Types of studies

We included individual randomised controlled trials (RCTs), cluster‐RCTs, and cross‐over trials. We excluded quasi‐RCTs (trials in which the method of allocating participants to a treatment is not strictly random, e.g. by date of birth, hospital record number, alternation).

Types of participants

We included people after stroke regardless of sex, age, and stroke severity and duration. Stroke is defined by the World Health Organization as a "neurological deficit of cerebrovascular cause that lasts more than 24 hours or leads to death within 24 hours" (WHO 1989). We included mixed participant groups that consisted of people after stroke and other brain diseases, such as traumatic brain injury, if more than half of the included participants had a diagnosis of stroke.

Types of interventions

We included trials comparing any type of active rPMS or rPMS plus rehabilitation for improving functional ability versus any type of control intervention (i.e. sham rPMS, sham rPMS plus rehabilitation for improving functional ability, or no intervention). Investigators conducted rPMS peripherally (not for the central nervous system such as brain or spinal cord) and non‐invasively (without the use of puncture needle or implantation techniques).

We investigated the following comparisons.

• Active rPMS only compared with sham rPMS.

• Active rPMS only compared with no intervention.

• Active rPMS plus rehabilitation compared with sham rPMS plus rehabilitation.

• Active rPMS plus rehabilitation compared with rehabilitation only.

Types of outcome measures

Electronic searches

We searched the Cochrane Stroke Specialised Register and the following electronic databases. 

• Cochrane Central Register of Controlled Trials (CENTRAL; 2021, Issue 10), in the Cochrane Library (searched 5 October 2021) (Appendix 1).

• MEDLINE in Ovid (1946 to 5 October 2021) (Appendix 2).

• Embase in Ovid (1980 to 5 October 2021) (Appendix 3).

• Cumulative Index to Nursing and Allied Health Literature (CINAHL), in EBSCO (1937 to 5 October 2021) (Appendix 4).

• PsycINFO in Ovid (1806 to 5 October 2021) (Appendix 5).

• Allied and Complementary Medicine Database (AMED), in Ovid (1985 to 5 October 2021) (Appendix 6).

• OTseeker: Occupational Therapy Systematic Evaluation of Evidence (www.otseeker.com/) (searched 5 October 2021) (Appendix 7).

• Physiotherapy Evidence Database (PEDro; www.pedro.fhs.usyd.edu.au/) (1929 to 5 October 2021) (Appendix 8).

• Ichushi‐Web (Japan Medical Abstracts Society (JAMAS)) (www.jamas.or.jp/) (searched 5 October 2021) (Appendix 9).

We developed the MEDLINE search strategy (Appendix 2) with the help of the Cochrane Stroke Group Information Specialist and adapted it for use with the other databases.

We also searched the following ongoing trials registers. 

• US National Institutes of Health Ongoing Trials Register ClinicalTrials.gov (www.clinicaltrials.gov; searched 5 October 2021) (Appendix 10).

• ISRCTN Registry (www.isrctn.com/; searched 5 October 2021) (Appendix 11).

• Stroke Trials Registry (www.strokecenter.org/trials/; searched 7 January 2019) (Appendix 12).

• World Health Organization (WHO) International Clinical Trials Registry Platform (ICTRP) (www.who.int/ictrp/search/en/; searched 5 October 2021) (Appendix 13).

• Japanese University hospital Medical Information Network (UMIN) Clinical Trials Registry (UMIN‐CTR) (www.umin.ac.jp/ctr/; searched 5 October 2021) (Appendix 14).

• Japan Registry of Clinical Trials (jRCT) (jrct.niph.go.jp/; searched 5 October 2021) (Appendix 15).

We did not search the Stroke Trials Registry (www.strokecenter.org/trials) for this version of the review as it is now inactive.

Searching other resources

To identify additional published and unpublished relevant studies for potential inclusion in the review, we:

• contacted experts in the field;

• screened the reference lists of relevant articles; and

• searched in Google Scholar (scholar.google.co.uk/).

Selection of studies

Two review authors (YW, MO) independently screened the titles and abstracts of references obtained by our searches and excluded obviously irrelevant reports. We retrieved the full‐text articles for the remaining references, and two review authors (YW, MO) independently screened these to identify studies for inclusion. We identified and recorded reasons for the exclusion of ineligible studies. Any disagreements were resolved through discussion or by consulting a third review author (TK) if required. We collated multiple reports of the same study so that each study, rather than each report, was the unit of interest in the review. We recorded the selection process and completed a PRISMA flow diagram (Moher 2009). We included studies presented only as abstracts if sufficient information was reported. We used Covidence software for reference handling (Covidence).

Data extraction and management

Two review authors (YW, MO) independently extracted the following data from the included studies and entered the data into Covidence (Covidence).

• Methods: study design, randomisation method, allocation concealment method, blinding methods.

• Participants: diagnosis (type, severity, and location of stroke), number in each group, age, sex, baseline comparability between two groups, time from onset, losses to follow‐up.

• Interventions: details of rPMS (frequency, intensity, duration, treatment session), target of stimulation, co‐exercise.

• Outcomes: types of outcomes, time points assessed.

• Other: setting, publication year, sources of funding, intention‐to‐treat analysis (ITT).

All disagreements were resolved by discussion.

Assessment of risk of bias in included studies

Two review authors (YW, MO) independently assessed risk of bias for each study according to the criteria outlined in the Cochrane Handbook for Systematic Reviews of Interventions (Higgins 2011), along with Covidence (Covidence). We used the Cochrane risk of bias tool, which includes the following domains: random sequence generation, allocation concealment, blinding of participants and personnel, blinding of outcome assessment, incomplete outcome data, selective outcome reporting, and other bias. We assessed each domain as having low risk, high risk, or unclear risk of bias (Higgins 2011). Any disagreements between review authors were resolved by discussion or by consultation with a third review author (TK).

Measures of treatment effect

For all outcomes, we carried out analyses as far as possible on an ITT basis, that is we attempted to include in the analyses all participants randomised to each group, and analysed all participants in the group to which they had been allocated, regardless of whether they received the allocated intervention. The denominator for each outcome in each trial was the number randomised minus any participants whose outcomes were known to be missing.

Unit of analysis issues

Dealing with missing data

If necessary, we contacted trial authors to obtain missing data, as well as data collected but not reported. We recorded levels of attrition for the included studies. We planned to perform sensitivity analysis to explore the impact of including studies with high levels of missing data in the overall assessment of treatment effect.

For all outcomes, we carried out analyses as far as possible on an ITT basis, that is we attempted to include in the analyses all participants randomised to each group, and analysed all participants in the group to which they had been allocated, regardless of whether they received the allocated intervention. The denominator for each outcome in each trial was the number randomised minus any participants whose outcomes were known to be missing.

Assessment of heterogeneity

We assessed statistical heterogeneity in each meta‐analysis using the I² statistic. We regarded heterogeneity as substantial if I² was greater than 50%. We used Review Manager 5 to assess heterogeneity (Review Manager 2020).

Assessment of reporting biases

We planned that if we found 10 or more studies, we would use funnel plots to detect publication bias. If asymmetry was suggested by visual assessment, we would perform exploratory analyses to investigate this. We also investigated selective outcome reporting through comparison of the methods section of articles with the reported results.

Data synthesis

Two review authors (YW, MO) independently extracted data from the included trials. One review author (TK) entered the data into Review Manager 5, and another review author (RM) checked the entries. Any disagreements were resolved through discussion, with reference to the original report.

We carried out statistical analysis using Review Manager 5 (Review Manager 2020). We used fixed‐effect meta‐analysis in combining data when it was reasonable to assume that studies were estimating the same underlying treatment effect, that is when trials were examining the same intervention, and when trial populations and methods were judged to be sufficiently similar. If clinical heterogeneity was sufficient to expect that underlying treatment effects would differ between trials, or if we detected substantial statistical heterogeneity, we used random‐effects meta‐analysis to produce an overall summary if an average treatment effect across trials was considered clinically meaningful. We treated the random‐effects summary as the average range of possible treatment effects, and discussed the clinical implications of differing treatment effects between trials. If the average treatment effect was not clinically meaningful, we did not combine trials. If we used random‐effects analyses, we presented results as the average treatment effect with 95% CI, along with estimates of Tau² and I². If it was inappropriate or impossible to pool data quantitatively, we provided a narrative summary of study results.

Subgroup analysis and investigation of heterogeneity

When we identified substantial heterogeneity in the primary outcomes, we investigated this by conducting subgroup analyses. We considered whether an overall summary was meaningful, and if so, used random‐effects analysis to produce it.

We planned to carry out the following subgroup analyses of primary outcomes if sufficient data were available.

• Location of stimulation: upper limb versus lower limb or trunk.

• Type of stroke: cerebral infarction versus cerebral haemorrhage.

• Duration of illness: acute to subacute phase (to six months after stroke) versus chronic phase (more than six months after stroke).

We assessed subgroup differences by checking if a statistically significant subgroup difference was detected using Review Manager 5 (Review Manager 2020). We reported the results of subgroup analyses by quoting the Chi² statistic and the P value, and results by providing the I² statistic.

Sensitivity analysis

If we identified two or more studies that evaluated our primary outcome, we would perform sensitivity analyses to determine how the results were affected by excluding:

• studies with inadequate allocation concealment and random sequence generation;

• studies in which outcome assessment was not blinded;

• studies in which loss to follow‐up was not reported or was greater than 10%; and

• unpublished studies.

Summary of findings and assessment of the certainty of the evidence

We used the GRADE approach to assess the certainty of the body of evidence related to the following main outcomes at the end of treatment (Guyatt 2008).

• ADLs.

• Upper limb function.

• Lower limb function.

• Spasticity.

• Muscle strength.

• Death.

We used GRADEpro GDT to import data from Review Manager 5 to create summary of findings tables (GRADEpro GDT; Review Manager 2020). We produced a summary of the intervention effect and a measure of certainty for each of the above outcomes using the GRADE approach (Ryan 2016). The GRADE approach is based on five considerations (study limitations, consistency of effect, imprecision, indirectness, and publication bias) and is used to assess the certainty of the body of evidence for each outcome. Evidence can be downgraded from 'high certainty' by one level for serious (or by two levels for very serious) limitations, depending on assessments for risk of bias, indirectness of evidence, serious inconsistency, imprecision of effect estimates, or potential publication bias.