Data Sources and Searches
PRISMA guidelines  were used for conducting this meta-analysis. We conducted a systematic search of six electronic databases: PubMed, Cochrane Library, Embase, Web of Science, ProQuest, and PsycINFO from inception to June 2019. No restrictions were used regarding language. The keywords included: anxiety OR anxious OR phobic OR fear OR fears OR phobia OR phobias, and adolesc* OR child* OR boy* OR girl* OR juvenil* OR minors OR paediatri* OR pediatri* OR pubescen* OR school* OR student* OR teen* OR young, and behavio* OR cogniti* OR CBT OR famil* OR “contingency management”, and parent* OR mother OR father, and random* OR allocate* OR assign* OR “cross over*” OR crossover* OR controlled. More details of literature search reports can be found in Additional file 1. Furthermore, to identify additional eligible randomized controlled trials (RCTs), the reference lists of relevant studies were scanned.
Studies Selection and Comparisons Design
To determine appropriate studies for our meta-analysis exploring the efficacy and acceptability for treatment of children and adolescents with anxiety disorder, we selected studies according to the following criteria: (1) we included any RCTs investigating the application of parent-only CBT for the treatment of anxiety disorder in children and adolescents, and comparing parenr-only CBT with WL or CBT with parents; (2) we included studies with children and adolescents who were under the age of 18; (3) All participants met a primary diagnosis of a current anxiety disorder, conforming to standardized diagnostic criteria（DSM-IV and K-SADS-PL）[20-22]. to enhance the reliability of our conclusions, we designed two comparisons that complemented each other. One group compared parent-only CBT with WL as a control group, while another group compared parent-only CBT with CBT with parents. In order to focus on anxiety disorder, we excluded studies in which more than 20% of participants had a primary diagnosis of other mental disorders. We adapt relatively strict criterion about including children with anxiety disorder, so studies in which patients were only described with anxiety symptoms rather than confirmed diagnoses were excluded. Because anxiety disorder is frequently comorbid other mental disorders, we did not exclude studies in which participants had a secondary diagnosis of comorbid psychiatric diseases such as major depression and attention deficit hyperactivity disorder. For avoiding influence of drug, trials were excluded if more than 20% of patients took psychotropic drugs. Previous literature introduced Primary Care Behavioral Health (PCBH) model designed by the Veteran’s Administration and the Bureau of Primary Care . The PCBH model recomends that the patients who came to the first consult with the psychologist needs 4-6 sessions CBT. And in accord with our previous study, we excluded trials if they met the following criteria: the duration of treatment was less than 6 weeks, or the number of sessions was less than 6. Finally, studies were excluded if we detected repeated publication.
The inclusion process was conducted by two independent reviewers (BY and TT). First, the reviewers scanned the abstract and title of potential papers, and identified studies to be read in full text. The final selection of studies was conducted by both reviewers. If there was any disagreement between the two reviewers, another reviewer was consulted to resolve the discrepancy (XZ).
The primary outcome of efficacy was the mean change scores of the anxiety rating scale from baseline to post-treatment. When there was more than one available anxiety rating scale in one study, we used the scores from the anxiety rating scale according to a predefined hierarchy, based on psychometric properties and frequency for use with children and adolescents. We also established a hierarchy of informants of anxiety rating scales, with the child or adolescent self-report first in the hierarchy, then the parent/teacher report and then the clinician report. Finally the hierarchy of anxiety symptom severity measurement scales are as below: (1) Revised Children’s Manifest Anxiety Scale (RCMAS), (2)Spence Child Anxiety Scale, Child and Parent Versions (SCAS), (3) Screen for Child Anxiety-Related Emotional Disorders (SCARED), (4), Clinician severity ratings (CSR) (5) Fear Survey for Children Revised (FSSC-R), (6) Child Behavior Checklist (CBCL), (7) other scale.
The second efficacy outcome was remission rate measured by the proportion of participants who did not meet the standardized diagnostic criteria for anxiety disorder after treatment.
The outcome of acceptability was all-cause discontinuation, defined as the proportion of patients in the treatment group who withdrew from treatment early for any reason.
Data Extraction and Methodological Quality
Two independent reviewers (BY and TT) used standardized data extraction forms to extract data of the main characteristics of all trials, and the methodological qualities of trials were also assessed. Standardized data extraction forms included data on study characteristics (e.g., publication year, first listed author, country, journal, sponsor, institution), intervention details (e.g., duration of treatment, session of treatment, treatment pattern), patients’ characteristics (the number of patients, diagnostic criteria for anxiety disorders), and outcome measures (e.g., remission rate, pre- and post-treatment outcomes). The risk of bias among all studies was assessed according to the Cochrane Collaboration Risk of bias tool described in the Cochrane Handbook for Systematic Reviews of Intervention . If there was any disagreement between the two reviewers, XZ was consulted to resolve the discrepancy. We did not determine the risk of bias across studies, because the number of included studies was too small.
We compared the relative efficacy and acceptability by performing a meta-analysis using Review Manager 5.3 (The Cochrane Collaboration of The Nordic Cochrane Center in Copenhagen). Because of various anxiety rating scales among included studies, there maybe exist underlying heterogeneity and the difference in the true treatment effect among studies. So the DerSimonian and Laird random-effects models were adopted for all meta-analyses.
Pooled estimates of standardized mean difference (SMD) were calculated with 95% confidence intervals (CIs) for continuous outcomes. An SMD of more than 0 indicates that the comparison conditions (WL or CBT with parents) were more effective. Conversely, an SMD value of less than 0 indicates that the parent-only CBT condition was more effective. Regarding the risk ratios (RRs), we calculated 95% confidence intervals for discontinuous outcomes. Values of more or less than 1 indicate that the comparison groups or parent-only CBT group more frequently involved events of concern, respectively. Additionally, heterogeneity of both effects among studies was assessed using the p-values of the Q statistic and I² statistic. For the primary outcome of efficacy（parent-only CBT compared with WL ), we realized significant heterogeneity（I²=81%，P=0.001）. Then we performed sensitivity analysis by excluding the outlier, the study of Cartwright-Hatton（2011）in forest plot Fig 2A.
To test significant differences in primary efficacy between the different categories of studies, we also performed subgroup analyses. The studies were divided into different categories based on the following factors: male to female ratio (more than 1 or not more than 1), the risk of bias according to the Cochrane Collaboration Risk of bias tool (high bias risk or unclear risk) and the anxiety rating scale (other-rated scale or self-rated scale), respectively.
As for publication bias, we performed Egger's teston STATA.