A preliminary search yielded 809 English-language studies and 3012 Chinese-language studies. After reviewing the titles and abstracts, 383 articles remained; following a duplication check and full-text reading, 57 studies were finally included for the network meta-analysis, comprising 63 comparisons. The steps for literature retrieval are shown in Fig. 1.

Steps of literature retrieval

The characteristics of 57 included studies [3, 15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70] are shown in Table 1, which involved 13 interventions, including psychotherapy/CBT, group psychotherapy, Mindfulness-Based Cognitive Therapy (MBCT), placebo/non-intervention, health education, exercise therapy, electro-acupuncture, drug, EEG biofeedback, rTMS, rTMS + CBT, drug + others, and electro-acupuncture + CBT. A total of 3538 patients with IA were included, and all included studies had comparable descriptions.

Bias risk assessment for included studies

Two reviewers strictly followed the recommended bias risk assessment tools in the Cochrane Handbook to assess the risk of bias for the included studies. For example, in terms of randomization methods, 22 studies were evaluated as "low risk" as they adopted randomized allocation methods such as random number tables, stratified randomization, and drawing lots. Another 28 studies only mentioned "randomization" without reporting specific randomization methods and were evaluated as "unclear risk." The remaining seven studies randomly assigned patients according to the admission order and were rated "high risk." All studies failed to report whether allocation concealment was performed and was rated as “unclear risk." Seven studies involved blinding and were rated as "low risk." All studies had complete data and were rated as "low risk." Other biases were not mentioned and were rated as "low risk."

A total of 57 randomized controlled trials (RCTs) reported the effectiveness of different interventions to treat IA, involving 13 interventions. The size of each node in the network diagram (Fig. 3) represents the sample size of the corresponding intervention, and the thickness of the lines that connect different interventions represents the number of studies comparing the two interventions.

Network figure about efficient evidence

Network meta-analysis was performed on the included studies, generating 78 pairwise comparisons with 95% confidence intervals for the SMD. Please refer to Table 2 for detailed information.

The results of the network meta-analysis showed that compared with the placebo/non-intervention group, drug + others (SMD = -2.26, 95% CI = -3.26 ~ -1.26), EEG biofeedback (SMD = -1.62, 95% CI = -2.28 ~ -0.95), rTMS (SMD = -1.22, 95% CI = -1.74 ~ -0.71) showed statistical significance in the treatment effect of IA. Compared to the health education group, drug + others (SMD = -4.25, 95% CI =—6.34 ~ -2.17), rTMS + CBT (SMD = -7.17, 95% CI = -9.82 ~ -4.53), electro-acupuncture + CBT (SMD = -3.24, 95% CI = -4.84 ~ -1.65), EEG biofeedback (SMD = -2.90, 95% CI = -5.73 ~ -0.08), rTMS (SMD = -3.36, 95% CI = -5.56 ~ -1.16), exercise therapy (SMD = -2.71, 95% CI = -4.78 ~ -0.64), group psychotherapy (SMD = -2.32, 95% CI = -4.35 ~ -0.30), psychotherapy/CBT (SMD = -2.40, 95% CI = -3.82 ~ -0.99), and MBCT (SMD = -1.90, 95% CI = -3.05 ~ -0.74) have been shown to be statistically significant in the treatment of IA. Compared to the psychotherapy/CBT group, rTMS + CBT (SMD = -4.77, 95% CI = -7.00 ~ -2.54), electro-acupuncture + CBT (SMD = -0.84, 95% CI = -1.58 ~ -0.10), reflect the difference in therapeutic effect compared to use CBT alone, combined physical therapy is essential for the curative effect. Similarly, drug + others (SMD = -2.12, 95% CI = -3.53 ~ -0.70) also showed statistically different advantages compared to interventions that only used drugs. Furthermore, compared to MBCT, psychotherapy/CBT group, psychotherapy, exercise therapy, electroacupuncture, rTMS, EEG biofeedback, and electroacupuncture + CBT, therapeutic efficacy in the rTMS + CBT group showed optimal differences, and the results were statistically significant (p < 0.05), which further demonstrating the unique therapeutic effect of rTMS + CBT. This combination of treatment modalities could provide a reference for the treatment of IA in the future.

In terms of efficiency, the ranking was rTMS + CBT > drug + others > rTMS > electro-acupuncture + CBT > EEG-biofeedback > exercise-therapy > psychotherapy/CBT > group-psychotherapy > drug > MBCT > placebo/non-intervention > electro-acupuncture > health-education. The specific rank order is shown in Table 3, and the cumulative probabilities are shown in Fig. 4.

The consistency of each closed-loop result was tested. Inconsistency factors (IF) showed p = 0.4042, indicating good consistency. All local p > 0.05, indicating good consistency among all groups.

The research was roughly symmetrically distributed on both sides of the midline, indicating that a small sample effect was less likely to exist as shown in Fig. 5.

Funnel plot about the 14 interventions in the treatment of IA. A placebo/non-intervention, B health-education, C MBCT, D psychotherapy/CBT, E group-psychotherapy, F exercise-therapy, G electro-acupuncture, H rTMS, I EEG-biofeedback, J electro-acupuncture + CBT, K rTMS + CBT, L drug, M drug + others