with the density of the μ-opioid receptor, as well as the expression of OPRM1 and OPRK1 genes. It is known that the endogenous opioid system has a vital role in social affiliative processes (Machin & Dunbar, 2011). Positron emission tomography studies in human revealed that μ-opioid receptor regulation in brain regions such as the amygdala, anterior insula, and the ACC may preserve and promote emotional well-being in the social environment (Hsu et al., 2013). Variation in the OPRM1 gene was associated with individual differences in rejection sensitivity, which was mediated by dorsal ACC activity in social rejection (Way et al., 2009). OPRM1 variation was also related to social hedonic capacity (Troisi et al., 2011). Pain tolerance, which is associated with activation of the μ-opioid receptor, was correlated with social network size in humans (Johnson & Dunbar, 2016). Social behaviors like social laughter and social touch increase pleasurable sensations and triggered endogenous opioid release to maintain social relationships (Dunbar, 2010; Manninen et al., 2017; Nummenmaa et al., 2016). Additionally, the opioid system has found to be associated with major psychiatric disorders especially depression (Peciña et al., 2019), which may help explain the association between social relationships and mental health problems.” (Lines 291-358, Pages 15-18)

6. In lines 181-184 it is stated that "Finally, same analyses were performed using the cross-sectional data collected at 2 years later, and the nonlinear associations of the number of close friends with ADHD symptoms and crystalized intelligence remained significant, with an average breakpoint of 4.83 {plus minus} 0.75 close friends (Figure S5)."

6a: So, all other found relations were not significant at follow up two years later? Please state this explicitly.

We have clarified the results of nonlinear association analyses using 2-year follow-up data.

“Finally, the same analyses were performed using the cross-sectional data collected 2 years later (Figure 2—figure supplement 5). The number of close friends was significantly associated with 10 out of 20 mental health measures, and 3 out of 6 cognitive scores. Significant nonlinear associations were observed between close friend quantity and 5 measures, with an average breakpoint of 4.60 ± 0.55 close friends. The greatest effect sizes of the quadratic terms were observed for attention problems (β = 0.10, t = 3.63, p = 2.9⨉10-4, ΔR2 = 0.27%) and crystalized intelligence (β = -0.24, t = -4.70, p = 2.7⨉10-6, ΔR2 = 0.36%) for mental health and cognition, respectively.” (Lines 180-187, Pages 9-10)

6b: In the discussion the authors do not elaborate on this result. What do the authors make from this?

There are two reasons to examine the nonlinear relationship between the number of close friends and mental health and cognition in the ABCD study at 2-year follow-up: (1) validate the nonlinear relationship observed at baseline, and (2) investigate the influence of age on the breakpoint of close friend quantity. In addition to show the reliability of nonlinear findings, this analysis confirmed the important hypothesis of stationarity for the cross-lagged panel model, which requires variables and relationships stay the same across time. We have now described the aim of this analysis in the Method and briefly stated the findings in the Discussion.

“To validate the findings from data at baseline and to test the hypothesis of stationarity for cross-lagged panel models (CLPM), we replicated the same analyses using the cross-sectional data collected at 2 years later.” (Lines 529-531, Page 26)

“In our study, we identified a robust nonlinear association of close friend quantity with various mental health and cognitive outcomes in the ABCD study at baseline and 2-year follow-up, and an independent social network dataset. This result demonstrates the persistence of the findings.” (Lines 293-297, Page 15)

7. Re. Figure S10e (explained in lines 230-232). Could the authors please explain how a correlation can be estimated between "the differences in cortical area related to the number of close friends in the two groups". This reads as if a correlation has been performed to test for between-subject differences.

In order to illustrate the patterns of nonlinear associations between the number of close friends and cortical area, we performed linear regression models in participants with ≤ 5 and > 5 close friends, respectively. Then, we examined the spatial correlation between the unthresholded t-statistic maps of two groups (i.e., obtained from linear regression). We found the correlation was not significant (r = -0.02, p = 0.78; Figure 3—figure supplement 5e), suggesting that the brain associative patterns of close friend quantity in two groups were not similar. Now we have revised the statement in the Results to avoid confusion.

“Moreover, the cortical area associative patterns of close friend quantity in the two groups were not correlated (r = -0.02, p = 0.78; Figure 3—figure supplement 5e).” (Lines 219-221, Page 11)

8. It is unclear what the authors mean with the three indicators of friendship network size from the independent social network dataset (indegree, outdegree, reciprocal degree). This makes it hard to interpret the results. Please explicitly explain these terms.

We agree with the Reviewer that these terms were not explicitly explained in the manuscript. In the social network dataset, participants were asked to report which other students in their school they chose to spend time with in the last few weeks, allowing us to generate a directed friendship network. Outdegree refers to the number of friendship nominations that a participant made to others (i.e., outward nomination), and is a measure of their sociability. Indegree is a measure of popularity and refers to the number of friendship nominations received from other participants (i.e., inward nomination). Reciprocal degree is defined as the number of outward nominations that are reciprocated by an inward nomination from the same person, to some extent reflecting the quality of friendship. Now we have clarified the definitions in the Methods.

“Participants were asked to report which other students (up to ten) in their school they chose to spend time with in the last few weeks, allowing us to generate a directed friendship network. Three kinds of network measures were created for each participant: (1) outdegree is a measure of sociability and refers to the number of friendship nominations that a participant made to other participants, (2) indegree is a measure of popularity and refers to the number of friendship nominations received from others, and (3) reciprocal degree refers to the number of outward nominations that are reciprocated by an inward nomination from the same person and to some extent reflects the quality of friendship.” (Lines 434-442, Pages 21-22)

9. Were the independent behavioral variables collected in the ABCD and independent dataset reliable?

In the ABCD study, mental health problems were rated by the parent using the Child Behavior Checklist (CBCL). The CBCL has high inter-interviewer reliability (ICC > 0.9), test-retest reliability (r for each scale > 0.8), internal consistency (mean Cronbach’s α for each scale = 0.85) and criterion validity, and therefore is widely utilized by child psychiatrists, developmental psychologists, and other mental health professionals for clinical and research purposes (Achenbach et al., 1987; Achenbach & Rescorla, 2001). Cognitive functions were assessed by the NIH Toolbox (Luciana et al., 2018). The toolbox has showed excellent test-retest reliability (ICC > 0.78), robust developmental effects across the childhood age range, and strong correlations with established measures of similar abilities and school performance (Akshoomoff et al., 2013; Weintraub et al., 2013). In the social network dataset, as no well-documented mental health questionnaire was available, we used three binary questions as Ren et al.’s study (Ren et al., 2022) to measure well-being. For cognition, we obtained the grade point average from school administrative records as an indirect index.

We have cited references to demonstrate the reliability and validity of behavioral variables used in these two datasets, and briefly stated in the Introduction.

“Mental health problems were rated by the parent using the Child Behavior Checklist (CBCL), which contains 20 empirically based subscales spanning emotional, social and behavioral domains in subjects aged 6 to 18 (Achenbach & Rescorla, 2001). The CBCL has high inter-interviewer reliability, test-retest reliability, internal consistency and criterion validity, and therefore is widely utilized by child psychiatrists, developmental psychologists, and other mental health professionals for clinical and research purposes (Achenbach et al., 1987). Raw scores were used in analyses, higher scores indicating more severe problems. Cognitive functions were assessed by the NIH Toolbox (Luciana et al., 2018), which has good reliability and validity in children (Akshoomoff et al., 2013). The toolbox consists of seven different tasks covering episodic memory, executive function, attention, working memory, processing speed, and language abilities, and also provides three composites of crystalized, fluid, and total intelligence (Weintraub et al., 2013).” (Lines 412-424, Pages 20-21)

“Well-being was assessed by three questions: “I feel like I belong at this school”, “I have stayed home from school because of problems with other students”, and “During the past month, I have often been bothered by feeling sad and down” (Ren et al., 2022). Cognitive function was indirectly measured by the GPA on a 4.0 scale, obtained from school administrative records.” (Lines 442-447, Page 22)

“These datasets provided reliable measures of close friend quantity, mental health, and cognition, and included a combined total of more than 23,000 participants (Figure 1a).” (Lines 123-125, Page 7)

Reviewer #1 (Recommendations for the authors):

Table 1 in the main manuscript described several characteristics of the ABCD dataset. More information would be helpful for the reader. Could you give a breakdown on all variables for the 2 groups (on the breakpoint of over and under 5 friends)? Are other, potentially relevant, variables available for the two groups? For example, position in family, family size, urban vs. rural dwelling etc. Perhaps rural dwellers have fewer opportunities to have a large circle of close friends, and perhaps rural dwellers are systematically different in other ways (e.g., diet, mental health).

Thank you for the helpful comment. We have now revised Table 1 to show detailed demographic characteristics at baseline in terms of the breakpoint of 5 close friends and the statistical differences between two groups (please see Table 1 below). According to the Reviewer’s suggestion, we also provided information of family size reported by the parent (question: “How many people are living at your address? INCLUDE everyone who is living or staying at your address for more than 2 months.”), and urbanicity by externally linked to census data. The Census Bureau identifies two types of urban areas, including urbanized areas of 50,000 or more people and urban clusters of at least 2500, but less than 50,000 people. In the ABCD study, we found children with no more than 5 close friends have slightly larger family while no difference of urbanicity compared with children with more than 5 close friends.

I have little expertise with cross-lagged panel models; can you confirm that the statistical assumptions needed for CLPMs have been met?

This suggestion has been addressed in the first question in Essential revisions.

I didn't find the inclusion of the second dataset especially convincing. I appreciate that ABCD is unique (and therefore finding a replication sample is very challenging), but the social network dataset was quite different in the measures used. After reading the manuscript I was left with the impression that calling the social network dataset results a 'validation' was somewhat of a stretch. The results of two datasets were broadly similar (breakpoint at 5 in ABCD, ~8 outward nomination in the social network dataset) rather than a validation per se.

We agree with the Reviewer that the social network dataset is not a direct out-of-sample validation as the measures of mental health and cognition are not identical to those in the ABCD due to the data limitation. However, as we stated before, the primary aim of the present study is to investigate the potential nonlinear relationship between close friend quantity and various mental health and cognitive outcomes. In this sense, we think the findings in these two independent datasets were similar. Moreover, the friendship measures obtained from a directed friendship network in the social network datasets are informative and could be a complementary to the one question of close friend quantity used in the ABCD study. Therefore, we think utilizing the social network dataset extends findings in the ABCD study. We have now avoided to use the term of validation and discussed this limitation in the manuscript.

“Second, it is worth noting that the measures used in the ABCD study and the social network dataset differed, and the breakpoints identified in each dataset were not equivalent. However, relative to the optimal number of close friends, the primary objective of the current study was to examine the nonlinear relationship between the number of close friend and different behavioral outcomes and brain structure. In this sense, the findings from both datasets were similar, and the social network dataset provided valuable information regarding friendship measures and objective cognitive index that extended the results obtained from the ABCD study.” (Lines 364-372, Page 18)

In places, the phrasing is such that the reader could infer a direction of the effect in the cross-sectional results (e.g., line 173: "The ideal number of close friends was 5 and the closer to that number, the better *for* participants' mental health." [my emphasis]).

This suggestion has been addressed in the second question in Essential revisions.

This is not a limitation of your study but, as I mentioned in the public review, the effect sizes are very small. For example, in the social network dataset the β for GPA was 0.001. I would rather read a paper with a huge sample size and small effect sizes than vice-versa but could you put the effect sizes into context for the reader?

This suggestion has been addressed in the third question in Essential revisions.

Looking at Figure 2, there is a grouping of close friend size between ~2 to ~10 (i.e., the bottom of the u is quite flat there). Although the breakpoint is 5 close friends, could one argue that poorer outcomes tend to occur at a higher number of close friends? That is, problems start when the slope of the upward curve starts to steepen (this would also suggest a result more closely aligned with the social network dataset, albeit the measures are different)? The discussion of 5 as the breakpoint is more appropriate when the curve is v-shaped rather than u-shaped.

This suggestion has been addressed in the fourth question in Essential revisions.

Reviewer #2 (Recommendations for the authors):

I am excited about this paper and believe it is of added value to the existing literature, but I would appreciate a clearer theoretical framework with regards to why certain biological constructs were assessed in this study (introduction) and interpretation of the results in the context of the existing literature (discussion) (see public review). I outline my remaining questions in more detail below.

We thank the Reviewer for the thorough review and very positive evaluation of our study. We have now revised the Introduction to provide a more detailed explanation of the rational for assessing the specific biological constructs, and also expended the Discussion to better contextualize our findings within the existing literature.

The authors do not specify anything about the specific age-range they were interested in for the study in the introduction/discussion.

This suggestion has been addressed in the fifth question in Essential revisions.

In lines 181-184 it is stated that "Finally, same analyses were performed using the cross-sectional data collected at 2 years later, and the nonlinear associations of the number of close friends with ADHD symptoms and crystalized intelligence remained significant, with an average breakpoint of 4.83 {plus minus} 0.75 close friends (Figure S5)."

(a) So, all other found relations were not significant at follow up two years later? Please state this explicitly.

(b) Furthermore, I believe in the discussion the authors do not elaborate on this result. What do the authors make from this?

This suggestion has been addressed in the sixth question in Essential revisions.

I do not follow what is exactly being tested in Figure S10e (explained in lines 230-232). Could the authors please explain how a correlation can be estimated between "the differences in cortical area related to the number of close friends in the two groups". This reads as if a correlation has been performed to test for between-subject differences.

This suggestion has been addressed in the seventh question in Essential revisions.

It is unclear what the authors mean with the three indicators of friendship network size from the independent social network dataset (indegree, outdegree, reciprocal degree). This makes it hard to interpret the results. Please explicitly explain these terms.

This suggestion has been addressed in the eighth question in Essential revisions.

Were the independent behavioral variables collected in the ABCD and independent dataset reliable?

This suggestion has been addressed in the ninth question in Essential revisions.

https://doi.org/10.7554/eLife.84072.sa2

Article and author information

Author details

  1. Chun Shen

    1. Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
    2. Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai, China
    3. State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science (Fudan University), Ministry of Education, Shanghai, China
    Contribution
    Formal analysis, Funding acquisition, Visualization, Methodology, Writing – original draft, Writing – review and editing
    Contributed equally with
    Edmund T Rolls
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-1034-0343
  2. Edmund T Rolls

    1. Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
    2. Department of Computer Science, University of Warwick, Coventry, United Kingdom
    3. Oxford Centre for Computational Neuroscience, Oxford, United Kingdom
    Contribution
    Conceptualization, Supervision, Validation, Methodology, Writing – review and editing
    Contributed equally with
    Chun Shen
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-3025-1292
  3. Shitong Xiang

    1. Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
    2. Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai, China
    Contribution
    Data curation, Formal analysis
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-5513-4714
  4. Christelle Langley

    1. Department of Psychiatry, University of Cambridge, Cambridge, United Kingdom
    2. Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge, United Kingdom
    Contribution
    Writing – review and editing
    Competing interests
    No competing interests declared
  5. Barbara J Sahakian

    1. Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
    2. Department of Psychiatry, University of Cambridge, Cambridge, United Kingdom
    3. Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge, United Kingdom
    Contribution
    Writing – review and editing
    Competing interests
    No competing interests declared
  6. Wei Cheng

    1. Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
    2. Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai, China
    3. Fudan ISTBI—ZJNU Algorithm Centre for Brain-Inspired Intelligence, Zhejiang Normal University, Jinhua, China
    4. Shanghai Medical College and Zhongshan Hospital Immunotherapy Technology Transfer Center, Shanghai, China
    5. Department of Neurology, Huashan Hospital, Fudan University, Shanghai, China
    Contribution
    Supervision, Funding acquisition, Visualization, Methodology, Writing – review and editing
    For correspondence
    wcheng.fdu@gmail.com
    Competing interests
    No competing interests declared
  7. Jianfeng Feng

    1. Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
    2. Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai, China
    3. State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science (Fudan University), Ministry of Education, Shanghai, China
    4. Department of Computer Science, University of Warwick, Coventry, United Kingdom
    5. Fudan ISTBI—ZJNU Algorithm Centre for Brain-Inspired Intelligence, Zhejiang Normal University, Jinhua, China
    6. Zhangjiang Fudan International Innovation Center, Shanghai, China
    Contribution
    Conceptualization, Resources, Supervision, Funding acquisition, Writing – review and editing
    For correspondence
    jffeng@fudan.edu.cn
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-8890-8288

Funding

National Natural Science Foundation of China (82101617)

  • Chun Shen

China Postdoctoral Science Foundation (2022M710765)

  • Chun Shen

National Natural Science Foundation of China (82071997)

  • Wei Cheng

Shanghai Rising-Star Program (21QA1408700)

  • Wei Cheng

National Key Research and Development Program of China (2018YFC1312904)

  • Jianfeng Feng

National Key Research and Development Program of China (2019YFA0709502)

  • Jianfeng Feng

Shanghai Municipal Science and Technology Major Project (2018SHZDZX01)

  • Jianfeng Feng

111 Project (B18015)

  • Jianfeng Feng

ZJ Lab

  • Jianfeng Feng

Shanghai Center for Brain Science and Brain-Inspired Technology

  • Jianfeng Feng

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank the children and families whose ongoing participation made this study possible. Data used in the preparation of this article were obtained from the Adolescent Brain Cognitive Development (ABCD) study (https://abcdstudy.org), held in the NIMH Data Archive (NDA). This is a multisite, longitudinal study designed to recruit more than 10,000 children age 9–10 and follow them over 10 years into early adulthood. The ABCD Study is supported by the National Institutes of Health and additional federal partners under award numbers U01DA041048, U01DA050989, U01DA051016, U01DA041022, U01DA051018, U01DA051037, U01DA050987, U01DA041174, U01DA041106, U01DA041117, U01DA041028, U01DA041134, U01DA050988, U01DA051039, U01DA041156, U01DA041025, U01DA041120, U01DA051038, U01DA041148, U01DA041093, U01DA041089, U24DA041123, U24DA041147. A full list of supporters is available at https://abcdstudy.org/federal-partners.html. A listing of participating sites and a complete listing of the study investigators can be found at https://abcdstudy.org/consortium_members/. ABCD consortium investigators designed and implemented the study and/or provided data but did not necessarily participate in the analysis or writing of this report. This manuscript reflects the views of the authors and may not reflect the opinions or views of the NIH or ABCD consortium investigators. Chun Shen is supported by grants from the National Natural Science Foundation of China (no. 82101617) and the China Postdoctoral Science Foundation (no. 2022M710765). Wei Cheng is supported by grants from the National Natural Science Foundation of China (no. 82071997) and the Shanghai Rising-Star Program (no. 21QA1408700). Jianfeng Feng is supported by National Key R&D Program of China (no. 2018YFC1312904 and no. 2019YFA0709502), Shanghai Municipal Science and Technology Major Project (no. 2018SHZDZX01), ZJ Lab, Shanghai Center for Brain Science and Brain-Inspired Technology, and the 111 Project (no. B18015). The funders had no role in study design, data collection, and interpretation, or the decision to submit the work for publication.

Ethics

In the ABCD study, parents' full written informed consent and all children's assent were obtained by each center. Research protocols were approved by the institutional review board of the University of California, San Diego (No.160091), and the institutional review boards of the 21 data collection sites (Auchter et al., 2018). In the social network dataset, all parents and students provided informed consent for the survey, and the research protocol was approved by the Princeton University Institutional Review Board.

Senior Editor

  1. Christian Büchel, University Medical Center Hamburg-Eppendorf, Germany

Reviewing Editor

  1. Robert Whelan, Trinity College Dublin, Ireland

Reviewers

  1. Robert Whelan, Trinity College Dublin, Ireland
  2. Lisa Schreuders, Leiden University, Netherlands

Version history

  1. Received: October 10, 2022
  2. Preprint posted: November 2, 2022 (view preprint)
  3. Accepted: May 31, 2023
  4. Version of Record published: July 3, 2023 (version 1)

Copyright

© 2023, Shen, Rolls et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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  1. Chun Shen
  2. Edmund T Rolls
  3. Shitong Xiang
  4. Christelle Langley
  5. Barbara J Sahakian
  6. Wei Cheng
  7. Jianfeng Feng
(2023)
Brain and molecular mechanisms underlying the nonlinear association between close friendships, mental health, and cognition in children
eLife 12:e84072.
https://doi.org/10.7554/eLife.84072

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https://doi.org/10.7554/eLife.84072

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