Computational simulation of intervention targets: elucidating coping style mechanisms in anxiety and depressive symptom networks in community populations.

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Learn more: PMC Disclaimer | PMC Copyright Notice BMC Psychol . 2026 Apr 21;14:812. doi: 10.1186/s40359-026-04442-4 Computational simulation of intervention targets: elucidating coping style mechanisms in anxiety and depressive symptom networks in community populations Zhenxuan Dong 1, 2 , Dingchao Wu 1, 2 , Xiujun Zhang 1, 2, ✉ , Haitao Wang 1, 2, ✉ , Hongge Luo 1, 2, ✉ Author information Article notes Copyright and License information 1 School of Psychology and Mental Health, North China University of Science and Technology, Hebei, China 2 Hebei Key Laboratory of Mental Health and Brain Science, Hebei, China ✉ Corresponding author. Received 2025 Oct 21; Accepted 2026 Mar 24; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13231770  PMID: 42015313 Abstract Background Depressive and anxiety disorders represent globally significant mental health burdens, imposing substantial impacts on individuals, societies, and healthcare infrastructure. In China, nationally representative epidemiological studies report a lifetime prevalence of 7.6% for anxiety disorders and 6.6% for depressive disorders. Both conditions demonstrate age-dependent heterogeneity, with older populations exhibiting significantly higher susceptibility and elevated comorbidity. Methods The cross-sectional study of community populations constructed Ising network models for different age groups, and then applied the NodeIdentifyR algorithm (NIRA) to identify dual-pathway intervention targets — nodes projected to alleviate (treatment) or aggravate (prevention) symptoms. Results The analysis indicated a heterogeneous link between coping styles and anxiety and depression, with notable age differences observed. Further simulation of intervention outcomes suggested that age-specific coping profiles emerged as viable targets for clinical intervention. Conclusions Using psychopathological network modeling, this study reveals age-related heterogeneity in the association patterns between coping styles and anxiety-depression symptoms, as well as in the corresponding intervention targets. Keywords: Anxiety symptoms, Depressive symptoms, Coping styles, Network analysis, Intervention simulations, Age Introduction Depressive and anxiety disorders rank among the most disabling mental health conditions globally, posing substantial burdens on individuals, societies, and healthcare systems [ 1 , 2 ]. In China, nationally representative epidemiological studies report a lifetime prevalence of 7.6% for anxiety disorders and 6.6% for depressive disorders. Both conditions demonstrate age-dependent heterogeneity, with older populations exhibiting significantly higher susceptibility [ 3 , 4 ]. Notably, comorbidity rates between anxiety and depressive disorders remain consistently elevated across all age groups [ 5 – 9 ], contributing to poorer prognoses, heightened functional impairment, and increased healthcare burdens [ 10 ]. Consequently, anxiety and depressive disorders constitute critical public health priorities in China. Implementing age-tailored psychological interventions is imperative to effectively mitigate symptom burden and improve clinical outcomes across developmental stages. Associations among age, coping style, depressive and anxiety First, existing research has predominantly focused on the relationship between coping styles and mental health within specific populations. To date, three studies have employed network analysis to explore the dynamic interactions between coping styles and symptoms of anxiety and depression, using medical postgraduates [ 11 ], university students [ 12 ], and informal caregivers [ 13 ] as respective study populations. However, the samples in these studies are characterized by relatively narrow age ranges or limited sample sizes. According to socioemotional selectivity theory [ 14 ] coping strategies exhibit age-related differences in usage frequency due to motivational changes across the lifespan [ 15 , 16 ]. Furthermore, the relationships between various coping styles and mental health outcomes also vary with age [ 17 – 19 ]. Therefore, it is necessary to investigate whether heterogeneous association patterns exist between coping styles and anxiety-depression symptom networks across different age groups. Second, given the potential age heterogeneity in the association patterns between coping styles and the anxiety-depression network, a key follow-up question arises: do core intervention targets also differ across age groups? Previous population-based network studies have mostly relied on Gaussian Graphical Models (GGM) (All abbreviations used in this paper are summarized in Table 1 ), identifying intervention targets via node centrality indices [ 20 – 22 ]. While centrality indices help pinpoint pivotal nodes, they do not fully capture the complexity of dynamic symptom interactions—a critical aspect for understanding the maintenance mechanisms of psychopathology and for developing effective interventions [ 23 ]. Table 1. Summary of Article Abbreviations Abbreviation Items SCSQ-1 Viewing the positive aspects of things positively. SCSQ-2 Exploring multiple strategies to solve problems. SCSQ-3 Modifying existing behavior patterns or personal issues. SCSQ-4 Learning from others’ experiences in coping with similar difficulties. SCSQ-5 Temporarily setting aside problems through rest or vacation. SCSQ-6 Believing time will change the situation and choosing to wait. SCSQ-7 Making an effort to dismiss the matter from one’s mind. SCSQ-8 Fantasizing about some miracle occurring to change the situation. GAD-1 Feeling nervous, anxious or on edge GAD-2 Not being able to stop or control worrying GAD-3 Worrying too much about different things GAD-4 Trouble relaxing GAD-5 Being so restless that it is hard to sit still GAD-6 Becoming easily annoyed or irritable GAD-7 Feeling afraid as if something awful might happen PHQ-1 Little interest or pleasure in doing things PHQ-2 Feeling down, depressed or hopeless PHQ-3 Trouble falling or staying asleep; or sleeping too much PHQ-4 Feeling tired or having little energy PHQ-5 Poor appetite or overeating PHQ-6 Feeling bad about yourself or that you are a failure or have let yourself or your family down PHQ-7 Trouble concentrating on things; such as reading the newspaper or watching television PHQ-8 Moving or speaking so slowly that other people could have noticed. Or the opposite - being so fidgety or restless that you have been moving around a lot more than usual PHQ-9 Thoughts that you would be better off dead or of hurting yourself in some way NIRA NodeldentifyR algorithm GGM Gaussian Graphical Models PHQ-9 Patient Health Questionnaire-9-item SCSQ Simple Coping Style Questionnaire GAD-7 Generalized Anxiety Disorder-7 BEI Bridge Expected Influence EBIC Extended Bayesian Information Criterion LASSO Least Absolute Shrinkage and Selection Operator eLasso enhanced Least Absolute Shrinkage and Selection Operator RFCBT Rumination-focused Cognitive Behavioral Therapy CBM Cognitive Bias Modification Open in a new tab The NodeIdentifyR algorithm (NIRA) is a computational tool grounded in dynamic systems theory. It assesses the network influence of target symptoms through bidirectional simulations of alleviating and aggravating interventions [ 24 ]. This approach allows for the precise identification of intervention targets that demonstrate the highest dynamic sensitivity within symptom networks. By integrating a dual-pathway optimization framework oriented toward both prevention and treatment, NIRA offers a computational model for accurately pinpointing intervention targets in psychological settings. The method has been empirically validated across multiple research contexts [ 25 , 26 ]. Therefore, adopting the NodeIdentifyR algorithm (NIRA) is warranted to explore and compare intervention and prevention targets across different age groups. The present study In summary, most studies adopt the Gaussian Graphical Model (GGM) network analysis to explore the relationships between coping styles and anxiety and depression in a specific population, and infer the intervention targets indirectly through centrality indices. Therefore, this study adopts the NIRA to identify the intervention targets with the highest dynamic sensitivity in symptom networks within an age-stratified framework, thereby providing empirical foundations for developing developmentally tailored precision psychological interventions. Two specific research questions guide this investigation: Whether heterogeneous association patterns exist between coping styles and anxiety-depression symptom networks across different age groups; If such heterogeneity exists, whether intervention targets demonstrate age‑group differences. Methods Participants and procedures This cross-sectional study, employing a cluster sampling approach, was conducted among residents of a community in Tangshan, China, between October 2022 and August 2024. Inclusion criteria: (1) residents of the selected community who had lived there for more than 6 months in the current year; (2) signed the informed consent form; (3) age range: 18 ~ 85 years. Exclusion criteria: (1) severe neurological or brain-related diseases; (2) organic diseases or drug-induced secondary depression; (3) a history of alcohol abuse, substance abuse, or addiction; (4) intellectual disability; (5) concurrent participation in other similar studies; or (6) incomplete responses on depression-related scales. Furthermore, records were excluded during quality control for missing key sociodemographic information, having questionnaires with extensive missing data on key variables (> 20% missing items), or containing obvious logical inconsistencies. From an initial pool of 5,000 recruited participants, 4,140 valid datasets were retained. As the sample size for individuals under 35 years was insufficient and lacked representativeness, only participants aged 35 years or older were included in the final analysis and were stratified into three groups: 35 ~ 49 years, 50 ~ 64 years, and ≥ 65 years. Demographic characteristics are presented in Table 2 . Table 2. Descriptive statistics of sample variables Items n total 4140 Age 35 ~ 49 1063 50 ~ 64 1791 ≥ 65 1286 Sex Male 2011 Female 2129 Open in a new tab Research tools Patient Health Questionnaire-9-item (PHQ-9) The Patient Health Questionnaire-9 (PHQ-9) serves as a screening instrument for depression severity assessment, comprising nine items each rated on a 0 ~ 3 scale. Total scores range from 0 to 27, with higher values indicating greater depressive symptom severity [ 27 , 28 ]. The validated Chinese version demonstrates robust psychometric properties [ 29 ]. In the subsequent network analysis, its nine items served as nodes to construct the network structure. Cronbach’s alpha coefficients across three groups were 0.92 (35 ~ 49 years), 0.90 (50 ~ 64 years), and 0.88 (≥ 65 years), demonstrating good internal consistency. Generalized Anxiety Disorder-7 (GAD-7) The Generalized Anxiety Disorder-7 (GAD-7) serves as a validated screening instrument for identifying generalized anxiety disorder, comprising seven items each rated on a 0 ~ 3 scale. Total scores range from 0 to 21, with elevated scores indicating greater anxiety symptom severity [ 30 , 31 ]. The Chinese adaptation demonstrates robust psychometric properties [ 32 , 33 ]. In the following network analysis, each of these seven items was utilized as a node for network estimation. Cronbach’s alpha coefficients across three groups were 0.90 (18 ~ 49 years), 0.86 (50 ~ 64 years), and 0.83 (≥ 65 years) across age strata. Simple Coping Style Questionnaire (SCSQ) The Simplified Coping Style Questionnaire [ 34 ] was employed to assess coping styles, utilizing four items measuring positive coping (SCSQ-1 to SCSQ-4) and four items measuring negative coping (SCSQ-5 to SCSQ-8), each rated on a four-point scale. In our network model, these eight items functioned as nodes to map the interconnected structure. Cronbach’s alpha coefficients across three groups were 0.93 (18 ~ 49 years), 0.91 (50 ~ 64 years), and 0.89 (≥ 65 years). Statistical analysis First, demographic statistical analyses for all variables were conducted using IBM SPSS 23.0. Analyses of variance and post-hoc tests were performed on the three age groups to examine the group differences. Second, the network analysis was conducted in R version 4.3.0 (R Core Team, 2023). We estimated the symptom network using the Ising model based on bivariate data. The Ising model was estimated via the IsingFit R package (Version 0.4), which adopts a binary variable framework to capture pairwise interactions while controlling for all other variables in the network. Consistent with the established methodology [ 20 ], depressive and anxiety symptoms were dichotomized as absent (0; scores = 0) or present (1; scores 1 ~ 3). Coping styles were similarly dichotomized as not used (0; scores = 0) or used (1; scores 1 ~ 3). The Ising model estimates parameters via logistic regression, iteratively regressing each variable against all other network variables [ 21 ]. In the Ising model, logistic regression intercepts represent item-specific threshold parameters, indicating baseline endorsement probabilities. Regression coefficients correspond to edge weights, quantifying the magnitude and direction of conditional associations between symptom pairs given all other network nodes. In the networks, edges represent partial correlations conditioned on all other variables in the network [ 35 ]. To minimize false-positive edge identification, networks were regularized via the adaptive Least Absolute Shrinkage and Selection Operator (LASSO), a technique that enforces sparsity through coefficient-specific penalization [ 36 ]. LASSO regularization implements the Extended Bayesian Information Criterion (EBIC) to enforce network sparsity, shrinking non-significant edge parameters to zero [ 37 ]. For binary variables, the Enhanced Least Absolute Shrinkage and Selection Operator (eLasso) were used. In network visualization, nodes correspond to variables and edges represent partial correlation coefficients between node pairs, conditional on all other network variables. Edge thickness scales with association strength, while color denotes valence: blue indicates positive associations and red signifies negative associations. This analytical framework was applied to investigate differential connectivity patterns between coping styles and anxiety-depression symptom networks while evaluating developmental differences across age groups [ 38 ]. Third, the Ising model and NIRA algorithm [ 39 ] were applied to identify optimal targets for prevention and intervention within networks comprising coping styles, depressive symptoms, and anxiety symptoms. Based on the parameters estimates from the Ising model, we implemented the NIRA algorithm to simulate dynamic intervention effects via the nodeIdentifyR package ( https://github.com/JasperNaberman/nodeIdentifyR.git ). The tuning we set uses the default setting of 0.25. The projected impact of specific perturbations on overall symptom activation was quantified through changes in network sum scores. Building upon Ising model parameter estimates, the NIRA algorithm simulated 5,000 participants to administer two intervention types per network node. Alleviating interventions depressed nodal thresholds by two standard deviations; a significant reduction in network sum scores following manipulation indicated that suppressing the node produced global symptom alleviation, thereby designating it a therapeutic target for cognitive restructuring or exposure therapy. Conversely, aggravating interventions elevated thresholds by two standard deviations; significant exacerbation of sum scores revealed nodes capable of initiating maladaptive symptom cascades, thus warranting preventive monitoring or cognitive-behavioral inhibition strategies [ 23 , 39 , 40 ]. The node exhibiting the largest absolute difference in network sum scores before versus after interventions was classified as the most effective intervention target within the dynamic symptom network [ 24 , 39 ]. Results Descriptive statistics for coping Style, depressive and anxiety symptoms Table 3 presents descriptive statistics for anxiety symptoms, depressive symptoms, and coping styles across three groups, as well as the results of the analysis of variance and post-hoc tests for each item. We found significant differences among the three age groups in some coping styles, anxiety symptoms, and depressive symptoms. Moreover, the ≥ 65-year group scored significantly higher on total and item scores of GAD‑7 and PHQ‑9 than the other two groups. Table 3. Basic information of scales and descriptive item statistic Symptoms 35 ~ 49① 50 ~ 64② ≥ 65③ F post-hoc testing M(SD) M(SD) M(SD) SCSQ-1 (Positive reframing) 1.49 (1.05) 1.44 (1.04) 1.35 (0.93) F = 5.78, p = 0.003 ①>③** SCSQ-2 (Strategy exploration) 1.46 (0.98) 1.44 (0.97) 1.33 (0.88) F = 6.97, p < 0.001 ②>③**, ①>③** SCSQ-3 (Behavior adjustment) 1.34 (0.96) 1.35 (0.96) 1.3 (0.89) F = 1.14, p = 0.321 SCSQ-4 (Experience borrowing) 1.30 (0.93) 1.31 (0.96) 1.31 (0.9) F<1 SCSQ-5 (Temporary disengagement) 1.04 (0.98) 1.12 (1.00) 1.15 (0.94) F = 4.13, p = 0.016 ③>①* SCSQ-6 (Passive waiting) 0.88 (0.96) 1.02 (0.97) 1.06 (0.93) F = 10.62, p < 0.001 ②>①**, ③>①** SCSQ-7 (Cognitive dismissal) 0.91 (0.95) 1.03 (0.96) 1.01 (0.95) F = 5.89, p = 0.003 ②>①**, ③>①* SCSQ-8 (Miracle fantasizing) 0.81 (0.88) 0.84 (0.89) 0.8 (0.87) F<1 GAD-7 total score 0.97 (2.53) 1.16 (2.52) 1.45 (2.60) F = 17.84, p < 0.001 ③>①**, ③>②** GAD-1 (Nervousness) 0.15 (0.44) 0.19 (0.47) 0.22 (0.50) F = 6.86, p = 0.001 ③>①** GAD-2 (Uncontrollable worry) 0.13 (0.43) 0.16 (0.44) 0.21 (0.49) F = 9.26, p < 0.001 ③>①**, ③>②** GAD-3 (Excessive worry) 0.16 (0.46) 0.17 (0.45) 0.23 (0.50) F = 7.16, p < 0.001 ③>②**, ③>①** GAD-4 (Relaxation difficulty) 0.16 (0.46) 0.20 (0.52) 0.23 (0.52) F = 5.99, p = 0.003 ②>①*, ③>①** GAD-5 (Restlessness) 0.12 (0.41) 0.15 (0.44) 0.20 (0.49) F = 9.71, p < 0.001 ③>①**, ③>②** GAD-6 (Irritability) 0.15 (0.43) 0.19 (0.50) 0.21 (0.49) F = 6.14, p = 0.002 ②>①*, ③>①** GAD-7 (Anticipatory fear) 0.09 (0.36) 0.10 (0.35) 0.14 (0.40) F = 6.97, p < 0.001 ③>①**, ③>②** PHQ-9 total score 1.70 (3.38) 2.08 (3.37) 2.52 (3.28) F = 10.76, p < 0.001 ③>①**, ③>②**, ②>①* PHQ-1 (Anhedonia) 0.28 (0.59) 0.30 (0.60) 0.34 (0.57) F = 4.16, p = 0.016 ③>①* PHQ-2 (Depressed mood) 0.22 (0.53) 0.26 (0.54) 0.31 (0.58) F = 7.55, p < 0.001 ③>②*, ③>①** PHQ-3(Sleep disturbance) 0.26 (0.60) 0.40 (0.75) 0.51 (0.81) F = 34.75, p < 0.001 ②>①**, ③>②**, ③>①** PHQ-4 (Fatigue) 0.30 (0.60) 0.30 (0.64) 0.33 (0.61) F<1 PHQ-5 (Appetite change) 0.18 (0.51) 0.20 (0.52) 0.26 (0.57) F = 6.99, p < 0.001 ③>②*, ③>①** PHQ-6 (Worthlessness/guilt) 0.14 (0.45) 0.15 (0.44) 0.18 (0.44) F = 3.06, p = 0.047 PHQ-7 (Concentration problems) 0.13 (0.42) 0.17 (0.45) 0.21 (0.47) F = 8.37, p < 0.001 ③>②*, ③>①** PHQ-8 (Psychomotor changes) 0.12 (0.40) 0.17 (0.46) 0.20 (0.48) F = 9.05, p < 0.001 ②>①**, ③>①** PHQ-9 (Suicidal ideation) 0.07 (0.31) 0.13 (0.39) 0.18 (0.44) F = 21.44, p < 0.001 ②>①**, ③>②**, ③>①** Open in a new tab Statistically significant differences are denoted as * p < 0.05 and ** p < 0.01 Network estimation using ising model Figure 1 (a)-(d) illustrates the network structures of coping styles, depressive symptoms, and anxiety symptoms derived from Ising models for the full sample and different age groups. The specific thresholds for each node are presented in Appendix A , Table 4, which shows estimated threshold parameters (intercepts) for each node in the Ising models, by age group. Results demonstrate robust connections between anxiety and depressive symptoms across all networks, revealing comorbid manifestations. Concurrently, coping styles showed strong associations with anxiety and depressive symptoms. The Ising models estimated for the full sample and the three age-stratified subsamples (35 ~ 49, 50 ~ 64, and ≥ 65 years) revealed distinct connectivity patterns between coping styles and anxiety-depressive symptoms. In the 35 ~ 49 years group, the network featured relatively sparse but targeted links, positive edges from SCSQ-2 (“Strategy exploration”) to PHQ-1 (“Anhedonia”) and from SCSQ-7 (“Cognitive dismissal”) to PHQ-6 (“Worthlessness/guilt”). In the 50 ~ 64 years group, coping-symptom connections were densest, with negative coping styles acting as central hubs; prominent strong positive edges included SCSQ-8 (“Miracle fantasizing”) to PHQ-1 (“Anhedonia”), PHQ-7 (“Concentration problems”), and PHQ-9 (“Suicidal ideation”), as well as SCSQ-7 (“Cognitive dismissal”) to PHQ-2 (“Depressed mood”), PHQ-6 (“Worthlessness/guilt”), and PHQ-3 (“Sleep disturbance”). In the ≥ 65 years group, dominated by a very strong positive edge between SCSQ-8 (“Miracle fantasizing”) and PHQ-5 (“Appetite change”), and a negative edge from SCSQ-1 (“Positive reframing”) to PHQ-8 (“Psychomotor changes”). Fig. 1. Open in a new tab Network of Coping Styles, Depressive, and Anxiety Symptoms Intervention simulations Before assessing specific intervention targets, a trend in baseline network activation was observed. As shown in Fig. 2 , the baseline symptom sum scores exhibited a progressive increase across age groups: 5.67 for the 35 ~ 49 group, 6.56 for the 50 ~ 64 group, and 8.02 for the ≥ 65 group. This indicates that overall symptom activation level intensifies with age. Fig. 2. Open in a new tab Results of Simulating Intervention on the Ising Model. Note. Fig. 2A displays the results of aggravating intervention and Fig. 2B displays the results of alleviating intervention. Black dots represent the network sum scores, while lines represent the 95 % confidence interval. The symptoms are listed based on the size of the intervention’s effects, along with the original total score before the intervention. Figure 2 A. Simulation of aggravating interventions revealed age-specific prevention targets. In the 35 ~ 49 group, elevating SCSQ-6 (“Passive waiting”) produced the greatest increase in network sum scores (from 5.65 to 7.02), identifying this coping item as the optimal prevention target within this demographic. In the 50 ~ 64 group, elevating SCSQ-7 (“Cognitive dismissal”) produced the greatest increase in network sum scores (from 6.55 to 7.67), implicating it as a key prevention target for this demographic. In the ≥ 65 group, PHQ-5 (“Appetite disturbance”) emerged as the primary prevention target (from 7.86 to 9.17). Complete data for all nodes are presented in Appendix A , Table 5, which summarizes simulated aggravating and alleviating node values. Figure 2 B. Simulation of alleviating interventions revealed age-specific treatment targets. In the 35 ~ 49 group, reducing SCSQ-2 (“Strategy exploration”) most substantially reduced the symptom sum score (from 5.67 to 4.04), identifying this coping item as the optimal intervention target within this age group. In the 50 ~ 64 group, reducing SCSQ-4 (“Experience borrowing”) yielded the greatest reduction in symptom sum scores (from 6.56 to 5.19). In the ≥ 65 group, targeting SCSQ-7 (“Cognitive dismissal”) decreased the sum score from 8.02 to 6.80, establishing it as the primary intervention target for this group. These findings indicate that therapeutic modulation of these specific coping styles may facilitate the reduction of anxiety-depression symptoms and enhance psychological well-being. These NIRA simulation outcomes address the second research question, confirming age-specific patterns for both intervention and prevention targets across symptom networks. Additional analysis This study also performed Gaussian Graphical Model (GGM) network analyses, with results shown in Appendix B , Figs. 3 and 4. Figure 3 shows the results for Network Estimation and Fig. 4 shows the results for Bridge Strength. Different indices (e.g., network estimation, bridge strength, and the NIRA algorithm described in the main text) identify different intervention targets. These differences reflect their distinct focuses: network estimation captures the strength of correlations among nodes, bridge strength highlights connections across network modules, and NIRA detects nodes with the strongest impact on the whole network. Because NIRA more accurately identifies intervention targets with the highest dynamic sensitivity in the symptom network, the main text focuses primarily on NIRA results. Discussion This study employed the NodeIdentifyR algorithm (NIRA) and psychopathological network modeling to elucidate age-related differential mechanisms of coping styles within anxiety-depression symptom networks. Age differences in coping styles and anxiety and depression The association patterns between coping styles and anxiety-depression symptom networks exhibited heterogeneity across different age groups, addressing the first research question. In the 35 ~ 49 age group, a significant positive association was observed between the active coping style SCSQ-2 (“Strategy exploration”) and the core depressive symptom PHQ-1 (“Anhedonia”). This finding suggests that, within this age range, repeatedly comparing different strategies may lead to cognitive exhaustion and a diminished sense of reward from problem-solving efforts, potentially reinforcing the withdrawal and loss of interest characteristic of anhedonia [ 41 – 43 ]. At the same time, the negative coping style SCSQ-7 (“Cognitive dismissal”) showed the most prominent association with symptom PHQ-6 (“Worthlessness”), indicating that avoidance-oriented coping may prevent effective resolution of stressors, with the resulting negative outcomes being internally attributed as personal failings and thereby intensifying feelings of worthlessness [ 44 , 45 ]. In the 50 ~ 64 group, the network structure displayed broad connections centered on negative coping styles. Among these, SCSQ-8 (“Miracle fantasizing”) emerged as one of the key nodes with the most connections, linking to multiple core depressive symptoms including PHQ-1 (“Anhedonia”), PHQ-7 (“Concentration problems”), and PHQ-9 (“Suicidal ideation”). This suggests that, at this life stage, a coping style characterized by relinquishing effort and resorting to external miracles may exacerbate multiple dimensions of depressive symptoms [ 46 ]. Furthermore, SCSQ-7 (“Cognitive dismissal”) maintained strong associations with PHQ-2 (“Depressed mood”) and PHQ-6 (“Worthlessness”), indicating that avoidant coping remains consistently linked to specific emotional symptoms [ 47 ]. In the ≥ 65 group, the most notable finding was the extremely strong association between SCSQ-8 (“Miracle fantasizing”) and PHQ-5 (“Appetite disturbance”). This may reflect a close connection between a helpless coping attitude—in the face of uncontrollable stressors such as health decline in older age—and somatic depressive symptoms such as appetite changes [ 48 , 49 ]. Additionally, this group exhibited a negative correlation between the active coping style SCSQ-1 (“Positive reframing”) and PHQ-8 (“Psychomotor changes”), implying that adopting a cognitive strategy of positive reappraisal may have a protective effect against psychomotor agitation or retardation [ 50 , 51 ]. In summary, although negative coping styles–particularly SCSQ-7 and SCSQ-8–consistently served as central nodes closely linked to anxiety and depression symptom networks across all age groups, the specific core symptoms associated with them varied by age. The associations involving positive coping styles showed clear age-specific patterns: coexisting with negative emotions in middle adulthood, while demonstrating protective value against certain symptoms in older adulthood. Age differences in intervention Beyond the heterogeneity in edge connections, a critical finding is the age-dependent escalation in baseline network activation. The progressively higher global symptom scores observed in older group (from 5.67 in early middle age to 8.02 in older age), which is consistent with epidemiological findings that older age groups have a higher prevalence of anxiety and depression [ 3 , 4 ]. This phenomenon may stem from new stressors in later life, such as cognitive decline, age-related physical illnesses, and retirement [ 49 ]. The higher baseline symptom activation level in older adults implies that they may require more intensive intervention to achieve symptom relief comparable to younger group. In the 35 ~ 49 age group, SCSQ-2 (“Strategy exploration”) and SCSQ-6 (“Passive waiting”) were identified as treatment and prevention targets, respectively. Although classified as an active coping strategy, the treatment target SCSQ-2 (“Strategy exploration”) showed a positive association with PHQ-1 in the Ising network model, consistent with intervention simulation results, indicating that reducing this node yields the greatest symptomatic relief. This suggests that within this age group—often facing multiple pressures from work and life—if the process of strategy exploration is inefficient or marked by hesitation, it may lose its adaptive function and instead contribute to sustaining the symptom network [ 52 , 53 ]. Therefore, interventions targeting this treatment focus should not merely encourage “active coping” but aim to enhance the efficiency of strategy exploration and the ability to translate decisions into action. The prevention target SCSQ-6 (“Passive waiting”) demonstrated strong connections with multiple anxiety and depression symptoms in the Ising network model, and intervention simulations confirmed its role as a key factor exacerbating symptom interactions. The underlying mechanism may be that passive waiting, as a form of avoidant coping, reduces the likelihood of proactive problem-solving, thereby maintaining or even reinforcing the symptom network [ 54 , 55 ]. Interventions addressing this prevention target should focus on mitigating its behavior-inhibiting effects, for example through action initiation training and schedule structuring, to help individuals replace avoidance with concrete, manageable micro-steps, thus interrupting the symptom cycle perpetuated by passive coping. SCSQ-4 (“Experiential borrowing”) and SCSQ-7 (“Cognitive dismissal”) were identified as treatment and prevention targets, respectively, in the 50 ~ 64 age group. The intervention simulation focusing on this node yielded a counterintuitive result: reducing the expression of SCSQ-4 led to greater overall symptom alleviation. This apparent contradiction may indicate that the role of SCSQ-4 in practice is conditional. Research suggests that SCSQ-4 (“Experiential borrowing”) does not merely involve replicating coping strategies from similar past events, but rather requires the integration of diverse life experiences to develop transferable adaptive resources [ 56 ]. When this process is inefficient, detached from the current problem, or drifts into mere fantasy, it may turn into an ineffective form of cognitive resource allocation [ 57 ]. Therefore, clinical interventions targeting this factor should go beyond simply encouraging or discouraging its use. Instead, they should incorporate a functional assessment to distinguish whether it operates as a “strategic resource” or as “an ineffective use of cognitive resources” and accordingly enhance the individual’s capacity for goal-directed integration and application of experience. The prevention target SCSQ-7 (“Cognitive dismissal”) showed positive associations in the network with both PHQ-3 (‘Sleep disturbance’) and PHQ-6 (“Worthlessness”), underscoring its central role. This may be related to stage-specific psychosocial developmental tasks during this life period. When confronted with age-related challenges such as health changes and social-role transitions, individuals may increasingly adopt avoidance strategies to regulate emotion [ 58 ]. However, rather than serving as an adaptive mechanism, such avoidance in this age group appears to be maladaptive, as it fails to resolve underlying stressors and instead maintains or exacerbates symptoms, particularly sleep difficulties and feelings of worthlessness. For the ≥ 65 group, the clinical significance of targeting SCSQ-7 (“Cognitive dismissal”) differs from that in the 50–64 age group, shifting toward treatment rather than prevention. In this older group, cognitive avoidance may no longer function merely as a emotion regulation strategy accompanying aging, but may instead become associated with declines in cognitive flexibility, diminished real-world problem-solving capacity, and contraction of social support networks, thereby transforming into a factor that maintains or even exacerbates psychological distress [ 59 – 61 ]. Therefore, interventions targeting this construct should aim to foster adaptive coping by helping older adults develop more acceptance-oriented and reality-focused management strategies when facing uncontrollable challenges, rather than relying solely on avoidance. Moreover, PHQ-5 (‘Appetite disturbance’) was identified as a prevention target in this age group. Network intervention simulations indicated that directly intervening on this symptom node yielded more significant overall network symptom reduction compared to intervening on related coping styles, suggesting that targeting specific psychophysiological symptoms may be more efficient than broadly adjusting coping strategies in this population. This may reflect more direct mind–body interactions in later life, whereby physiological symptoms such as Appetite disturbance can rapidly affect emotional and cognitive functioning [ 62 , 63 ]. Furthermore, the network structure revealed a strong connection between the prevention target PHQ-5 (‘Appetite disturbance’) and the coping style SCSQ-8 (‘Miracle fantasizing’). This implies that for adults over 65, clinical prevention should address both symptoms and linked coping patterns concurrently. Thus, an optimal intervention pathway for this group would involve directly alleviating core symptoms—such as appetite-related issues—as a primary step, while also assessing and modifying closely associated maladaptive coping strategies, such as overreliance on unrealistic fantasy. This dual approach would facilitate rapid relief of current distress while reducing future psychological risk. Limitations This study employed the NodeIdentifyR (NIRA) algorithm to identify potential intervention targets within psychopathological networks. While offering useful theoretical insights, several limitations warrant acknowledgement to guide future research. First, the generalizability of the findings may be constrained by the geographically restricted sampling frame and the underrepresentation of individuals aged 18 ~ 35 years. Future studies should prioritize more diverse and representative samples to enhance external validity. Second, the current NIRA framework identifies only an optimal initial target, operating under a static network assumption. It does not account for the dynamic reorganization of network parameters following an intervention, nor does it address heterogeneity in individual symptom processes. In practice, an effective first intervention may alter the network structure, potentially shifting the optimal target for a subsequent intervention. Future work should develop longitudinal designs and computational methods, such as multi-step “intervention decision trees,” to model and explore optimal sequential intervention strategies. Third, the identified targets represent a theoretical optimum derived from network simulations. The extent to which these simulated effects translate into actual therapeutic outcomes remains an open empirical question. Prospective clinical trials are needed to validate the real-world effectiveness of NIRA-informed interventions, a critical step for translating theoretical models into clinically actionable tools [ 42 ]. In addition, different methods for identifying intervention targets can yield different recommendations. Future studies may compare the effectiveness of intervention recommendations generated by NIRA and other alternative network analysis methods, to verify which method can better guide clinical interventions and improve therapeutic effects. Conclusion This study employed psychopathological network modeling and intervention simulation analysis to arrive at a core conclusion: the mechanisms and interventional value of coping styles in the anxiety-depression symptom network exhibit distinct age-group specificity. Specifically, the research found heterogeneous associative patterns in the symptom network structures across different age groups. While negative coping styles consistently constituted the core of the networks, the specific symptom dimensions they connected to varied by age group. More importantly, intervention simulation results revealed that the “key nodes”—that is, the optimal intervention targets capable of maximally disrupting and alleviating the overall symptom network—differed significantly across age groups. Acknowledgements We are appreciative of the students and teachers who participated and the people who assisted in our study. Appendix A Table 4. Estimated threshold parameters (intercepts) for each node in the Ising models, by age group Item All age groups 35~49 50~64 ≥65 SCSQ-1 -1.42 -1.70 -1.51 -0.73 SCSQ-2 -2.11 -2.19 -2.10 -1.75 SCSQ-3 -2.76 -2.41 -2.24 -2.18 SCSQ-4 -2.52 -3.02 -2.91 -1.78 SCSQ-5 -3.04 -2.69 -2.85 -2.87 SCSQ-6 -2.80 -3.26 -2.89 -1.58 SCSQ-7 -2.75 -2.68 -2.66 -2.37 SCSQ-8 -2.88 -2.24 -2.59 -3.05 PHQ-1 -2.84 -2.86 -2.75 -1.93 PHQ-2 -2.81 -4.13 -2.79 -2.37 PHQ-3 -2.18 -2.55 -2.09 -1.64 PHQ-4 -2.76 -2.61 -2.78 -2.53 PHQ-5 -3.35 -3.65 -3.22 -2.96 PHQ-6 -4.26 -5.37 -4.21 -3.51 PHQ-7 -3.25 -4.12 -3.60 -2.95 PHQ-8 -3.54 -4.42 -3.32 -3.07 PHQ-9 -3.72 -4.13 -3.84 -3.51 GAD-1 -3.45 -3.57 -3.49 -2.94 GAD-2 -3.60 -3.62 -3.61 -3.20 GAD-3 -3.64 -4.08 -3.51 -3.21 GAD-4 -3.50 -4.08 -3.17 -3.17 GAD-5 -3.81 -4.18 -4.15 -2.95 GAD-6 -3.47 -3.71 -3.43 -3.11 GAD-7 -4.13 -3.51 -3.67 -3.52 Open in a new tab Table 5. Summary of simulated aggravating and alleviating node values Threshold Iteration Aggravating Alleviating Mean Sum Score Confidence Interval Lower Confidence Interval Upper Mean Sum Score Confidence Interval Lower Confidence Interval Upper 35~49 Original 5.66 5.58 5.73 5.67 5.59 5.74 GAD-1 5.96 5.88 6.03 5.56 5.49 5.64 GAD-2 5.85 5.77 5.93 5.6 5.52 5.67 GAD-3 5.93 5.85 6.01 5.53 5.46 5.6 GAD-4 5.91 5.83 5.99 5.6 5.53 5.67 GAD-5 5.83 5.75 5.9 5.56 5.48 5.63 GAD-6 5.81 5.73 5.88 5.52 5.45 5.6 GAD-7 5.72 5.64 5.79 5.59 5.52 5.67 PHQ-1 6.39 6.31 6.47 5.41 5.34 5.48 PHQ-2 6.11 6.03 6.19 5.51 5.44 5.58 PHQ-3 6.1 6.01 6.18 5.46 5.39 5.53 PHQ-4 6.4 6.32 6.48 5.41 5.34 5.48 PHQ-5 6.05 5.97 6.13 5.51 5.43 5.58 PHQ-6 5.67 5.59 5.74 5.55 5.48 5.62 PHQ-7 5.87 5.79 5.95 5.57 5.5 5.64 PHQ-8 5.76 5.68 5.83 5.6 5.52 5.67 PHQ-9 5.66 5.58 5.73 5.54 5.47 5.62 SCSQ-1 6.23 6.17 6.3 4.28 4.2 4.36 SCSQ-2 6.23 6.17 6.29 4.04 3.96 4.13 SCSQ-3 6.3 6.23 6.36 4.08 4 4.16 SCSQ-4 6.32 6.26 6.38 4.06 3.99 4.14 SCSQ-5 6.81 6.75 6.88 4.43 4.36 4.5 SCSQ-6 7.03 6.96 7.09 4.71 4.64 4.77 SCSQ-7 6.88 6.81 6.95 4.62 4.55 4.69 SCSQ-8 6.73 6.66 6.8 4.79 4.72 4.86 50~64 Original 6.55 6.46 6.64 6.56 6.47 6.65 GAD-1 6.93 6.83 7.03 6.44 6.36 6.52 GAD-2 6.91 6.82 7.01 6.45 6.36 6.53 GAD-3 6.92 6.82 7.01 6.44 6.36 6.53 GAD-4 6.99 6.9 7.09 6.37 6.29 6.46 GAD-5 6.81 6.72 6.91 6.49 6.41 6.57 GAD-6 7 6.9 7.09 6.41 6.33 6.5 GAD-7 6.66 6.57 6.75 6.5 6.42 6.59 PHQ-1 7.27 7.17 7.36 6.23 6.15 6.31 PHQ-2 7.26 7.16 7.36 6.3 6.22 6.38 PHQ-3 7.26 7.16 7.35 6.23 6.15 6.32 PHQ-4 7.17 7.08 7.27 6.29 6.21 6.37 PHQ-5 7.03 6.94 7.13 6.42 6.34 6.5 PHQ-6 6.95 6.85 7.04 6.42 6.33 6.5 PHQ-7 6.99 6.89 7.08 6.44 6.36 6.53 PHQ-8 6.85 6.76 6.95 6.42 6.34 6.5 PHQ-9 6.78 6.69 6.88 6.52 6.44 6.6 SCSQ-1 7.14 7.06 7.22 5.41 5.32 5.51 SCSQ-2 7.19 7.11 7.27 5.31 5.22 5.41 SCSQ-3 7.26 7.19 7.34 5.29 5.19 5.38 SCSQ-4 7.29 7.21 7.36 5.19 5.1 5.28 SCSQ-5 7.54 7.46 7.62 5.22 5.14 5.31 SCSQ-6 7.58 7.51 7.66 5.31 5.23 5.4 SCSQ-7 7.67 7.59 7.75 5.2 5.11 5.28 SCSQ-8 7.63 7.55 7.71 5.54 5.46 5.62 ≥65 original 7.87 7.77 7.96 8.02 7.93 8.12 GAD-1 8.91 8.8 9.03 7.66 7.57 7.74 GAD-2 9 8.88 9.12 7.75 7.67 7.84 GAD-3 9.04 8.93 9.16 7.71 7.63 7.8 GAD-4 8.93 8.81 9.04 7.73 7.64 7.82 GAD-5 8.87 8.76 8.98 7.74 7.65 7.82 GAD-6 9.04 8.93 9.16 7.73 7.64 7.81 GAD-7 8.67 8.56 8.78 7.82 7.73 7.9 PHQ-1 9.03 8.92 9.14 7.44 7.35 7.52 PHQ-2 9.03 8.92 9.14 7.54 7.45 7.62 PHQ-3 8.86 8.75 8.96 7.42 7.33 7.5 PHQ-4 9.11 9 9.22 7.52 7.43 7.61 PHQ-5 9.17 9.06 9.28 7.59 7.5 7.68 PHQ-6 8.88 8.77 8.99 7.71 7.62 7.79 PHQ-7 8.97 8.86 9.08 7.77 7.68 7.85 PHQ-8 8.92 8.8 9.03 7.75 7.67 7.84 PHQ-9 8.78 8.67 8.9 7.77 7.69 7.86 SCSQ-1 8.37 8.28 8.46 7.08 6.98 7.18 SCSQ-2 8.42 8.34 8.51 6.97 6.87 7.07 SCSQ-3 8.57 8.49 8.66 6.91 6.81 7.02 SCSQ-4 8.5 8.41 8.59 6.88 6.78 6.98 SCSQ-5 8.65 8.56 8.74 6.84 6.74 6.94 SCSQ-6 8.79 8.71 8.88 6.9 6.8 7 SCSQ-7 8.83 8.74 8.91 6.8 6.71 6.89 SCSQ-8 8.99 8.9 9.08 7.05 6.96 7.14 Open in a new tab Appendix B Data analytic plan For transparency and provenance purposes, the main aim of this additional analysis is to demonstrate how alternative network metrics can yield different candidate intervention targets. While the primary manuscript utilizes the NodeIdentifyR (NIRA) algorithm to identify targets based on the dynamic propagation of symptom activation, this appendix explores the structural connectivity among coping styles, depressive symptoms, and anxiety symptoms using continuous data and bridge centrality. By comparing these approaches, this section serves to remind other researchers of the importance of selecting the most suitable network metrics tailored to their specific research questions—whether the goal is to simulate dynamic intervention effects or to identify static structural bridges between distinct symptom communities. The network analyses were conducted in R (Version 4.3.0) in three steps: 1) network estimation; 2) network bridge centrality; and 3) assessment of network accuracy and stability. This study used the bootnet package (Version 1.7.1) to estimate network structures and their stability and accuracy [ 35 ], the qgraph package (Version 1.9.8) to visualize the networks [ 64 ], and the networktools package (Version 1.6.0) to calculate bridge centrality indices. Network estimation We estimated a network composed of coping styles, depressive symptoms, and anxiety symptoms via a Gaussian Graphical Model (GGM) using the networktools package in R. In GGM, associations between two nodes refer to partial correlations after controlling for all other nodes in the network [ 36 ]. To remove possible false-positive edges, the networks were regularized using the adaptive least absolute shrinkage and selection operator (LASSO). LASSO applied an Extended Bayesian Information Criterion (EBIC) to shrink all edges in the network and sets small edges to zero [ 37 ]. In the network analysis, a node represents a variable, and an edge represents the partial correlation coefficient between two nodes after considering all other nodes. A thicker edge indicates a greater association between two nodes. A red edge signifies a negative association and a blue edge signifies a positive association. Bridge strength To examine the importance of different coping styles in connecting with depressive and anxiety symptom clusters, we calculated bridge strength for each node in the network using the networktools package. Bridge strength is defined as the sum of the edge weights connecting a specific node to all nodes in other designated communities (e.g., a coping style node connecting to depression and anxiety nodes). A node with a higher bridge strength indicates that it plays a more critical role in activating or deactivating symptoms in other symptom communities within the network [ 65 ]. Stability of bridge strength Given that the primary objective of this additional analysis was to elucidate the specific structural roles of coping styles in linking depressive and anxiety symptom clusters, our robustness evaluation specifically focused on the stability of the bridge centrality indices. We employed a case-dropping bootstrapping procedure (1,000 samples) using the bootnet package to assess the stability of bridge strength. This approach calculates the proportion of data that can be dropped to retain a 95% certainty of a correlation of at least 0.7 with the original bridge strength coefficients. The correlation stability coefficient (CS-coefficient) of the bridge strength is considered acceptable if above 0.25, and preferable if above 0.5 [ 35 ]. This targeted evaluation ensures that the identified bridging nodes are robust and reliable across the sample. Result Network estimation Figure 3 illustrates the estimated Gaussian Graphical Model (GGM) networks of coping styles, depressive symptoms, and anxiety symptoms for the total sample (All Age Groups) and the three age-stratified subgroups (35~49, 50~64, and ≥65 years). Each network consisted of 24 nodes. The networks demonstrated that nodes within the depressive (PHQ) and anxiety (GAD) symptom communities were densely connected with predominantly positive (blue) edges, reflecting a high degree of symptom comorbidity. In contrast, the edges connecting the coping styles community (SCSQ) to the symptom communities were relatively sparse but exhibited distinct age-specific topological patterns, comprising both positive (blue) and negative (red) partial correlations. This structural variation indicates that the interplay between coping styles and psychopathological symptoms is highly heterogeneous across different developmental stages. Fig. 3. Open in a new tab Network estimation Bridge strength To examine the role of different coping styles in activating or deactivating the depressive and anxiety symptom clusters, standardized bridge strength was calculated for each node, as shown in Fig. 4 (the results for bridge strength). Nodes with higher bridge strength act as critical hubs linking their own community to other communities in the network. In the total sample (All age groups), SCSQ-1 (Positive reframing) had the highest bridge strength among all coping style nodes, serving as the primary bridge between coping behaviors and mood symptoms. However, subgroup analyses revealed distinct age-related shifts in the bridging role of specific coping styles: in the 35~49 age group, the active coping style SCSQ-2 (Strategy exploration) had the highest bridge strength across the entire network, followed closely by SCSQ-1 (Positive reframing), which ranked third overall. This highlights the dominant bridging role of active problem-solving and cognitive reappraisal strategies in connecting to psychopathological symptoms during this life stage. In the 50~64 age group, SCSQ-2 (Strategy exploration) and SCSQ-1 (Positive reframing) remained the coping styles with the highest bridge strength (ranking 6th and 9th overall, respectively), indicating these active cognitive and behavioral strategies continue to play a crucial bridging role in anxiety and depressive symptoms during late middle age. In the ≥65 age group, a change was observed in older adults, where the negative coping style SCSQ-8 (Miracle fantasizing) had the highest bridge strength among all coping style variables, reflecting a transition where maladaptive, avoidant cognitive patterns (e.g., unrealistic fantasies) become the primary hubs linking coping styles to anxiety and depression symptom clusters. Fig. 4. Open in a new tab Bridge strength Stability of bridge strength The case-dropping bootstrapping procedure demonstrated excellent stability for the bridge strength indices across all estimated networks. Specifically, the correlation stability coefficient (CS-coefficient) for bridge strength in the 35~49 age group was 0.673. For the total sample, the 50~64 age group, and the ≥65 age group, the CS-coefficients all reached 0.75, which represents the maximum stability threshold typically evaluated in this procedure. The results indicate that the hierarchical importance and the bridging roles of the identified coping styles are highly robust and reliable across the different developmental stages. Authors’ contributions Zhenxuan Dong, Dingchao Wu, and Luo Hongge designed the study. Zhenxuan Dong collected the data, was responsible for the statistical analysis and interpretation of the results, and wrote the draft version of the paper. Luo Hongge, Xiujun Zhang, and Haitao Wang assisted with writing the paper, supervised the data collection, supervised the analysis, and reviewed the paper. All authors have approved the final article. Funding statement This research was funded by STI2030-Major Projects (Grant No. 2021ZD0200701), Basic Scientific Research Operation Funds for Universities in Hebei Province(Grant No. jjc2024062), Post-funding Project of North China University of Science and Technology (Grant No. 2024SKHQ0902). Data availability The data that support the findings of this study are available from the corresponding author upon reasonable request. Declarations Ethics approval and consent to participate Each participant signed an informed consent form. The research protocol was conducted in accordance with the Declaration of Helsinki and received ethical approval from the Clinical Trial Research Center Ethics Committee of The Second Xiangya Hospital, Central South University (No.2022S010). 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