Mapping the interplay between anxiety symptoms during the COVID-19 lockdown in Belgium: A undirected and Bayesian network perspective
Creators: name: Heeren, Alexandre
name: Lits, Grégoire
name: HANSEEUW, Bernard
name: Cougnon, Louise-Amélie
Publisher: name: Open Science Framework
Year: 2020
Subjects: subject: Public Health
subject: Social and Behavioral Sciences
subject: Psychiatry and Psychology
subject: Medicine and Health Sciences
subject: Psychology
subject: FOS: Psychology

description: Template: We are preregistering this exploratory data analysis of preexisting data, as suggested by Weston, Ritchie, Rohrer, and Przybylski (2019). https://doi.org/10.1177/2515245919848684 More details regarding the template can be found here: https://osf.io/v4z3x/ Context and Research Questions: Pandemic yields severe and long-lasting consequences on mental health (for a systematic review, see Brooks et al., 2020), and the COVID-19 pandemic is no exception to this statement. Early data indicate that the COVID-19 pandemic has a significant impact on mental health (e.g., Asmunsdon &amp; Taylor, 2020; Wang et al., 2020; for a systematic review, see Xiong et al., 2020), with anxiety symptoms being one of the most commonly reported problems (e.g., Quiu et al., 2020; Mertens et al., 2020; Xiong et al., 2020). In Belgium, the number of people reporting anxiety symptoms increased substantially during the lockdown of March 2020 compared to similar data collected two years before (Sciensano, 2020). And similar findings have been reported across different countries (e.g., González-Sanguino et al., 2020; Zhao et al., 2020). And that should not come as a surprise. The profound health, economic, and social consequences of COVID-19 lockdown are likely to be anxiogenic for many, regardless of whether or not they have had direct exposure to the virus (Heeren, 2020; Park, Velez, Kannan, Chorpita, 2020). However, in most of the studies that have been published so far regarding the impact of the lockdown on anxiety symptoms, researchers have relied on a unitary approach to anxiety by collapsing the different features of anxiety into one sum-score and thus ignoring any possibility that these distinct features could interact in different ways. Recently, a network approach to psychopathology has appeared, conceptualizing mental disorders as network systems of interacting symptoms. In this way, instead of investigating mental disorders as reflecting a single, unitary construct, a network approach allows an investigation into the structure of, and associations between, the symptoms themselves. Though only recently pioneered by Borsboom and his colleagues (e.g., Borsboom et al., 2011, Borsboom &amp; Cramer, 2013), this approach has quickly become a hot topic in contemporary clinical psychology. Many studies have accordingly used this framework to investigate the interrelations between systems of symptoms and speculate as to the clinical implications (for systematic reviews, see Contreras et al., 2019; Robinaugh et al., 2019). Although a few studies have already applied a network analytic framework to examine the interdependence between different factors assumedly involved in the psychological responses to the COVID-19 pandemic, and especially regarding the fear of infection or the anxious response to the structural impact of the pandemic (e.g., Papini et al., 2020; Taylor et al., 2020), none of these studies focused on the network structure of the connections between the distinct features of anxiety during the lockdown. In this project, we thus seek to map the network structure of the hallmark features of anxiety during the lockdown. To do so, we will implement the network computational tools via a reanalysis of an existing dataset (Lits et al., 2020; see below) that includes the GAD-7 (Spitzer et al., 2006)—one of the most commonly used self-reported screening tools in epidemiological and clinical research of anxiety disorders (e.g., Schalet et al., 2014)—in a large and representative sample of participants living in the French-speaking part of Belgium who took part to an online survey conducted during the first weeks following the (first) Belgian national lockdown (March 2020). Especially, we have three primary goals. First, we endeavor to clarify the pairwise connections among the distinct anxiety symptoms during the lockdown. To do so, we will compute a graphical Gaussian model (GGM). In this undirected network, edges signify conditional independence relationships between nodes (here, symptoms of anxiety), controlling for the effects of all other nodes. Of critical interest is the computation of centrality metrics that disclose the most potentially influential nodes maintaining the GGM network structure. We will then test whether these nodes cohere as a unitary network system of interacting elements or whether they instead constitute distinct communities (or subnetworks) of nodes (i.e., symptoms) serving different functions. Finally, we will use Bayesian computational methods to compute a directed acyclic graph (DAG) to estimate the probabilistic dependencies among the distinct anxiety features. A DAG is a directed network whereby each edge has an arrow tip on one end, signifying the direction of probabilistic dependence (McNally, 2016; McNally, Heeren, &amp; Robinaugh, 2017). To generate directed edges, DAGs encode the conditional independence relationships and characterize the variables' joint probability distribution. DAGs can thus be decomposed as a product of the conditional distribution of each node given its parent nodes in the graph, thus rendering DAG analysis capable of indicating whether the existence of node A ("downstream") probabilistically implies the existence of node B ("upstream") more than vice versa (e.g., Heeren, Bernstein, &amp; McNally, 2020). Although DAGs have occasionally been used in clinical psychology, they have increasingly become popular in other fields, especially in epidemiology and environmental sciences, wherein numerous illustrations are available. Therefore, we computed DAGs to generate a computationally driven model of the probabilistic dependencies among the distinct symptoms of anxiety reported during the lockdown. These complementary computational approaches can provide a novel perspective and clues to generating new hypotheses about the functional relations among the anxiety symptoms reported during the COVID-19 lockdown. Data description: The data we plan to use come from an online survey carried out between March 30 and April 10 by the Observatoire de Recherche sur les Médias et le Journalisme (ORM – UCLouvain; i.e., Lits et al., 2020). This survey aimed to gauge the extent of the COVID-19 infodemic in French-speaking Belgium during the COVID-19 lockdown. The survey also included data related to anxiety symptoms (as assessed using the well-validated and broadly used Generalized Anxiety Disorder 7-item scale, hereafter GAD-7) because the authors also wanted to evaluate the association between infodemic related behaviors and anxiety feelings during the Belgian lockdown. To do so, they rely on a sum-score of the seven items of the GAD-7. The final report of this survey (i.e., Lits et al., 2020) involves 1,817 French-speaking Belgians. The present re-analysis will focus on the item's responses of GAD-7's (and not the tally-score of the GAD-7) of these participants. Is the data publicly available: Yes, a summarized version can be found here: https://osf.io/z3r4e/ Date of access: 5 October, 2020 Data source: Collected by Grégoire Lits, Louie-Amélie Cougnon, Alexandre Heeren, Bernard Hanseeuw, &amp; Nathan Gurnet, all from UCLouvain, Belgium. Note that the statistical analyst of this pre-registered data re-analysis (i.e., Alexandre Heeren) was involved in the initial data collection. Sampling and data collection procedures: The data collection procedure is well documented in the following research report (available online): Lits, G., Cougnon, L.-A, Heeren, A., Hanseeuw, B., &amp; Gurnet, N. (2020, May 11). Analyse de « l’infodémie » de Covid-19 en Belgique francophone. https://doi.org/10.31235/osf.io/wsuj3. The sample was built upon a quota sampling method based on age, gender, and education level, and weighted by gender and educational level (following the results of the STATBEL 2019 governmental survey on workforce) to be representative of the characteristics of the population living in the French-speaking part of Belgium over the age of 16. Prior work based on the dataset: The statistical analyst of this preregistration (i.e., Alexandre Heeren) was not the statistical analyst of the two previous research reports based on the initial dataset. So far, the data have been analyzed and reported by Nathan Gurnet and Grégoire Lits for Lits et al., 2020) and by Bernard Hanseeuw and Nathan Gurnet for Hanseeuw et al., 2020). Prior knowledge of current dataset: The variable we are interested in from this dataset has already been processed in two previous publications aiming at depicting the COVID-19 infodemic-related behaviors in French-speaking Belgium (e.g., Hanseeuw, Cougnon, Heeren, Gurnet, &amp; Lits, 2020; Lits, G., Cougnon, L.-A, Heeren, A., Hanseeuw, B., &amp; Gurnet, N., 2020). However, these publications did not focus on the GAD-7, and only relied on a sum-score of the GAD-7 (i.e., there was no distinction between the seven features of anxiety). Finally, this dataset has never been analyzed via a graph theoretical framework. Here, for the first time, we will re-analyze the data related to anxiety in an exploratory fashion using a network approach (aka graph-theoretical framework). Moment of preregistration: Registration before any analyst on this team handling or analyzing the GAD-7 data using a network approach. Measured variables (that will be included in analyses): Given our research questions (see above), we plan to include the seven items of the Generalized Anxiety Disorder 7-item scale (GAD-7). Transformations: Following guidelines in using network analysis in clinical psychology (e.g., Epskamp &amp; Fried, 2018), we will apply, for each variable, the nonparanormal transformation via the R package huge (Jiang et al., 2019). Data Inclusion: We will include all participants of the research report of Lits et al. (2020). Outliers: N/A Sample size: For our analyses, the sample size will be 1,817 (as in Lits et al., 2020). Missing data: The final sample of Lits et al. (2020) does not include participants with missing values. Statistical plan: The measured variables (i.e., the 7 variables of the GAD-7; see above) will be included as nodes in the network models and processed as follows: 1. Data Preparation. First, we will test whether our correlation matrix is positive definite (reflecting that nodes are not linear combinations of other nodes). Second, we will search for potential pairs of redundant nodes, that is, nodes that are highly inter-correlated and that correlate to the same degree with other variables. To do so, we will implement the Hittner method for comparing dependent correlations (Hittner, May, &amp; Silver, 2003) via the goldbricker function of the R package networktools (Jones, 2018). If pairs of redundant nodes are identified, they will be combined via the reduce_net function of networktools—i.e., reducing the redundant variables via a principal component analysis of the two variables and creating a new variable. 2. Graphical Gaussian Model. We will use a graphical Gaussian model (GGM) to estimate the undirected network. In this network, edges signify conditional independence relationships between nodes, controlling for the effects of all other nodes (Epskamp &amp; Fried, 2018). We will present GGMs that will be regularized via the graphical LASSO (Least Absolute Shrinkage and Selection Operator) algorithm, which serves two primary functions (Friedman, Hastie, &amp; Tibshirani, 2011). First, it computes regularized partial correlations between pairs of nodes, thereby eliminating spurious associations (edges) attributable to the influence of other nodes in the network. Second, it shrinks trivially small associations to zero, thereby removing potentially “false positive” edges from the graph and producing a sparse graph comprising only the strongest edges. We will use the R package qgraph (Epskamp et al., 2012) that automatically implements the graphical LASSO regularization in combination with Extended Bayesian Information Criterion (EBIC) model selection (Foygel &amp; Drton, 2011). In this procedure, 100 models with varying degrees of sparsity are estimated; a final model is selected according to the lowest EBIC value, given a specific hyperparameter gamma (γ), which controls the trade-off between including false-positive edges and removing true edges. The hyperparameter γ is usually set between zero and 0.5 (Epskamp &amp; Fried, 2018). The closer one chooses a value of γ near 0.5, the more the EBIC will favor a simpler model containing fewer edges, whereas the closer one chooses a value of γ near zero, the more the EBIC will favor a model with more edges. We will opt to set γ to 0.5 to be confident that our edges are genuine, assuming that the true model is, indeed, sparse (Epskamp &amp; Fried, 2018). To estimate the stability of edges, we will bootstrap the confidence regions of the edge weights via the R package bootnet (Epskamp, Borsboom, &amp; Fried, 2018). We will set the bootstraps to 1,000. To quantify the importance of each node in the resulting graphical LASSO network, we will compute the expected influence centrality index (Robinaugh, Millner, &amp; McNally, 2016). The expected influence of a node is the sum of the edge weights incident on a given node, including positive and negative values. Higher expected influence values indicate greater centrality and thus greater importance in the network. We will evaluate the stability of the centrality metrics by implementing a subset bootstrap procedure (Costenbader &amp; Valente, 2003). To do so, we will repeatedly correlate the centrality metrics of the original dataset with the metrics calculated from a subsample of participants missing via person-dropping bootstraps (we will set the bootstraps to 1,000) as implemented in the R package bootnet (Epskamp et al., 2018). We will also calculate the centrality stability correlation coefficient (CS-coefficient) to quantify the effects of this person-dropping procedure. The CS-coefficient represents the maximum proportion of participants that can be dropped while maintaining a 95% probability that the correlation between centrality metrics from the full data set and the subset data are at least .70. Based on a simulation study (Epskamp et al., 2018), a minimum CS-coefficient of .25 (and preferably ≥ .50) is recommended for interpreting centrality indices. Using a bootstrapped difference test, we will then capitalize on this subset bootstrap procedure to test whether nodes statistically differ between them in terms of expected influence values. Because recent commentators have argued that differential variability—that is, the phenomenon that variables have drastically different variances—may distort conclusions about node centrality (e.g., Fried, 2016; Terluin, de Boer, &amp; de Vet, 2016), we will also compute the correlations between the standard deviation and the expected influence centrality value of each variable. This approach will allow us to test whether there is an association between nodes' importance in the network and its variability. Finally, we will test whether the nodes denoting the hallmark features of anxiety feelings during COVID-19 cohere as one or multiple subnetworks (“communities”). Following prior network research (e.g., Heeren, Bernstein, &amp; McNally, 2018; Robinaugh, LeBlanc, Vuletich, &amp; McNally, 2014), we will implement the spin-glass algorithm (Reichardt &amp; Bornholdt, 2006), a modularity-based community detection procedure suitable for uncovering the structure of relatively small networks with negative edge values (e.g., Traag &amp; Bruggeman, 2009). We will use the spinglass.community function (γ = 1, start temperature = 1, stop temperature = .01, cooling factor = .99, spins = 7) of the R package igraph (Csardi &amp; Nepusz, 2006). Nodes within a community are more strongly interconnected than they are with nodes in another community. In case of community structure, we will identify important nodes that may serve as bridges between the resultant communities by computing the bridge expected influence index via the bridge function of the R package networktools (Jones, 2018). Bridge expected influence is the sum of the edge weights connecting a given node to all nodes in the other community or communities (Jones, Ma, &amp; McNally, 2019). As for the centrality metrics, in the case of a community structure, we will evaluate the stability of the bridge centrality estimates via person-dropping bootstraps (we will set the bootstraps to 1,000) as implemented in the R package bootnet and compute the related CS-coefficient (Epskamp et al., 2018). Using a bootstrapped difference test, we will also capitalize on this subset bootstrap procedure to test whether nodes statistically differ between them in terms of bridge expected influence values. 3. Directed Acyclic Graph (DAG). Finally, we will compute a DAG to estimate a directed, potentially “causal” structure of the system (Pearl et al., 2016). We will use a Bayesian hill-climbing algorithm implemented via the R package bnlearn (Scutari, 2010). As implemented by bnlearn, the bootstrap function computes the structural aspects of the network model by adding edges, removing them, and reversing their direction to ultimately optimize the goodness-of-fit target score, i.e., the Bayesian Information Criterion. This involves an iterative process of randomly restarting this process with different possible edges linking different node pairs, perturbing the system, and using 50 different random restarts to avoid local maxima. Following our previous works (Bernstein, Heeren, &amp; McNally, 2017; Heeren, Bernstein, &amp; McNally, 2020; McNally, Heeren, &amp; Robinaugh, 2017), we will perform 100 perturbations (i.e., attempts to insert, delete, or reverse an edge) for each restart. As this iterative procedure unfolds, the function returns the best fitting network based on this random restart/perturbation procedure. To ensure the stability of the resultant DAG, we will then bootstrap 10,000 samples (with replacement), compute a network for each sample, and average across the resulting networks to produce a final network structure (e.g., Blanchard, Roskam, Mikolajczak, &amp; Heeren, 2020; Heeren, Bernstein, &amp; McNally, 2020; McNally, Heeren, &amp; Robinaugh, 2017), involving a two-step procedure. First, we will determine how frequently a given edge appeared in the 10,000 bootstrapped networks. We will then use the optimal cut-point method of Scutari and Nagarajan (2013) for retaining edges, which yields networks having both high sensitivity and high specificity. Second, we will ascertain the direction of each surviving edge in the 10,000 bootstrapped networks. 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