The relations between different components of intolerance of uncertainty and symptoms of generalized anxiety disorder: a network analysis

The Ethics Committee of the First Affiliated Hospital of the Fourth military medical university approved this study under the number No. KY20182047-F-1. With the help of Wenjuanxing (www.​wjx.​cn), we conducted this survey from 16 December 2020 to 18 December 2020. First the participants will read an informed consent. After they agreed to participate, they will finish the following items. Participants were also reminded that the survey was anonymous and personal information would not be disclosed.

We used a dimensional approach that considered individual differences in different components of IU along a full range of normal to abnormal symptom severity levels of GAD (see Research Domain Criteria) [33]. Therefore, there were no eligibility requirements for participants in this study. Based on the fact of numerous active users of WeChat in China, it was used for the dissemination of this survey [34]. In the present network, we need to estimate 19 nodes and 171 edges. Although there are no clear guidelines yet as to how many participants we need per parameter, a rule of thumb put forward was at least three people per parameter [35]. Thus, the present network may need recruit at least 570 participants. A total of 633 university students from Xijing University participated in our study. All of these participants were Chinese speaking undergraduate students. Nine questionnaires were excluded due to their demographic information is incomplete. At last, a total of 624 questionnaires were obtained.

We used Gaussian graphical model (GGM) to estimate the final network [43]. Within a GGM, the edges represent the partial correlation between nodes after controlling for all other nodes in the network. As recommended by Epskamp and Fried, we used the nonparametric Spearman rho correlations to estimate the network structure in order to account for the ordinal nature of the IUS-12 and GAD-7 [44]. The regularization of the GGM was conducted via the graphical lasso algorithm [45]. This regularization process shrunk all edges, and the edge with small partial correlation was shrunk to zero, thus the easier to interpret and more stable network can be obtained [44, 45]. At the same time, the tuning parameter was set to 0.5, which was a good balance between the sensitivity and specificity of extracting true edge [44, 46]. The visualization of the network was conducted by the Fruchterman-Reingold algorithm [47]. In the visualized network, the blue edge represents the positive correlation, while the red edge represents the negative correlation. A thicker edge means a stronger correlation between two connected nodes. The network was constructed and visualized using R-package qgraph [48].

The node expected influence was calculated via R-package qgraph [48]. Node expected influence is more appropriate for the network with both negative and positive edges when compared with the traditional node centrality index (e.g., node strength) [49]. Expected influence is defined as the sum of the value of all edges connecting to a given node. The higher the expected influence, the more important node is in the network. Moreover, the node bridge expected influence was computed by R-package networktools [50]. Bridge expected influence is defined as the sum of the value of all edges connecting a given node with nodes in the other community. Higher bridge expected influence values mean greater extent for increasing risk of contagion to other communities [50]. In the present network, we divided nodes into two communities in advance: one community is IU, which includes 12 components of IU (IUS-12) and the other community is GAD, which consists of seven anxiety symptoms (GAD-7). In addition, the predictability of node was calculated via R-package mgm [30]. Predictability represents the extent to which the variance of a node can be explained by all of its connected nodes.

The robustness of network was evaluated by R-package bootnet [51]. The accuracy of edge weight was evaluated by computing 95% confidence intervals using a non-parametric bootstrap approach with 2000 samples and calculating bootstrapped difference tests for edge weight. The stability of node expected influence and node bridge expected influence were evaluated via calculating correlation stability coefficient using a case-dropping bootstrap approach with 2000 samples, and by calculating bootstrapped difference tests for node expected influence and bridge expected influence. The value of correlation stability coefficient preferably should be above 0.5 and should not be below 0.25 [51].

In fact, recent bifactor analyses have found that in clinical and non-clinical samples the IUS-12 is best represented by a general factor, which explains most of the reliable variance across the items [52‐55]. These findings indicate that a total score is an appropriate index of IU [9]. Thus, we also constructed one network consisting of eight nodes (i.e., one node represents the total score of IUS-12 and seven nodes represent the seven items of GAD-7) and calculated the related indexes.

The mean age of these 624 university students (43% male) was 19.38 ± 1.12 years (mean ± SD, range 18–25 years). In addition, 246 participants were sole offspring and 378 participants were non-sole offspring. Participants’ GAD-7 scores represented almost the full range of symptom severity. On the GAD-7 (M = 4.63, SD = 3.86), a total of 333 participants had minimal anxiety symptoms (range = 0–4), 236 had mild anxiety symptoms (range = 5–9), 37 had moderate anxiety symptoms (range = 10–14), and 18 had severe anxiety symptoms (range = 15–21). Furthermore, the scores on the IUS-12 (M = 35.08, SD = 7.44, range = 15–55) almost covered the full range of IU. Together, the distributional characteristics of the variables basically allowed the present investigation to estimate the strength of the relations among individual differences in different components of IU and symptoms of GAD. Table 1 shows abbreviation, mean scores, standard deviations and predictability for each variable selected in the present network. Table S1 showed the nonparametric Spearman rho correlation matrix of these variables (in Supplemental Material).

Network structure of different components of IU and symptoms of GAD is shown in Fig. 1. This network shows some characteristics as below. First, 102 edges are not zero (60%) among 171 possible edges and most of these edges are positive except four negative edges. Second, we find six strongest edges in the final network. Four of the strongest edges are between IU’s components IU1 “Unforeseen events upset me greatly” and IU2 “It frustrates me not having all the information I need” (weight = 0.39), IU11 “The smallest doubt can stop me from acting” and IU12 “I must get away from all uncertain situations” (weight = 0.30), IU9 “When it’s time to act, uncertainty paralyses me” and IU10 “When I am uncertain I can’t function very well” (weight = 0.27), and IU10 “When I am uncertain I can’t function very well” and IU11 “The smallest doubt can stop me from acting” (weight = 0.26). Among anxiety symptoms, we find two strongest edges are between A5 “Being so restless that it is hard to sit still” and A7 “Feeling afraid as if something awful might happen” (weight = 0.30), and A3 “Worrying too much about different things” and A4 “Trouble relaxing” (weight = 0.28). It is noted that those strongest edges have no one which linked IU’s components and anxiety symptoms. Bootstrapped 95% confidence interval suggesting the accuracy of edge weights was relatively accurate and reliable (Figure S1 in the supplementary material). Moreover, in the present network, bootstrapped difference test for edge weights indicates that six strongest edge weights are significantly stronger than about 80 to 100% proportion of the other edge weights (Figure S2 in the supplementary material). Third, node predictability is depicted as circle around node in Fig. 1. The value of node predictability ranges from 13 to 58%, and the average is 42%. This indicates that on average, 42% of the variance of nodes in the present network can be explained by their neighboring nodes. Anxiety symptom A3 “Worrying too much about different things” has the highest predictability, indicating that 58% of its variance can be explained by its neighbors. And IU’s components IU7 “I should be able to organize everything in advance” and IU3 “One should always look ahead so as to avoid surprises” have the lowest predictability, indicating that both 13% of their variances can be explained by their neighbors (see Table 1).

The node expected influence is shown in Fig. 2a. A3 “Worrying too much about different things” and IU2 “It frustrates me not having all the information I need” have the highest expected influence, indicating that these two variables are the most associated nodes in the present network from the perspective of statistics. IU7 “I should be able to organize everything in advance” of IU has the lowest expected influence, indicating that this variable is the least associated node in the present network from the perspective of statistics. The correlation stability coefficient of expected influences is 0.75, indicating that the estimation of expected influences is adequately stable (Figure S3 in the supplementary material). Moreover, bootstrapped difference tests for expected influences show that in the present network, the expected influences of A3 “Worrying too much about different things” and IU2 “It frustrates me not having all the information I need” are significantly higher than about 30 to 60% proportion of the expected influences of other nodes and the expected influence of IU7 “I should be able to organize everything in advance” is significantly lower than all other nodes’ expected influences (Figure S4 in the supplementary material).

The node bridge expected influence is shown in Fig. 2b. In the community of IU, IU2 “It frustrates me not having all the information I need” has the highest bridge expected influence. This indicates that in the community of IU, IU2 “It frustrates me not having all the information I need” has the strongest connections with GAD symptoms. In the community of GAD, A3 “Worrying too much about different things” and A2 “Not being able to stop or control worrying” have the highest bridge expected influences. This indicates that in the community of GAD, these two symptoms have the strongest connections with IU’s components. The correlation stability coefficient of bridge expected influences is 0.44, indicating that the estimation of bridge expected influences meets the requirement (Figure S5 in the supplementary material). Bootstrapped difference tests for bridge expected influences show that in the present network, the bridge expected influences of A3 “Worrying too much about different things”, A2 “Not being able to stop or control worrying”, and IU2 “It frustrates me not having all the information I need” are significantly higher than about 30 to 60% proportion of the bridge expected influences of other nodes (Figure S6 in the supplementary material).

The network consisting of eight nodes (i.e., one node represents the total score of IUS-12 and seven nodes represent the seven items of GAD-7) shows that IU is directly related to all GAD symptoms. The relations between IU and A3 “Worrying too much about different things” and A2 “Not being able to stop or control worrying” are the strongest relations. Readers interested in this network can find related results in the supplementary materials (Table S2 and Figure S7).