Clarifying Fundamental Role of Symbol Coding in Cognitive Networks in Schizophrenia and Healthy Controls Leveraging Gaussian Graphical Models and Bayesian Networks

Abstract

Background and Hypothesis

Cognitive impairments in patients with schizophrenia initiate a cascade of effects on daily functioning. A single impairment can affect the functioning of the entire cognitive system. However, the relative interdependence among individual neuropsychological measures—whether the performance of a specific test depends on other tests—remains poorly understood.

Study Design

The study included a total of 1027 participants (522 patients with schizophrenia and 505 healthy controls) from China. All participants completed the comprehensive 9-test Measurement and Treatment Research to Improve Cognition in Schizophrenia Consensus Cognitive Battery. To examine cognitive relationships, we employed Gaussian Graphical Models for undirected relationships and Bayesian networks for directed relationships among cognitive tests.

Study Results

Symbol Coding played a central role and exhibited downstream associations with other cognitive tests in both patients and controls. Network analysis showed significant between-group edge differences in undirected networks, particularly between Continuous Performance and Spatial Span (SS), and between Symbol Coding and Managing Emotions (P = .018). A consistent sequential pattern (Symbol Coding → SS → Maze → Trail Making) was identified in both networks. Notably, the Symbol Coding → Managing Emotions connection was uniquely present in the patient’s network. Importantly, Symbol Coding and SS were identified as central variables in schizophrenia, showing extensive connectivity with other cognitive tests.

Conclusions

Symbol Coding is a fundamental cognitive test in both patients and controls. The association between Symbol Coding and Managing Emotions appears to be a stable feature in schizophrenia. These findings may inform mechanistic insights into cognitive architecture.

Introduction

Cognitive impairment in schizophrenia (SCZ) is one of the core characteristics and contributes to poor functional outcomes.¹ Meta-analyses indicate that individuals with SCZ exhibit deficits in various cognitive domains, notably in processing speed, memory, and attention/vigilance.^2–5 It is important to recognize that cognitive functions are interconnected, and the impairment in one can impact the entire cognitive system.⁶ Thus, clarifying the relative interdependence among cognitive tests—how the performance of specific tests depends on others—can give some implications for treatment and intervention strategies.

The Measurement and Treatment Research to Improve Cognition in Schizophrenia (MATRICS) Consensus Cognitive Battery (MCCB), developed in 2004,⁷ provides a standardized approach to assess cognitive function for researching cognitive-enhancing medications in schizophrenia. The MCCB has been translated into Chinese⁸ and utilized in over 100 studies to evaluate cognition in SCZ.⁴ The mainland Chinese MCCB comprised 9 tests evaluating 7 cognitive domains—processing speed, attention/vigilance, verbal learning, working memory, problem-solving, visual learning, and social cognition—identified as specific to schizophrenia via factor analysis.⁶ The cognitive deficits observed between schizophrenia and controls are primarily attributed to differences in speed of processing.^9,10 There are 3 tests in the Speed of Processing Domain: Symbol Coding test, Trail Making Test (TMT), and Category Fluency test. Research indicates that the Symbol Coding test and TMT are highly sensitive in identifying cognitive deficits in Chinese patients with first-episode schizophrenia.³ Symbol Coding test is regarded as a key aspect of cognitive impairment in SCZ.¹¹ On the other hand, these 3 tests can be regarded as polyfactorial tests. Good performance in Symbol Coding necessitates unimpaired motor speed, attention, and visuoperceptual abilities, encompassing scanning and writing capabilities.¹² TMT offers insights into visual search speed, scanning, processing speed, mental flexibility, and executive functioning.¹³ In the category fluency test, perseveration errors may indicate deficits in semantic search and response monitoring, while increased switching might reflect poor working memory.¹⁴ Therefore, studying the interrelations between cognitive tests, rather than focusing on individual cognitive domains, could provide more comprehensive clues for interventions. Given that environmental and cultural factors may influence cognition,¹⁵ it is crucial to examine the cognitive deficit patterns in middle-income countries such as China. We hypothesize that the cognitive deficits observed between schizophrenia and controls are related to differences in processing speed, with central tests such as Symbol Coding playing a pivotal role in the cognitive network.

Network analysis is well-suited to examine the interdependence of different cognitive tests, as it can reveal how the tests are associated with each other in schizophrenia and healthy controls. It does not presuppose a specific model of causal relationships among variables and generates spatially organized networks, enabling the identification of cognitive tests that are most central in the network.¹⁶ Gaussian Graphical Models (GGMs) and Bayesian network analysis are 2 approaches that construct undirected and directed networks, respectively. In GGMs, edges represent the strength of association between variables, accounting for the association of all other variables in the network.¹⁷ In Bayesian networks, arrows between variables denote more than mere correlation; they signify statistical directional conditional dependencies, though these should not be interpreted as causal without additional supporting evidence or assumptions. An arrow from A to B signifies that A is conditionally dependent on B, irrespective of other network variables.¹⁸ In this study, we used GGMs and Bayesian network analysis to explore the structure of cognitive networks, examining not only the interdependencies but also the centrality of individual tests like Symbol Coding in the network.

Additionally, considering the association of established confounders like symptom severity is essential for maintaining model accuracy.¹⁹ In patients with SCZ, cognitive function correlates with symptom severity. Clinical symptoms, mainly negative symptoms could act as the mediator of the relationship between cognition and functional outcome.^20,21 The meta-analysis showed that global negative symptoms had small significant correlations with all MATRICS neurocognitive domains.²² Verbal memory was linked to positive symptoms involving poor and disorganized emotional expression, language, and thought.²³ Greater general psychopathology prospectively could predict a 2-year change in executive function in youth.²⁴ Thus, accounting for symptom severity and other confounders in a Bayesian network structure is essential for accurately estimating the interdependence among cognitive tests.

The present study aims to test the hypothesis that there are interdependencies among cognitive tests, specifically focusing on how the performance of tests like Symbol Coding affects other cognitive functions, using GGMs and Bayesian networks. Utilizing data-driven approaches, GGMs can evaluate the network structure and identify differences between patients with schizophrenia and control subjects, while Bayesian network analyses can elucidate the directionality of network connections. The findings could inform hypotheses for longitudinal or experimental studies, where specific network variables (eg, key central tests) are manipulated to assess cognitive improvement and treatment outcomes.

Methods

Participants

The study included 522 patients diagnosed with SCZ and 505 healthy community controls. We confirmed diagnoses using the Structured Clinical Interview for Diagnostic and Statistical Manual of Mental Disorder, Fourth Edition (DSM-IV)²⁵ Participants were recruited from Peking University Sixth Hospital and the local community. The institutional ethics review board of Peking University Sixth Hospital approved this study. All participants provided written informed consent in accordance with the Declaration of Helsinki. Symptom severity in SCZ patients was evaluated using the Positive and Negative Syndrome Scale. Details regarding participant recruitment criteria, and clinical assessments are presented in Supplementary Methods.

Cognition Assessment

Neurocognition and social cognition were assessed using MCCB.²⁶ The battery assesses 7 cognitive domains—processing speed, verbal learning, visual learning, working memory, reasoning and problem-solving, and attention/vigilance. Shi and colleagues translated the MCCB into simplified Chinese, co-normed, and standardized it, excluding the letter number span test from the English version due to the unfamiliarity of many Chinese participants with the English alphabet.⁸ Thus, our study included 9 tests: Hopkins Verbal Learning Test-Revised, immediate recall (HVLT), Brief Visuospatial Memory Testt-Revised (BVMT), Neuropsychological Assessment Battery, mazes subtest (Maze), Continuous Performance Test, Identical Pairs (CPT-IP), Wechsler Memory Scale-Third Edition, Spatial Span (SS), TMT, Part A (TMT-A), Brief Assessment of Cognition in Schizophrenia, Symbol Coding subtest (SymbC), Category Fluency Test, animal naming (CFT), Mayer-Salovey-Caruso Emotional Intelligence Test, managing emotions branch (ME; Supplementary Table S1). Three of these tests fall under the Speed of Processing Domain. Each of the 9 MCCB tests provides continuous raw and T-scores. T-scores for each test are calculated by comparing an individual’s raw scores to a normative sample of 656 individuals from 6 locations in China.⁸ The scores are normalized with a mean of 50 and a standard deviation of 10.

Statistical Analyses

Bivariate Correlations

Analyses were conducted with R (Version 4.3.2). The correlation matrix was generated using the psych package with each cognitive performance from 9 tests as the input for both patients and controls.

Gaussian Graphical Models (Undirected Networks)

Network Estimation

 Networks were estimated using the bootnet package,²⁷ in which nodes represent cognitive variables from 9 tests and edges between nodes represent undirected partial correlations. The Extended Bayesian Information Criterion form of Least Absolute Shrinkage and Selection Operator regularization technique,^27,28 with a gamma tuning parameter of 0.5, was used to estimate networks for SCZ patients and controls. Edge weight accuracy was assessed using 95% confidence intervals derived from 5000 bootstrap samples of the study population with the bootnet package.

Based on the estimated networks, strength centrality was used to identify the cognitive tests with the strongest associations within the network. Node strength centrality was calculated by summing the absolute weights of edges linked to each node. The robustness of the strength centrality metrics was assessed through case-dropping bootstrap analysis using the bootnet package.²⁷This evaluation yielded CS-coefficients, indicating the highest proportion of cases that can be excluded while ensuring a correlation of 0.7 with a minimum of 95% confidence. Ideally, CS-coefficients should exceed 0.5, but a minimum threshold of above 0.25 is recommended.²⁹

Network Comparison

 We employed the R package NetworkComparison Test³⁰ with 2000 iterations to assess significant differences between GGMs of patients with SCZ and healthy controls. The Network Invariance Test assessed the structural differences between the networks of the 2 groups. The Global Strength Invariance Test was utilized to assess the sum of all absolute edge weights. Both invariance tests were carried out using permutation-based M-tests and S-tests.

Bayesian Networks (Directed Networks)

Network Estimation

Bayesian networks employ variables represented as nodes in directed acyclic graphs (DAGs), interconnected by arcs signifying directed connections, which can be positive or negative.³¹ These networks depend on key assumptions, including the lack of bidirectional causality (A → B and B → A) or feedback loops (A → B, B → C, and C → A), as well as the presence of all necessary variables within the network.³² Meeting the requirement of all essential variables is challenging due to the numerous third variables associated with cognition. We utilized the same variables as GGMs to estimate DAGs and standardized all variables. The hill-climbing algorithm³³ in bnlearn³⁴ was employed to estimate Bayesian networks. The algorithm optimizes goodness of fit according to the Bayesian Information Criteria (BIC) by exploring single-edge additions, removals, and reversals. The algorithm begins with an empty DAG and iteratively refines the candidate network until it identifies an optimally fitting DAG.

Network Stability Assessment

To ensure the stability of the network, we employed a bootstrapping approach with 1000 samples.³⁵ This approach involved creating a network for each sample, computing the average of all networks, and examining the arcs’ frequency and direction. Arcs included in the final Bayesian network were those present in at least 85% of bootstrapped DAGs and consistently directed in over 51% of them.³⁶ We computed the standardized Beta coefficient for each arc in the final network to quantify the impact of a unit change in a parent node on its descendant nodes. The BIC was utilized to evaluate the overall fit of Bayesian networks.

Bayesian Network Comparison

The Jaccard similarity coefficient was employed to assess variations in the structure of Bayesian networks concerning arc presence. The calculation involved dividing the count of common arcs with identical directions by the total number of unique arcs present in both networks.³⁶ The Jaccard similarity coefficient ranges between 0 and 1. The matrix was bootstrapped using 1000 iterations.

Analysis Included Symptoms and Sensitivity Analysis

To address potential confounding effects of symptoms on cognition, GGMs and a Bayesian network incorporating cognitive variables and symptoms of positive, negative, and general psychopathology were included using the previously mentioned methods. Stepwise regression analysis was performed using the caret package in R to identify the optimal predictors of cognitive test performance that are not directly dependent on the parent node in the Bayesian network.

Results

We included 522 patients with SCZ and 505 community controls in the study. Compared to controls, schizophrenia patients had lower education attainment (t(1025) = 36.078, P < .001), with a similar age [t(1025) = 1.885, P = .060] and a similar proportion of males [χ²(1, N = 1027) = 3.111, P = .078]. Demographic information is presented in Table 1. Patients with SCZ were all medicated except 2 patients and chlorpromazine dose equivalents (CPZE) based on defined daily doses³⁷ was (398.20 ± 7.11) mg (n = 505 with missing data of 17 patients). The median of duration is 1 year (Range: 0–3 years). The heat map of bivariate correlations between 2 of the 9 cognitive tests is shown in Figure 1. The probability values were adjusted using the Holm correction³⁸ (details in Supplementary Table S2&S3). The significant correlation magnitude ranged from 0.423 (CFT and TMT-A) to 0.872 (Symbol Coding and ME) in patients, and 0.134 (ME and CPT-IP) to 0.409 (Symbol Coding and CPT-IP) in controls. The heat map of bivariate correlations in patients included positive, negative, and general psychopathology symptoms are shown in Supplementary Figure S1 and Table S4.

GGM Networks

GGM networks and centrality estimates are shown in Figure 2 and  Supplementary Table S5 and S6. The strongest edge was between Symbol Coding and ME (r_p = .730) in schizophrenia, whereas between Symbol Coding and CPT-IP (r_p = .284) in controls. The most central nodes (strength) in the 2 networks were Symbol Coding (1.410 in the patient’s network; 0.517 in the control’s network, Supplementary Figure S2). The edge accuracy of the network a was estimated and showed relatively narrow confidence intervals (Supplementary Figure S3). The CS-coefficient of strength centrality remained 0.75 at patient’s network, suggesting the relationships between variables remained stable. The CS coefficient for the control network was 0.283 at an acceptable level.

The Global Network Invariance Test revealed significant structural differences between the schizophrenia and control network (M = 0.740, P = .0005). The patient network exhibited a significantly higher global strength compared to the control group (3.660 vs. 1.264, S = 2.397, P = .0005). The significant edges included the edge between Continuous Performance and SS (E = 0.261, P = .018), and the edge between Symbol Coding and Managing Emotions (E = 0.740, P = .018). Both edges exited in patients but not in controls.

Bayesian Networks

Figure 3 shows the Bayesian networks for schizophrenia patients and controls, and blue arcs signify positive predictions. Arc thickness signifies confidence from one node to another in the direction of the prediction depicted. The BIC value was −5298.70 for the schizophrenia network and −6333.04 for the control network. The most important arc was “Symbol Coding → ME” in the patient network, while “Symbol Coding → CPT-IP” in the control network (Table 2).

In both patients and controls, Symbol Coding was a parent of 3 other neurocognition domains, including CPT-IP, SS, and BVMT. One sequential pattern emerged from Symbol Coding to TMT-A (Symbol Coding → SS → Maze → TMT-A) in both networks.

The confidence in edge direction between SS and Maze (0.896) was high in patients, but low (0.516) in controls. The directional dependency between neurocognition and social cognition only emerged in the patient network. Symbol coding was the only parent of ME, with directional probabilities of 0.556.

The Jaccard similarity coefficient of 0.375 indicates a moderate degree of similarity between the arc sets of the 2 networks. A score of 0.375 indicates that about 37.5% (6/16) of the arcs are shared between schizophrenia and control networks. All the 6 common arcs between schizophrenia patients and controls share the same direction.

Network Analysis Including Symptoms and Sensitivity Analysis

 Supplementary Figure S4 presents the Bayesian network, which includes 9 cognitive variables along with positive, negative, and general psychopathology symptoms. The network was evaluated to address the potential confounding effects of symptoms on cognitive function. The 9 cognitive tests showed no correlation with positive, negative, or general psychopathology symptoms. All directional dependencies between cognition identified in the initial Bayesian network were also present in this network. The stepwise regression model for predicting Maze performance in patients included 4 predictors and demonstrated good performance (R² = 0.48, MAE = 7.48, RMSE = 9.21). Symbol Coding (β = 0.42, P < .001) emerged as the strongest predictor, followed by SS (β = 0.44, P < .001). Similarly, the model predicting CFT included 4 predictors (R² = 0.41, MAE = 6.11, RMSE = 7.52). Symbol Coding (β = 0.14, P = .003) emerged as the fourth predictor (Supplementary Table S8). These results underscore the foundational role of Symbol Coding and its associations with spatial memory and verbal fluency in patients.

Discussion

This study uniquely employs GGMs and Bayesian networks to analyze both unidirectional and directional dependencies in cognition using the mainland Chinese version of MCCB, involving a large cohort of SCZ patients and healthy participants. Symbol Coding consistently emerged as a foundational element, exhibiting downstream associations with other cognitive tests across both networks and groups. Critically, these directional dependencies in patients remained after including symptoms. These findings may help clarify causality and inform the development of targeted interventions to enhance cognition.

Symbol Coding was identified as the parent node in our analysis, with TMT-A and Category Fluency as descendant nodes. This aligns partially with previous studies indicating that processing speed is a key marker of neurocognitive deficits in schizophrenia, with these 3 tests commonly categorized within the processing speed domain.⁹ The hierarchical relationship observed, with Symbol Coding as the foundational task and TMT-A and Category Fluency as dependent tests, raises an important question: Does Symbol Coding measure processing speed in a more automatic, straightforward way? While all 3 tests belong to the processing speed domain, their roles in assessing cognitive processes differ. Symbol Coding may represent a core, automatic processing speed that requires minimal executive functioning. In contrast, TMT-A and Category Fluency likely engage additional cognitive functions such as reasoning, problem-solving, and executive control. In our analysis, Symbol Coding serves as the baseline for processing speed, while TMT-A and Category Fluency require more complex cognitive resources. TMT-A, for instance, engages visuospatial tracking,³⁹ numeric sequencing and visual attention, and Category Fluency taps into lexical retrieval and verbal executive control,^14,40 while the Symbol Coding test assesses visual processing speed. In SCZ patients of our study, performance in TMT-A depends directly on tasks like Maze, CPT, and Symbol Coding, while performance in Category Fluency is more dependent on HVLT. This suggests that Symbol Coding, while related to processing speed, might not require the same level of cognitive effort as TMT-A or Category Fluency. This result underscored the foundational nature of Symbol Coding in understanding broader cognitive dysfunctions in schizophrenia.

An additional and potentially more revealing aspect of our findings lies in the interconnectedness of the cognitive network in patients with SCZ. Compared to controls, schizophrenia patients exhibited a denser and more interdependent cognitive network, where cognitive functions appear more tightly coupled. This could reflect a lack of functional modularity or compartmentalization within the cognitive processing. The increased interconnectedness might suggest that difficulties in one cognitive domain can propagate across other domains, leading to a more fragile and vulnerable cognitive system in schizophrenia. In essence, the cognitive network in patients may be more susceptible to disruptions or cognitive impairments in a way that affects multiple domains at once. The delicate network may offer insights into the gradual deterioration of problem-solving efficiency, fine motor skills, and episodic memory in the later stages of SCZ.⁴¹ The differences in patients and controls were also mainly shown by the role of SS in the network. For patients, SS was the second most important node and directly impacted attention, visual, and verbal learning ability consistent with previous studies,⁴² which made the network more complex and easier to damage than controls. This finding gives some implications for treatment and intervention strategies. For instance, interventions targeting one cognitive domain, such as Symbol Coding, may have a wider and more generalized impact across other cognitive functions due to the dense interconnections within the schizophrenia network, providing a more holistic approach to therapeutic interventions.

The literature debates the degree of overlap between social cognition and neurocognition in schizophrenia. Neurocognition is considered essential, yet insufficient on its own, for effective social cognition in schizophrenia.^43,44 The ability of emotion regulation was accounted for partially by neurocognition to some extent. Managing emotions involves being receptive to feelings and regulating them in oneself and others to enhance personal insight. Patients with SCZ are insensitive to basic social cues and also struggle with recognizing more complex social cues,⁴⁵ as indicated by Corrigan and Green.⁴⁶ Difficulties with Symbol Coding could lead to delays in interpreting these social cues and emotional expressions, resulting in problems with emotional management. This delay could disrupt the flow of social interaction and make it harder to understand the emotional intent behind them. It should be noted that the edge direction between Symbol Coding and emotional management was 0.56, indicating a potential reciprocal relationship. This suggests modeling their directionality may be challenging, yet they maintain a stable association in undirected networks. The stable association between Symbol Coding and emotional management in schizophrenia across network analyses highlights the significance of implicit social cue processing for understanding others’ intentions, goals, and beliefs. Deficiencies in this effortless processing may result in misattributions of others’ emotional states.⁴⁵

Interestingly, in the overlapped sequential pattern from Symbol Coding to TMT (Symbol Coding → SS → Maze → TMT-A), SS plays the second important node in the patient’s network, but not in controls. The edge direction from SS to Maze was 0.90 in patients vs. 0.50 in controls, suggesting Maze performance is more likely to be dependent on SS in schizophrenia than in controls. Maze performance involves logically synthesizing information to draw conclusions and resolve problems. Individuals with SCZ may exhibit impaired reasoning, characterized by biased information gathering, event interpretation, and belief formation. A meta-analysis of 40 studies involving over 2100 participants found that cognitive training significantly affects reasoning and problem-solving (Cohen’s d = 0.57), as well as memory, including verbal learning and memory (d = 0.41) and verbal working memory (d = 0.35).⁴⁷

The high network density observed in our study suggests that cognitive domains in schizophrenia are highly interconnected, with individual tests showing strong associations with one another. While our findings highlight the centrality of specific tests like Symbol Coding, the dense network structure also raises the possibility that a total or composite score of cognition could be a valuable metric for guiding interventions. A composite score may capture the overall cognitive functioning more comprehensively, particularly in a population where cognitive impairments are widespread and interrelated. Future studies could explore whether interventions targeting a composite score, rather than individual domains, might yield broader improvements in cognitive functioning and daily outcomes for patients with schizophrenia.

Considering the limitations of our study is crucial. A limitation was our dependence on cross-sectional rather than longitudinal data. Despite cognition being generally stable,⁴⁸ future research should explore its dynamic aspects to identify the appropriate timescale and temporal distance at which cognitive processes interact over time. Secondly, Bayesian network analysis is more suitably applied to longitudinal or genetic datasets, where assumptions about directionality and feedback are more inherently supported and meet the starting assumptions. In our study, this approach was exploratory, aimed at uncovering potential dependencies among cognitive tests, and our results should be viewed as hypothesis-generating with caution in interpreting them. Thirdly, a high anticholinergic medication burden was reported to be associated with cognitive impairment in schizophrenia⁴⁹ and we have reported the CPZE. We chose not to experimentally control medication effects considering a valid comparison to the control networks as the previous study³⁶ did. Furthermore, the bivariate correlations included CPZE and duration showed no significant correlations with all nines cognitive tests (Supplementary Figure S5). Fourthly, the social cognition task in our study was limited to the emotional management test in MCCB. Our findings on the central role of Symbol Coding in cognitive networks align with the results of Abplanalp et al.,³⁵ who identified processing speed as a fundamental domain for nonsocial cognition in schizophrenia. This supports our observation that Symbol Coding, a task closely related to processing speed, plays a foundational role in the cognitive network. Additionally, their study highlighted facial affect identification as a key domain for social cognition, suggesting that future research should integrate both social and nonsocial cognitive tasks to provide a more comprehensive understanding of cognitive functioning in schizophrenia. While our study focused on cognitive tests in MCCB, the inclusion of social cognitive tasks, such as facial affect identification, could further elucidate the interplay between these domains and inform targeted interventions.

Conclusion

Our research on cognitive interdependence in a large cohort of SCZ patients and healthy individuals revealed that Symbol Coding serves as a foundational element, strongly correlated with other cognitive assessments. These findings help clarify the relationships between different cognitive tests and may guide the development of targeted interventions aimed at improving cognition.

Funding

This work was supported by the National Natural Science Foundation of China (82301687; 82330042), National Key R&D Program of China (2023YFE0119400); Capital’s Funds for Health Improvement and Research (2024-1-4111); Fundamental Research Funds for the Central Universities (Peking University Medicine Fund for world’s leading discipline or discipline cluster development, BMU2022DJXK007); Beijing Municipal Health Commission Research Ward Programme (3rd batch); China Postdoctoral Science Foundation (2022M720302); National Postdoctoral Program for Innovative Talents (BX20240029); Beijing Nova Program (20230484425).

Conflict of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References