Patient and public involvement

This work will be based on published studies; therefore, patient or public involvement will be not required. Relevant results will be published in peer-reviewed journals.

Eligibility criteria

Any studies not meeting following inclusion criteria will be excluded.

1. Participants: patients with unipolar and bipolar depressions according to any international diagnostic criteria.

2. Interventions: we considered studies examining any ketamine or esketamine as a standalone treatment or in combination with psychotropic medications or psychotherapies. Any route of administration is acceptable.

3. Comparators: placebo including inactive control (eg, saline) and active control (eg, other antidepressants or anxiolytics).

4. Outcome measures:

The primary outcomes

1. Study-defined response at endpoint assessment (eg, ≥50% reduction from baseline in Montgomery–Åsberg Depression Rating Scale (MADRS)23 or Hamilton Depression Rating Scale (HAMD)24and study-defined remission at endpoint assessment (eg, MADRS total score ≤1216 or 10).10 When both the MADRS and HAMD were reported, only the MADRS will be used.

2. Dropouts due to adverse events (tolerability), measured as the proportion of patients who withdrew from the study, either during the acute-phase treatment or during the continuation/maintenance treatment, due to any adverse events (including specific adverse events and withdrawal symptoms).

3. Other adverse drug reactions.

Secondary outcomes

1. Study-defined response and remission at study-defined time points apart from treatment endpoint.

2. Severity of depressive symptoms as measured by standardised rating scales such as the MADRS.23

3. Suicide risk as measured by standardised rating scales, such as the Scale for Suicidal Ideations.25

4. Socio-occupational disability as measured by the Sheehan Disability Scale.26

E. Study design

We will include studies with double-blind RCTs focusing on the comparative efficacy and side-effect profile of ketamine and esketamine in the treatment of unipolar and bipolar depressions. Cross-over and cluster randomised trials will be included, while quasirandomised trials will be excluded. For cross-over studies, to address concerns around possible ‘carry over’ effects, we will use data from the precrossover phase.27 For studies that fail to report precrossover phase data, we will contact study authors to obtain this data.

Searching strategy

The relevant articles will be identified by searching the electronic bibliographic databases: PubMed, Web of Science, EMbase, Wanfang Data, China National Knowledge Infrastructure (CNKI). Medical subject headings will be used. The searching strategies of PubMed (English) and CNKI (Chinese) are shown in table 1 as examples to replicate for the other databases.

Selection process

We will use EndNote V.X7 software (Thomson Reuters, New York, USA) to collate search results and perform filtering. After removing duplicates, two independent reviewers will review the title and abstract of the identified studies and will exclude irrelevant parts. The full article will then be obtained and re-examined for more details to be included. Any conflict will be resolved through a discussion involving the third reviewer. This process will be completed by 25 February 2021.

Data collection

The data will be extracted independently by three investigators, and when inconsistencies are encountered, they will be resolved by consensus or discussion with another investigator. Information extracted will include publication information (eg, title, first author, publishing time, unit, country and funding support), details of interventions (eg, ketamine or esketamine dose and route of administration, concomitant medications dose and route of administration), details of comparator (eg, names of control measures, dose and route of administration), details of methodology (eg, participants, sample size, diagnostic criteria, demographic characteristics, data analysis strategies, clinical assessment and clinical variables) and outcome measures. If necessary, we will contact the first/corresponding author by e-mail to obtain additional information when the meta-analysis data were not reported.

Quality assessment

The risk of bias of individual trials and the certainty of evidence contributing to network estimates of the primary outcomes will be assessed by the Cochrane Collaboration Risk of Bias Tool (http://handbook-5-1.cochrane.org/), including the following criteria:

1. random sequence generation or allocation concealment.

2. Blinding of outcome assessment.

3. Selective outcome reporting.

4. Incomplete data assessment.

Two reviewers (ZX and XW) will carry out the quality assessment independently. Any disagreement will be resolved by discussion with the third reviewers (ZZ).

GRADEPro software (V.3.2 for Windows) will be used to evaluate the overall quality of the evidence.

Data synthesis

We will generate descriptive statistics for the trial, and study population characteristics across all eligible trials, describing the types of comparisons and some important variables, either clinical or methodological (such as year of publication, age, severity of illness, sponsorship and clinical setting). We will draw the network diagram to graphically present the available evidence.

Assessment of heterogeneity (pairwise meta-analysis)

We will conduct a pairwise meta-analysis comparing ketamine and esketamine versus placebo to investigate the effects of antidepressants in the treatment by visually inspecting the forest plots. For this analysis, heterogeneity will be assessed using Cochran X² test and further quantified using I² to decide which effect models are used for meta-analysis. A fixed-effect model will be used to analyse the data if there is no evidence of heterogeneity (p≥0.1, I² ≤50%). A random-effect model will be used if heterogeneity exists (p<0.1, I² >50%) and the possible causes from both clinical and methodological will be searched. In this analysis, we will consider all primary and secondary outcomes. We will assess heterogeneity using the tool described in the Cochrane Collaboration Handbook as a reference guide (http://handbook-5-1.cochrane.org/).

Assessment of the transitivity assumption of network meta-analysis

To assess whether the distribution of potential effect modifiers is balanced across treatment comparisons, we will check for significant differences in the distribution of the following factors among different comparisons: severity of depression before randomisation, age, average number of previous episodes and clinical and demographic characteristics such as age, gender, dose and severity of symptoms. We will group studies by treatment comparisons and obtain descriptive statistics regarding these important covariates. If significant discrepancies are found in the corresponding distributions, our network meta-analysis will be limited to studies which are considered sufficiently similar.

Network meta-analyses

Network meta-analysis will be performed to synthesise the evidence if there is no evidence against the transitivity assumption. We will use a random-effect network meta-analysis model28 fit in a frequentist setting, assuming a common heterogeneity parameter across all treatment comparisons. We will present the results including all estimated treatment effects and the corresponding 95% CIs. For the assessment of the extent of heterogeneity, the estimated value for the heterogeneity SD and the corresponding empirical distributions will be compared in each outcome. Furthermore, we will calculate the ranking probabilities for all treatments (including all available single drugs and combinations) of being at each possible rank for each intervention, using the surface under the cumulative ranking. The network meta-analyses (NMA) will be performed by the package ‘netmeta’ (V.0.5–0) in R (V.3.0.2, The R Foundation for Statistical Computing). We will use package ‘igraph’29 and package ‘ggplot2’30 to visualise the networks and the distribution of ranking probability distribution.

Assessment of inconsistency

Another key assumption for performing an NMA is the consistency in the agreement between the direct and indirect sources of the network. A common evaluation method of inconsistency is hypothesis test. Since our network meta-analysis focuses on two interventions, ketamine and esketamine, we will use the Z-test to assess the consistency. The Z-test31 is often used to evaluate the consistency of a network meta-analysis of two-arm RCTs. For continuous variables, we will use the difference of the mean difference (the difference between the direct and indirect comparison results) and its 95% CI to assess the inconsistency.The p value will be calculated to assess whether there is statistical agreement between direct and indirect evidence on the same comparisons. p<0.05 will be considered to be statistically significant. For continuous variables, we will calculate directly according to the result (mean difference).

Sensitivity analyses and subgroup analyses

We will conduct a sensitivity analysis to verify the robustness of the study conclusions and assess the impact of methodological quality, study design, sample size and the effect of missing data as well as the analysis methods on the result of this review.32 Studies meet the following criterion will be analysed to evaluate the sensitivity of our conclusions:

1. Studies with balanced doses in all arms.

2. Studies with low risk of bias.

3. Head-to-head studies.

We will also conduct the network meta-regression on primary outcomes for the:

1. Sex ratio.

2. The types of depression.

3. Duration treatment.

4. Depressive severity at baseline.

5. Dosing schedule. We excluded combinations of drugs from the network meta-regression because we cannot be sure whether some combinations can affect the dose effects.

Assessment of publication bias and small study effect

In order to minimise the potential impact due to publication bias or other reporting biases, we will conduct a comprehensive retrieval and choose the eligible studies totally by strict standard. Funnel plots will be used to assess the existence of small study effects and publication biases.33 We will use the Harbord test34 to formally test for asymmetries in the funnel plots. If we identify an important association of the reported effect with the trials’ precision, we will try to adjust for it in a sensitivity analysis. Then a network meta-regression with the trial precision as a study-level covariate will be performed. If the results indicating that there is strong evidence of small study effects or publication bias, we will clearly report it and interpret our results cautiously.

Ethics and dissemination

Ethical approval is not required as primary data will not be collected. This review will be published in a peer-reviewed journal.