Types of studies

Only randomised controlled trials (RCTs) will be included, as the best study design for assessing an intervention. All RCTs will be included regardless of quality, but measures of risk of bias will be recorded. We will exclude observational and case‐control studies.

We will include cross‐over RCTS, although only the first study phase of cross‐over trials will be used in analyses, to avoid carry‐over effects.

Cluster RCTs will be included in primary analyses, where the cluster will act as the unit of investigation. We think cluster and especially cross‐over RCTs are unlikely to be used in this field. Our aim is to include as many relevant studies as possible to avoid limitations and bias, while recording possible confounding and investigating this where numbers allow.

Types of participants

Types of interventions

Types of outcome measures

We will include studies that meet the above criteria, regardless of whether they report on all of the following outcomes.

Electronic searches

Searching other resources

We will check the reference lists of all included studies and relevant systematic reviews to identify additional studies missed from the original electronic searches.

We will contact authors of relevant publications (reports of included studies) and principle investigators of currently registered trials for information on unpublished or ongoing studies or to request additional trial data.

Selection of studies

Two review authors (RP, HS) will independently screen for inclusion the titles and abstracts of all the studies we identify as a result of the search, and code them as 'retrieve' (eligible or potentially eligible/unclear) or 'do not retrieve'. We will retrieve the potentially‐relevant full‐text study reports/publication and two review authors (RP, HS) will independently screen the full‐text and identify studies for inclusion, and identify and record reasons for exclusion of the ineligible studies. We will resolve any disagreement through discussion or, if required, we will consult a third person (KA). We will identify and exclude duplicate records, and we will collate multiple reports that relate to the same study, so that each study rather than each report is the unit of interest in the review. Titles or abstracts which may be relevant, but where relevance is not clear, will be included in the list and obtained. Articles in foreign languages will be obtained and translated where necessary, as may be the case, particularly for unpublished or preliminary data. We will record the selection process in sufficient detail to complete a PRISMA flow diagram and 'Characteristics of excluded studies' table.

Data extraction and management

We will use a data collection form, developed specifically for this work, to extract study characteristics and outcome data, which has been piloted on at least one study in the review. Two review authors (HS and KA or RP) will extract study characteristics and outcome data from included studies. We will extract the following study characteristics.

1. Methods: study design, total duration of study, details of any 'lead in' period, use of several study centres, study location, study setting, and date of study.

2. Participants: N, mean age, age range, gender, severity of condition, diagnostic criteria, inclusion criteria, and exclusion criteria, withdrawals.

3. Interventions: intervention, comparator, concomitant medications, and comorbidities.

4. Outcomes: primary and secondary outcomes specified and collected, and time points reported.

5. Notes: funding for trial, and notable conflicts of interest of trial authors.

Where multiple reports of the same study are available, data will be abstracted from all reports on separate data extraction forms and subsequently combined. Discordances will be resolved by independent abstraction and then discussion with a third author. Where data are unavailable as required, corresponding authors will be contacted directly for relevant information.

We will note in the 'Characteristics of included studies' table if outcome data were not reported in a usable way. We will resolve disagreements by consensus or by involving a third person (RC, AN). Two review authors (RP, HS) will transfer data into the Review Manager (RevMan 2012) file. We will double‐check that data are entered correctly by comparing the data presented in the systematic review with the study reports. A second review author (KA) will spot‐check study characteristics for accuracy against the trial report.

Assessment of risk of bias in included studies

Three review authors (KA, RP, HS) will independently assess the risk of bias for each study using the criteria outlined in the Cochrane Handbook for Systematic Reviews of Interventions (Higgins 2011). We will resolve any disagreements by discussion or by involving another author (RC, AN). We will assess the risk of bias according to the following domains.

1. Random sequence generation.

2. Allocation concealment.

3. Blinding of participants and personnel.

4. Blinding of outcome assessment.

5. Incomplete outcome data.

6. Selective outcome reporting.

7. Other bias.

We will judge each potential source of bias as high, low or unclear risk and provide a supporting quotation from the study report together with a justification for our judgment in the 'Risk of bias' table. We will summarise the risk of bias judgements across different studies for each of the domains listed. Where information on risk of bias relates to unpublished data or correspondence with a triallist, we will note this in the 'Risk of bias' table. When considering treatment effects, we will take into account the risk of bias for the studies that contribute to that outcome.

Measures of treatment effect

Unit of analysis issues

Dealing with missing data

We will contact investigators in order to verify key study characteristics and obtain missing numerical outcome data where possible (e.g. when a study is identified as abstract only). We will document all correspondence with trialists and report which trialists responded in the full review.

Standard deviations which remain missing once authors have been contacted will be imputed from standard deviation data from all other trials using the same measure for depression in the review (Furukawa 2006).

Assessment of heterogeneity

Heterogeneity will be investigated using Higgins’ I² statistic (Higgins 2002; Higgins 2004). I² statistics and appropriate P values will be reported. Four bands of the I² statistic will be used for interpretation, as recommended in theCochrane Handbook (Higgins 2011). These bands are 0% to 40%: might not be important; 30% to 60%: may represent moderate heterogeneity; 50% to 90% may represent substantial heterogeneity; and 75% to 100%: considerable heterogeneity. Possible sources of heterogeneity will be identified a priori, to include publication bias, comparator used, use of n3PUFAs as a sole or adjunct therapy, presence/absence of comorbid conditions (physical and psychiatric), and risk of bias. Publication bias will be investigated using funnel plot asymmetry (Sterne 2001). Investigations of heterogeneity and sensitivity analyses on possible sources of heterogeneity will be conducted if possible. We suspect these investigations may be limited by the small number of studies likely to be identified.

Assessment of reporting biases

Publication bias will be investigated using funnel plot asymmetry (Sterne 2001). This will only be undertaken if there are more than 10 studies available. It should be noted that publication bias is one of several possible causes of asymmetry in funnel plots.

Data synthesis

Data from trials reporting mean and standard deviation data will be combined using meta‐analysis (Sterne 2001). Analyses will be conducted twice: once using only studies at low risk of bias, and once using all included studies. Intention‐to‐treat (ITT) data will be used, where possible, and will be sought if not publicly available. If ITT data cannot be obtained, we will use available data.

For continuous data, the standardised mean effect for all trials will be calculated using Hedges' adjusted g (Deeks 2001). Hedges’ adjusted g is a formulation of effect size used in the SMD method that includes an adjustment to correct for small sample bias (Deeks 2001). Studies will be weighted using the inverse‐variance method. Random‐effects models will be used primarily to estimate the SMDs for all analyses (Deeks 2001; Egger 2001; Sterne 2001). Fixed‐effect models will also be applied as sensitivity analyses. Effect sizes will be provided as means and standard deviations, and related to specific scales to allow understanding by clinicians and practitioners.

For dichotomous data, we will use the Mantel‐Haenszel method.

Adverse effects and failure to complete data will not be statistically summarised.

If data from a single study cannot be included in a statistical combination, this will be reported and outcomes of that single study will be reported separately.

Subgroup analysis and investigation of heterogeneity

We will conduct subgroup analyses investigating effects of n3PUFAs on MDD in:

1. individuals with comorbid conditions versus those without. This analysis will demonstrate effects due to participant characteristics which may affect treatment recommendations and outcomes. Separate analyses will be conducted using the same methods as for the main analyses, using only studies in which participants are clearly identified as having comorbid conditions, and using only studies in which participants are clearly identified as being without comorbid conditions. Studies where participants with and without comorbid conditions are mixed, and studies that do not clearly identify whether participants have comorbid conditions or not, will not be included in this analysis. Caution should be exercised in interpreting these analyses due to the increased bias in selective samples;

2. individuals receiving medications versus those without. This analysis will demonstrate effects due to participant characteristics which may affect treatment recommendations and outcomes. Separate analyses will be conducted using the same methods as for the main analyses, using only studies in which participants are clearly identified as receiving medication or adjunct therapy, and using only studies in which participants are clearly identified as not receiving medication or other adjunct therapy. Studies where participants with additional medications and therapies are mixed, and studies that do not clearly identify whether or not participants were receiving additional medication or therapies, will not be included in this analysis. Caution should be exercised in interpreting these analyses due to the increased bias in selective samples.

Sensitivity analysis

We will conduct sensitivity analyses to investigate the impact of:

1. including all studies versus only studies that are at low risk of bias. This will demonstrate the importance of the use of only those trials at low risk of bias, and the levels of confidence and caution that should be exercised in considering the analyses on all studies. Separate analyses will be conducted using the same methods as for the main analyses, using all studies, and using only the studies that are identified as being at low risk of bias. Low risk of bias will be defined as in the Cochrane Handbook (Higgins 2011);

2. using fixed‐effect models as opposed to random‐effects models. Random‐effects models will be used for all main analyses. Fixed‐effect analyses will be conducted using the same methods as for the main analyses.