Network analysis of anxiety and depressive symptoms one year after traumatic brain injury

We used network analysis to explore interrelationships between anxiety and depressive symptoms after traumatic brain injury (TBI). At one year post-injury, 882 adult civilians who received inpatient rehabilitation for moderate-severe TBI self-reported anxiety and depressive symptoms (Hospital Anxiety and Depression Scale). The severity of TBI was characterized acutely by the duration of post-traumatic amnesia (PTA), and TBI-related functional disability was rated by an examiner at one year post-injury using a structured interview (Glasgow Outcome Scale – Extended). We estimated two cross-sectional, partial correlation networks. In the first network, anxiety and depressive symptoms were densely interconnected yet formed three distinct, data-driven communities: Hyperarousal, Depression , and General Distress . Worrying thoughts and having difficulty relaxing were amongst the most central symptoms, showing strong connections with other symptoms within and between communities. In the second network, TBI severity was directly negatively associated with hyperarousal symptoms but indirectly positively associated with depressive symptoms via greater functional disability. The results highlight the potential utility of simultaneous, transdiagnostic assessment and treatment of anxiety and depressive symptoms after moderate-severe TBI. Worrying thoughts, having difficulty relaxing, and the experience of disability may be important targets for treatment, although future studies examining symptom dynamics within individuals and over time are required.


Introduction
Sustaining a traumatic brain injury (TBI) is associated with elevated rates of anxiety and depressive symptoms, often emerging during the first year, but remaining prevalent in the long-term (Alway et al., 2016;Ashman et al., 2004;Gould et al., 2011b). These symptoms are linked to poorer outcomes including greater functional disability (Gould et al., 2011a). Yet, the factors contributing to emotional distress, including injury-related factors (e.g., TBI severity), remain poorly understood (Mayer and Quinn, 2022;Ponsford et al., 2018). Moreover, many individuals with TBI experiencing anxiety and depression do not improve appreciably with treatment (e.g., Hicks et al., 2022;Little et al., 2021).
Challenges in understanding and addressing anxiety and depression after TBI may in part be attributed to reliance on traditional psychiatric classification systems (viz., the Diagnostic and Statistical Manual of Mental Disorders and International Classification of Diseases). Traditional psychiatric diagnoses are highly heterogenous and overlapping categories which do not appear to fully accommodate the experiences of individuals with TBI (Gould et al., 2011b;Simms et al., 2021), highlighting a need for alternative perspectives.

The current study
This study had two aims: (1) to visualize and analyze the network structure of anxiety and depressive symptoms one year after moderatesevere TBI in civilians; and (2) to clarify the paths by which TBI severity and TBI-related functional disability are linked to anxiety and depressive symptoms. Whilst our analyses were exploratory, we had four general hypotheses: (1) the network of anxiety and depressive symptoms would be dense (defined as >40% of possible edges present; Johal and Rhemtulla, 2021); (2) despite a dense network overall, some edges would be significantly stronger than others and some symptoms would have significantly higher centrality in the network; (3) anxiety and depressive symptoms would form several data-driven communities, but with fuzzy boundaries indicated by the presence of important bridge symptoms; and (4) individual anxiety and depressive symptoms would demonstrate differential associations with TBI severity and TBI-related functional disability.

Methods
We follow guidelines for transparent reporting of psychological network analyses in cross-sectional data (Burger et al., 2022). Data and measures are available by emailing the corresponding author. Analysis code is provided in Supplementary Appendix S1. Data were analyzed using the R statistical software environment, version 4.2.1 (R Core Team, 2022). This study was not preregistered.

Participants
Participants were recruited between 1998 and 2019 from consecutive inpatient admissions to an Australian hospital providing TBI rehabilitation, under a no-fault accident compensation scheme that ensured treatment regardless of socioeconomic status. Individuals were eligible if they were aged 16 years or older at injury and had sustained a moderate-severe TBI according to the Mayo Classification System (Malec et al., 2008). Under this system, an individual is considered to have a moderate-severe TBI according to at least one indicator: worst score of ≤12 on the Glasgow Coma Scale (GCS; Teasdale and Jennett, 1976) in the first 24 h after injury; ≥1 day of post-traumatic amnesia (PTA); intracranial abnormality detected on computed tomography (CT) scan. Individuals were excluded if they had sustained a mild TBI (according to Mayo criteria) or penetrating head injury or had another neurological condition.

Anxiety and depressive symptoms
The Hospital Anxiety and Depression Scale (HADS; Zigmond and Snaith, 1983) is a self-report measure of past-week anxiety and depressive symptoms recommended for use with individuals with moderate-severe TBI (Honan et al., 2019). The HADS is valued because it is relatively free of medical symptoms which may overlap with TBI sequalae. Fourteen items are rated on a variable 4-point Likert scale from 0 to 3 (variable response labels). Separate subscales for anxiety and depression (seven items each) can be scored and interpreted (subscale score range 0-21), although some psychometric evidence suggests the presence of a strong general distress factor (total score range 0-42; Carmichael et al., 2023;Schönberger and Ponsford, 2010). Higher scores equate to greater distress. The HADS has been previously shown to distinguish between individuals with TBI with and without affective disorders diagnosed via structured interview, providing evidence of its criterion validity (Whelan-Goodinson et al., 2009).

TBI-Related variables
TBI severity was measured prospectively and continuously on the inpatient ward using the Westmead PTA Scale (Shores et al., 1986). Longer PTA duration is indicative of more severe TBI. PTA duration is a strong measure of TBI severity, associated with the extent of neuropathology and long-term functional and cognitive outcomes (Ponsford, Spitz et al., 2016).
The Glasgow Outcome Scale -Extended (GOSE) was used as an objective measure of global functional disability after TBI (e.g., disruption to occupational, social, and leisure activities), administered as a structured interview and scored by the examiner. One of eight categories can be assigned, six of which are relevant to this study: (8) upper or (7) lower good recovery, (6) upper or (5) lower moderate disability, (4) upper or (3) lower severe disability. The GOSE has high inter-rater reliability (κ = .85; Wilson et al., 1998).

Procedures
Demographic and injury-related information were collected from medical records. Participants were administered the HADS and GOSE over the phone by a trained psychologist-researcher as part of a followup research interview conducted at approximately one year post-injury .

Variable selection
Prior to performing network analysis, we checked for the presence of uninformative HADS items (Mullarkey et al., 2019) and topological overlap/collinearity within the HADS (i.e., item redundancy; Fried and Cramer, 2017). No HADS item was below the threshold for informativeness (i.e., 2.5 SDs below the mean item SD). However, some topological overlap was detected. Topological overlap was assessed using the goldbricker function from the R package networktools (Jones, 2022), a package of assorted tools for identifying important nodes in psychometric network analysis. The function compares correlations that each node has with the rest of the nodes to see whether there are pairs of nodes with very similar connectionsrepresenting duplicates. This was worthwhile examining because different HADS items may measure the same underlying construct (Carmichael et al., 2023;Schönberger and Ponsford, 2010) and because topological overlap can result in biased estimation (e.g., inflated centrality of duplicate nodes; Fried and Cramer, 2017). We used the default settings in the goldbricker function, searching for pairs of HADS items which 1) were correlated at ≥.50 with one another and 2) which had <25% significantly different correlations with the other HADS items (i.e., at least three-quarters of their correlations within the HADS were the same). Two problematic pairs of items were identified: HADS Items 4 (Laugh) and 10 (Appearance) and Items (Laugh) 4 and 14 (Book/TV). Since Laugh featured in both pairs with topological overlap, we chose to remove only this item from the analysis.
Two networks were estimated. We used the remaining 13 HADS items (i.e., excluding Laugh) to explore the interrelationships and topology of post-TBI anxiety and depressive symptoms. Second, to examine the links between anxiety and depressive symptoms and TBI, we included the 13 HADS items, PTA duration, and GOSE scores. Missing data rates were extremely low for HADS items (0-0.23%), low for PTA (2.23%), and higher for GOSE (22.34%). We used pairwise estimation of edges with adjusted sample size (minimum sample size of n = 679 used to estimate the PTA-GOSE edge).

Network estimation
Network models were estimated via the bootnet wrap-around package in R (Epskamp et al., 2018). This package contains the estimate-Network function which allows for the estimation of a wide range of networks by calling upon a variety of other R packages and model frameworks. Due to the ordinal nature of the HADS items, we chose to estimate Gaussian graphical models (GGMs) based on Spearman's rank-order correlations. GGMs are a type of network model in which nodes are connected by undirected edges (i.e., do not specify directional associations) representing partial correlation coefficients (i.e., relationship between two nodes after controlling for all other relationships in the network). We selected the ggmModSelect algorithm within the estimateNetwork function. This algorithm is a non-regularized method for estimating GGMs (i.e., does not shrink parameters to zero as occurs in regularization). The algorithm finds the optimal model of 100 estimated models based on the extended Bayesian information criterion (EBIC; Isvoranu and Epskamp, 2021). Non-regularized methods perform well in the context of low-dimensionality data (i.e., number of participants much greater than number of nodes), large samples (n ≥ 600), and dense networks (>40% of possible edges present; Isvoranu and Epskamp, 2021;Johal and Rhemtulla, 2021;Williams et al., 2019).
Networks were visualized using the qgraph package (Epskamp et al., 2012), which can be called upon by the bootnet wrap-around package (Epskamp et al., 2018). Nodes were depicted as circles and edges/partial correlations as lines connecting the circles. Edge thickness and saturation were allowed to scale freely with wider and more saturated edges signifying stronger conditional associations. Positive edges were shown in blue and negative edges in red. The layout was based on the Fruchterman-Reingold algorithm, whereby more interconnected nodes are arranged near one another and towards the center of the network (Fruchterman and Reingold, 1991).

Network description
To describe the topology of post-TBI anxiety and depressive symptoms in Network 1, we first considered the density/overall connectivity of the network, with >40% of possible edges present considered to be a dense network. It has also been suggested that ~30% of possible edges present = low degree of density, ~50% edges = medium density, and ~70% edges = high density (Johal and Rhemtulla, 2021). A dense network would signify the intertwined nature of anxiety and depressive symptoms after TBI and, according to the network theory, suggest that activation of one symptom is more likely to trigger a cascading effect throughout the network, potentially culminating in an entrenched, self-sustaining mental disorder (Borsboom, 2017). Network density is therefore important to consider as it carries potentially significant implications for our understanding of the nature of post-TBI anxiety and depressive symptoms and could inform future assessment and treatment approaches.
To determine the presence of distinct communities of anxiety and depressive symptoms in Network 1, we used the probabilistic Spinglass algorithm (Reichardt and Bornholdt, 2006), performed 1000 times via the igraph package (Csardi and Nepusz, 2006). The Spinglass algorithm performs relatively well compared with many other community-detection algorithms (Christensen et al., 2023) and can accommodate negative edges. In GGMs/partial correlation networks, negative edges (i.e., negative partial correlation coefficients) may arise between otherwise positively associated symptoms because the common variance has been removed. It is important to take this into account so that pairs of symptoms with a negative edge are more likely to be placed in different communities rather than the same community. Detection of distinct symptom communities would provide valuable information about anxiety and depressive symptoms that are more likely to co-occur after TBI. These distinct symptom communities may represent different underlying constructs, which may become the focus of future research and intervention efforts.
We described the importance of individual nodes to the networks by computing centrality indices in qgraph (Epskamp et al., 2012). Highly central HADS items may represent symptoms which are especially important in the experience (e.g., maintenance, etiology) of post-TBI anxiety and depression. We chose to focus on the 1-step expected influence (1EI), which is more relevant and robust for psychopathology networks than other indices (Bringmann et al., 2019;Epskamp et al., 2018). 1EI is calculated as the non-absolute sum of edge weights/partial correlations (i.e., retaining negative signs) directly connected to a node (Robinaugh et al., 2016) and can be thought of as a node's activating potential throughout the anxiety-depression network (McNally, 2021). We also computed the bridge 1EI, which is a version that only sums the edges connecting nodes between communities , which may help in understanding comorbid anxiety and depression. Node centrality was of greater interest in Network 1.
To explore links with TBI in Network 2, we were more interested in interpreting individual edges extending from the PTA and GOSE nodes. To compare the network approach with a more traditional sum-score approach, we also correlated the HADS scale sum-scores (total, anxiety subscale, depression subscale) with these TBI-related variables.

Stability and accuracy analysis
We tested the robustness of the network results using the bootstrapping procedures provided in bootnet (Epskamp et al., 2018). We then used these bootstrapping results to test for significant differences between edge weights and node centralities. The bootstrapping procedures are described in detail in Supplementary Appendix S2.

Investigating the influence of age
Due to the broad age range (17-91 years) in the sample, we investigated whether the network results were influenced by age. First, we added age as a node to Network 1 and Network 2, thereby removing variance attributable to age, and examined whether there were any differences in the presence of edges compared with the original networks. Second, we re-estimated each network in three sub-samples: young adults (≥17 and <40 years old; n = 481), middle-aged adults (≥40 years and <60 years old; n = 241), and older adults (≥60 years old; n = 160). We visually compared the resulting networks. However, any differences detected visually may represent differences in sample size and/or sampling variability (e.g., insufficient power in smaller groups to detect an edge). Therefore, we also conducted pairwise statistical model comparisons using the NetworkComparisonTest package (van Borkulo et al., 2022). The network comparison tests involved comparing the networks on two key properties: 1) global strength, identifying whether there was a significant difference in the overall network density/connectivity, and 2) network structure, identifying any significant differences in edge weight. These omnibus tests can be followed-up by post-hoc comparisons to identify specific nodes or edges responsible for the group differences. The network comparison test procedure is described in greater detail in Supplementary Appendix S3.

Sample selection and characteristics
Data extraction yielded 951 individuals with TBI who received inpatient rehabilitation between 1998 and 2019. We excluded 12 individuals who completed less than half of the HADS. Other individuals were excluded because of having mild TBI (n = 19), penetrating head injury (n = 1), age under 16 years at injury (n = 7), another serious neurological condition (n = 27), or a combination (n = 3; final sample n = 882), resulting in a final sample size of 882. Excluded individuals were significantly older (M = 46.20 vs. 40.56 years, p = .045) and more likely to not be in the labor force (22.81% vs. 11.22%, p = .032). There were no significant differences in terms of other demographic variables, HADS scores, PTA duration, or GOSE scores (all p>.05).
Approximately three-quarters of the sample were male (Table 1); they ranged widely in age (17-91 years). All participants had sustained a moderate-severe TBI according to at least one severity indicator, with ~97% having a moderate or severe TBI based on PTA duration alone. Most participants sustained their TBI in a road traffic accident, ~67% in a car or motorcycle accident. Most were living independently in the community at one year post-injury, approximately half were engaged in work or study, and slightly less than half were currently in a romantic relationship.

Network 1: topology of post-TBI anxiety and depressive symptoms
The zero-order correlations between the 13 HADS items included in the network analysis (lower diagonal of Table 2) were moderate-tostrong (mean r = .46, SD = .09, range = .25-.68), illustrating the close relationship between anxiety and depressive symptoms one year post-TBI. However, the partial correlations (upper diagonal of Table 2), calculated after conditioning on all other symptoms, imply that much of this was driven by shared variance across the items (mean |r| = .08, SD = .08, range = .00-.37). Network analysis allows the simultaneous examination of all these conditional associations, with the removal of shared variance helping to uncover which symptoms and associations may be the most important in the experience of anxiety and depression after TBI. Network 1, containing the 13 HADS items, is represented visually in Fig. 1. The model was accurate and stable. On average, edges estimated to be non-zero were present in ~81% of the 2500 bootstrapped analyses. Only one edge, Fright-Relax, was included in the bootstrap less than half (~46%) of the time and should be interpreted with caution. Centrality estimates were stable, with each correlation stability coefficient (CScoefficient) above .50 (1EI = .75; bridge 1EI = .75; full accuracy and stability results in Supplementary Table S1 and Supplementary Figures  S1 and S2).
This network of anxiety and depressive symptoms can be considered a dense network, having 38 of 78 (48.72%) possible edges present (i.e., medium density). This highlights the intertwined and co-occurring nature of the anxiety and depressive symptoms assessed. All conditional associations were positive, except the edge Restless-Look Forward. In other words, when holding constant for all other symptoms in the network, higher levels of restlessness were associated with a greater propensity to look forward to things with enjoyment. Other edges were absent from the model, indicating that some symptoms were statistically independent of one another (i.e., could be explained by shared relationships with other symptoms) or that the conditional association was insufficiently strong.
In 941 of 1000 analyses, the Spinglass algorithm detected three distinct symptom communities, with each community potentially representing a different underlying construct. One community comprised three items from the HADS anxiety subscale -Fright, Butterflies, and Panicwhich we named the Hyperarousal community (colored pink). The remaining four anxiety subscale items, Tense, Worry, Relax, and Restless, formed a separate community reflecting non-specific symptoms of negative affect; we called this General Distress (colored orange). Finally, the six HADS depression subscale items formed a Depression community (colored blue). The strongest edges occurred within communities: Enjoy-Look Forward (.37), Fright-Butterflies (.34), and Butterflies-Panic (.31), suggesting frequent co-occurrence of these symptoms. Nonetheless, every symptom was directly connected to at least one symptom of another community.
Visually, no symptom appeared isolated in the network. Yet, symptoms were not equally connected or important, with some edges/partial Table 2 Means, standard deviations, and spearman's correlations between HADS items included in the network analysis (n = 882). Note. HADS = Hospital Anxiety and Depression Scale. Odd-numbered items are part of the HADS anxiety subscale; even-numbered items are part of the depression subscale. Individual HADS item responses can range from 0 to 3.Values in the lower diagonal represent zero-order correlations; the upper diagonal contains partial correlations. The partial correlations are calculated by controlling for all other symptoms included in the network and therefore have a lower magnitude than the zeroorder correlations. correlation coefficients (range = − .10-.37) and many node centralities (1EI range = 0.54-1.27; bridge 1EI range = 0.06-0.69) found to be statistically significantly different (see Figs. 2 and 3; for significant differences between individual edges, see Supplementary Figure S3). Two of the most central symptoms in the network (even if ignoring the less robust Fright-Relax edge) included Relax (1EI = 1.14) and Worry (1EI = 1.13) of the General Distress community. In other words, these symptoms had a large statistical influence on the network and may be theorized to play especially important roles in the experience (e.g., etiology, maintenance) of anxiety and depression after TBI. These symptoms also had the highest bridge centrality (Relax: bridge 1EI = 0.67; Worry: bridge 1EI = 0.69), demonstrating the strongest connections with symptoms in other communities (i.e., forming 'bridges' between symptoms of General Distress, Hyperarousal, and Depression), thereby potentially helping to understand the comorbidity of anxiety and depressive disorders observed in this population. Relax was significantly more influential in the network than over half of the symptoms (Fig. 2) and both Relax and Worry had significantly higher bridge centralities than most other symptoms (Fig. 3). The relative importance of Relax was driven by edges with Restless (.26) within its own community and with Book/TV (.19) and Cheer (.17) in the Depression community. Worry displayed prominent edges with Tense within its own community (.24) and with Fright (.23) and Panic (.15) in the Hyperarousal community. Panic was a stronger bridge symptom of the Hyperarousal community (bridge 1EI = 0.55), and Cheer had a higher bridge centrality within the Depression community (bridge 1EI = 0.40).
On the other hand, Restless and Slow had the lowest centrality values (1EI = 0.54 and 0.67, respectively), demonstrating the least statistical influence on the network. Restless also possessed the lowest bridge centrality (bridge 1EI = 0.06). Lastly, although Enjoy had a relatively high centrality (1EI = 1.06), its bridge centrality was low (bridge 1EI = 0.12), possessing many connections with other Depression symptoms but not symptoms in other communities.

Network 2: links between anxiety and depressive symptoms and TBI
To examine links between anxiety and depressive symptoms and TBI, we estimated a second network model which contained the 13 HADS items in addition to PTA duration (measure of TBI severity) and GOSE scores (measure of TBI-related functional disability). These results were also robust (CS-coefficients: 1EI = .75; bridge 1EI = .75), with edges estimated to be non-zero included in an average of ~82% of the 2500 bootstrap analyses. Three edges were included in only half or fewer of the bootstraps and should be interpreted cautiously: Fright-Relax (50%), Cheer-Slow (45%), and Slow-PTA (42%; full accuracy and stability results in Supplementary Table S2 and Supplementary Figures S4 and S5).
Network 2 is shown in Fig. 4. The interrelationships between the anxiety and depressive symptoms were similar to the first network model (centrality indices and significant difference tests in Supplementary Figures S6-S8). Here, the edges extending from the new TBIrelated variables, PTA and GOSE, were of most interest.
First, adopting a sum-score approach (Table 3), the HADS total and depression subscale scores were not significantly associated with PTA duration. HADS anxiety subscale scores were weakly negatively associated with PTA duration (i.e., higher anxiety symptoms associated with less severe TBI), although this was not a particularly robust finding (p = .048). On the other hand, all HADS scores were robustly, moderately correlated with GOSE scores (all p˂.001). In other words, higher levels of emotional distress were associated with greater functional disability.
However, network analysis painted a more nuanced picture of the paths by which TBI severity and TBI-related functional disability were linked with anxiety and depressive symptoms. Overall, the TBI-related variables only had unique, direct associations with four symptoms of Hyperarousal or Depression, but not General Distress. When controlling for all other variables in the network, PTA duration only displayed two direct, negative associations with Hyperarousal symptoms: Fright (− .09) and Butterflies (− .10). This means that participants who experienced a more severe TBI were less likely to report frightened feelings and stomach butterflies at one year post-injury. Note. Numbers in the diagonal are the raw 1-step expected influence (1EI) values of each symptom. Symptom labels are color-coded according to the data-driven community: General Distress (orange), Hyperarousal (pink), and Depression (blue). Cell color indicates the results of the bootstrapped difference tests between the estimated 1EI values. Black cells indicate a significant difference between the two corresponding symptoms at p˂.05. Gray cells indicate a non-significant difference. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 3. Network 1: Bridge expected influences and significant differences (n = 882). Note. Numbers in the diagonal are the raw bridge 1-step expected influence (1EI) values of each symptom, representing the potential for a symptom to activate symptoms in other communities. Symptom labels are color-coded according to the data-driven community: General Distress (orange), Hyperarousal (pink), and Depression (blue). Cell color indicates the results of the bootstrapped difference tests between the estimated 1EI values. Black cells indicate a significant difference between the two corresponding symptoms at p˂.05. Gray cells indicate a non-significant difference. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Note. Nodes (circles) are individual items of the HADS (Hospital Anxiety and Depression Scale; higher scores indicate greater distress), TBI severity as measured by duration of PTA (post-traumatic amnesia; higher scores indicate more severe TBI) and TBIrelated functional disability as measured by score on the GOSE (Glasgow Outcome Scale -Extended; higher scores indicate less disability). 'Forward' = Look Forward and 'Appear' = Appearance. HADS items are color-coded by their membership to a data-driven community, indicated by the figure legend. Undirected edges, indicated by lines between nodes, represent partial correlations between HADS items, after controlling for relationships with all other nodes. Edges were estimated pairwise (adjusted sample size n = 679-882; mean n = 854.47). Blue lines between the circles indicate positive conditional associations and the negative conditional associations are represented by red lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Table 3 Pearson's zero-order correlations HADS scores and TBI-related variables (n = 691-859). Note. TBI = Traumatic brain injury. HADS = Hospital Anxiety and Depression Scale. PTA = post-traumatic amnesia. GOSE = Glasgow Outcome Scale -Extended. CI = confidence interval.
PTA had one direct association with a Depression community symptom (Slow), although as previously noted, the bootstrapping procedure suggested that this association was not particularly robust. Instead, PTA appeared to have indirect positive associations with depressive symptoms including Enjoy, Slow, and Appearance via greater functional disability (PTA-GOSE = − .22, GOSE-Enjoy = − .17, GOSE-Slow = − .14, GOSE-Appearance = − .10). Greater functional disability was also directly associated with more frightened feelings (GOSE-Fright = − .08).

Investigating the influence of age
Because of the sample's broad age range, we investigated the influence of age on the network results. When age was added as a node to Network 1, three edges that were originally present were now absent (Tense-Slow, Worry-Relax, and Slow-Look Forward), and two new edges emerged (Tense-Panic and Relax-Slow). When age was added as a node to Network 2, only one new edge was present (Worry-Slow), with no other differences in the presence of edges. The edges that disappeared or emerged were amongst the weaker associations estimated (edge weights = .08-.11). In addition, we re-estimated each network in subsamples of young adults (≥17 and <40 years old; n = 481), middleaged adults (≥40 years and <60 years old; n = 241), and older adults (≥60 years old; n = 160) and compared the resulting networks. The agebased networks are displayed in Supplementary Figure S9. Visually, some differences were apparent. The networks of young adults (the largest group) appeared to have a greater number of edges, whilst there were no direct conditional associations between PTA and any emotional distress symptoms amongst the older adults (the smallest group). Nonetheless, the network comparison tests found no statistically significant differences across the age groups in terms of global strength or overall network structure (p-values = .091-.979; full statistics in Supplementary Table S3) and thus no post-hoc comparisons were conducted. Therefore, differences detected visually may represent differences in sample size and/or sampling variability (van Borkulo et al., 2022). For example, the edges extending from PTA to emotional distress symptoms in the overall sample were amongst the weakest, and there may not have been sufficient power in the older adult group (n = 160) to detect these. Overall, these analyses suggested that the influence of age on the conditional associations between anxiety and depressive symptoms and TBI-related variables was minimal.

Discussion
We used network analysis to explore interrelationships between anxiety and depressive symptoms one year after civilian moderatesevere TBI and examine associations with TBI-related variables. We formed four general hypotheses which were supported. First, the network of anxiety and depressive symptoms was dense, with nearly half (48.72%) of all possible edges present. Second, some symptom associations were stronger than others and there were various differences in the importance of individual symptoms to the network. Worrying thoughts and having difficulty controlling worry/restlessness appeared particularly important. Third, three data-driven communities of highly interconnected symptoms were identified: Hyperarousal, Depression, and more non-specific symptoms of General Distress. These symptom communities displayed fuzzy boundaries, with notable connections occurring between symptoms of different communities. In particular, bridges were identified between worrying thoughts and hyperarousal symptoms and between having difficulty relaxing and depressive symptoms. Fourth, we observed nuanced, differential associations with TBI-related variables. TBI severity was directly negatively associated with hyperarousal symptoms. On the other hand, TBI severity was indirectly positively associated with depressive symptoms via greater functional disability. The influence of age on the network results appeared minimal.

Network 1: topology of post-TBI anxiety and depressive symptoms
The first network of anxiety and depressive symptoms was of medium density, with 38 unique, conditional associations present between symptoms. This demonstrates the interconnected nature of anxiety and depressive symptoms after TBI and is line with previous studies on the comorbidity and reciprocity of anxiety and depression in this population (Gould et al., 2011b;Wang et al., 2021). Perhaps due to reliance on traditional diagnostic classification, previous studies of post-TBI psychopathology have often been confined to either anxiety or depression. However, this is likely to result in an incomplete picture of the clinical reality faced by individuals with TBI. Our results highlight the importance of the simultaneous assessment of anxiety and depressive symptoms and potential value of transdiagnostic treatment for this population. Network analysis can address the intertwined nature of anxiety and depressive symptoms, with the removal of shared variance and computation of centrality indices enabling the identification of symptoms and symptom associations which may be especially important. Our results suggest that, one year after moderate-severe TBI in civilians, worrying and having difficulty relaxing may play unique and important roles in holding the anxiety-depression network together and may function as important symptoms bridging different symptom communities. Activation of these symptoms may result in especially rapid, spreading activation throughout the rest of the anxiety-depression network. These symptoms may help to understand the comorbidity of post-TBI anxiety and depression and may be promising targets for transdiagnostic treatment.
Whilst one should avoid over-interpreting the clinical relevance and causality of results from cross-sectional networks, it is worth elaborating on the central symptoms identified in this study. Worrying appears to be one of the most common emotional distress symptoms experienced during the first year after TBI (Hart et al., 2016;Jorge et al., 1993;Wang et al., 2021). Although traditionally conceived as a symptom of anxiety (American Psychiatric Association, 2022;Zigmond and Snaith, 1983), one study found that up to 69% of individuals with TBI diagnosed with major depressive disorder reported problems with worry (Jorge et al., 1993). Worrying has also been identified as highly central in network models of anxiety and depressive symptoms estimated in samples characterized by varied and comorbid psychiatric diagnoses, extending beyond anxiety (Beard et al., 2016;Kaiser et al., 2021). Moreover, amongst individuals with TBI endorsing clinically significant anxiety symptomatology at one year post-injury, 70% reported finding it difficult to control their worry or relax (Hart et al., 2016). It needs to be acknowledged that individuals with moderate-severe TBI have much to worry about, as they face uncertainty about recovery and the need to adapt to a broad range of disabilities. However, worrying after TBI may be exacerbated by the presence of cognitive impairment which may further decrease the person's ability to cope with everyday situations and stressors (e.g., worry about keeping up at work or in conversation; Gould et al., 2014).
For individuals with TBI presenting with worry and having difficulty relaxing, our results suggest it may be beneficial to target these symptoms earlier in treatment, potentially resulting in a cascading positive effect throughout the rest of the anxiety-depression network. These symptoms could be addressed, for example, using strategies of cognitive behavioral therapy (CBT) such as structured problem-solving and worry exposure (Ponsford, Lee et al., 2016). In addition, the node Relax may not only be related to difficulty in controlling worry but also restlessness. Treatment for the latter may include options which address psychomotor activity, such as mindfulness-based approaches, relaxation, and behavioral activation (Ponsford, Lee et al., 2016).

Network 2: links between anxiety and depressive symptoms and TBI
In the second network, we extended our analysis to examine the roles of TBI-related variables. The extant literature has been inconclusive regarding the role of TBI severity in post-injury emotional distress (e.g., cf. Gertler and Tate, 2020;Hart et al., 2014;Wardlaw et al., 2018). On the one hand, longer PTA duration is a strong predictor of higher levels of disability (Sherer et al., 2008), and emotional distress may be experienced as a psychological reaction to this disability (Pagulayan et al., 2008). In addition, more severe TBI has been associated with more extensive neuropathology (Wilde et al., 2006), including in brain regions responsible for emotional processing, suggesting a possible biological gradient (Mayer and Quinn, 2022). On the other hand, severely injured individuals are more likely to have reduced self-awareness of injury-related changes, which may buffer against emotional distress, although awareness may increase with time (Malec et al., 2007).
Our results using network analysis suggest that both these possibilities may apply within the same sample of individuals with moderatesevere TBI, depending on the specific symptoms. TBI severity, as measured by PTA duration, was characterized acutely in hospital, whilst the HADS was administered one year later, suggesting that injury severity may influence future endorsement of emotional distress symptoms. We found that positive associations between PTA duration and depressive symptoms at one year post-injury occurred via the degree of functional disability, as assessed on the GOSE. This result suggests that addressing disability, through rehabilitation and accommodations to maximize participation in valued activities, may help to avoid spreading activation throughout the network of anxiety and depressive symptoms. Importantly, treating only the emotional distress may not address the root of the problems and may not have the ultimate desired effects of improving quality of life, wellbeing, and meaningful participation after TBI (Pagulayan et al., 2008). We also found more severe TBI was directly negatively associated with symptoms of hyperarousal; this relationship may be mediated by the individual's level of self-awareness (Malec et al., 2007). As individuals with moderate-severe TBI develop awareness of their injury and its impacts, they may require psychological support to assist in adaptive self-appraisal of their post-injury self and to prevent the development of anxiety and depressive symptoms (Ponsford et al., 2012).

Study strengths and limitations
The strength of our study lies in the use of network analysis as an innovative methodological tool to generate novel clinical insights about anxiety and depressive symptoms after TBI. Post-TBI anxiety and depression remain poorly understood and addressed, and there is a need to adopt alternative perspectives to advance the field. The network approach to psychopathology offers a promising alternative that can potentially overcome challenges of traditional diagnostic classification systems, such as symptom heterogeneity and diagnostic comorbidity. Our study is one of only a handful of empirical studies to date to employ network analysis in individuals with TBI. Network analysis is a powerful, exploratory framework that can relate symptoms to other symptoms whilst removing common variance. In doing so, it can reveal nuance in the data not noticeable with established approaches. In this study, we have shed light on potential targets for effective treatment of post-TBI anxiety and depression, paving the way for future interventionfocused studies. Moreover, our results help to clarify the complex relationship that exists between the injury and anxiety and depressive symptoms, a relationship which has remained largely elusive in the literature. We hope that our study will encourage other researchers to adopt network analysis and other alternative, transdiagnostic or symptom-oriented approaches to address mental health difficulties after TBI in new and helpful ways.
One limitation of this study was the cross-sectional design and grouplevel analyses. Most data were collected contemporaneously, meaning that we could only examine the strength of associations, not their directionality or dynamic, causal nature. Further, we do not know whether the findings at a group level will generalize to individual people. Nonetheless, studies have suggested that the results of cross-sectional, partial correlation networks predict symptom change across time (Robinaugh et al., 2016;Rodebaugh et al., 2018); our exploratory, hypothesis-generating study has identified symptoms of worrying thoughts and having difficulty controlling worry/restlessness as promising avenues for future research. Longitudinal network studies will be required to understand the causal roles and underpinnings of these symptoms after TBI. Further, idiographic/personalized networks, modeling within-individual relationships, will help to reveal the extent to which particular symptoms and symptom associations are equally or differently important across individuals with TBI. By administering repeat assessments (e.g., via ecological momentary assessment), a network model can be constructed for each individual (rather than an overall sample), showing how the individual's symptoms predict one another across time (Wright and Woods, 2020). This could potentially support the development of more personalized treatment informed by within-individual symptom dynamics (e.g., Levinson et al., 2023).

Conclusions
We found that emotional distress symptoms are interrelated in a complex fashion in civilians one year after moderate-severe TBI. Our findings point to the utility of simultaneous, transdiagnostic assessment and treatment of anxiety and depressive symptoms for this population. Worrying and having difficulty relaxing were identified as symptoms which may be especially important to the maintenance and comorbidity of post-TBI anxiety and depressive symptoms and may be promising initial targets for transdiagnostic treatment. The results suggest that, beyond directly treating emotional distress symptoms, clinicians should also address disability, its functional impacts, and the adjustment process. Next steps include to investigate causation and within-individual processes via longitudinal and idiographic network studies.

Funding
This work was supported by the Transport Accident Commission through the Institute for Safety Compensation and Recovery Research; and JC was supported by an Australian Government Research Training Program (RTP) Scholarship. The funding sources had no involvement in the study design, in the collection, analysis, or interpretation of data, in the writing of the report, or in the decision to submit the article for publication.

Declaration of Competing 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.