2.1

The NMA was conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-analyses extension statement for reporting of systematic reviews incorporating network meta-analyses. The principles of the Preferred Reporting Items for Systematic Review and Meta-analysis 2021 were applied for reporting NMAs . The protocol was registered with the International Prospective Register of Systematic Reviews on June 15, 2025 (registration number CRD420251074257).

2.2

Databases, including PubMed, Cochrane Library, EMBASE, Medline, Web of Science, CNKI, and Wanfang, were searched for studies from their inception to June 15, 2025. References in the identified articles and relevant published reports were manually surveyed to identify studies eligible for inclusion in our review. The main search strategies were as follows: (‘metatarsus primus varus’ OR ‘metatarsus adductus’ OR ‘hallux valgus’ OR ‘bunion’ OR ‘first ray hypermobility’) AND (‘stretching’ OR ‘exercise’ OR ‘toe-spread-out’ OR ‘short foot’ OR ‘foot mobilization’ OR ‘physical therapy’).

2.3

The inclusion criteria for studies were as follows: (1) RCTs assessing the effectiveness of exercise therapy for hallux valgus correction; (2) participants diagnosed with hallux valgus with HVA greater than 15 degrees; (3) the intervention group or control group received exercise therapy (including active exercises, passive exercises, or a combination of both), or pairwise comparisons between intervention and control groups were conducted to evaluate the effectiveness of exercise therapy; (4)outcomes comprised HVA and pain(VAS/NAR).The analysis of this study was based on the changes relative to the baseline values. The exclusion criteria for studies were as follows: (1) The same literature collected in each database; (2) conference articles, review research, and secondary research literature; (3) studies where pairwise comparisons between intervention and control groups were conducted but were unable to evaluate the effectiveness of exercise therapy (4) valid data could not be obtained, or the experimental results are not reported by HVA.

2.4

The search was conducted by the first author and recorded in a Microsoft Excel file. Duplicate entries were removed. Each title and abstract were manually reviewed by two independent reviewers. If necessary, a third reviewer was consulted for resolution. All full texts that met the inclusion criteria were included. A pre-set standardized form was used by two reviewers who independently extracted the main information. Disagreements were resolved by discussion with a third reviewer. Extracted data included: (1) participant characteristics (sample size, age, sex, rehabilitation program); (2) intervention details (name, frequency, duration, process, follow-up); (3) outcomes (HVA and pain, VAS/NRS).

2.5

Risk of bias was assessed by two authors independently using the Revised Cochrane risk-of-bias tool for randomized trials (RoB 2) . This tool assesses risk of bias in five domains: bias arising from the randomization process, Bias due to deviations from intended interventions, Bias due to missing outcome data, Bias in measurement of the outcome, Bias in selection of the reported result. For each criterion, risk of bias was assessed as (1) low risk of bias, (2) some concerns, (3) high risk of bias . Conflicts of opinion were discussed with a third review author until consensus is reached. If necessary, additional information was retrieved from the study authors. The overall risk of bias for each study was then determined based on this individual domain assessment. Studies with minimal risk across all domains were classified as having a “low” overall risk of bias. Studies with some domains raising concerns were categorized as having “some concerns” overall.

2.6

NMA was performed using Stata 18.0 software. Continuous variables were analyzed, with mean difference (MD) and 95 % CI as effect size indicators. The analysis of this study were based on the changes relative to the baseline values. The results of the analysis included all possible pairwise comparisons, incorporating mixed comparisons that combined direct and indirect comparisons. The efficacy of different therapies was estimated based on the surface under the cumulative ranking curve (SUCRA). The SUCRA value ranges from 0 % to 100 %, where a SUCRA value of 100 % indicates that the treatment was the most effective, and the smaller the value, the poorer the treatment effect . Heterogeneity was assessed by estimating the between-study variance (τ²) . Publication bias was assessed visually by funnel plots. Local inconsistency was evaluated using the node-splitting method, and global inconsistency was assessed with the design-by-treatment interaction model ^, . Heterogeneity was addressed through sensitivity analyses for primary outcomes by excluding studies with high risk of bias, while subgroup analyses and meta-regression were conducted to explore potential effect factors.

2.7

The certainty of evidence for direct evidence, indirect evidence, and network estimates was assessed using the Grading of Recommendations Assessment Development and Evaluation (GRADE) framework used for NMA. Five downgrading factors were considered: risk of bias, inconsistency, imprecision, indirectness, and publication bias. For indirect evidence, the transitivity assumption was additionally evaluated. For NMA estimates, the rating was based on the higher of the direct and indirect evidence, with further downgrading applied if inconsistency or other concerns were identified. Each domain was rated as “not serious” (no downgrade), “serious” (downgraded by one level), or “very serious” (downgraded by two levels).

3.1

As illustrated in Fig. 1 , A total of 1259 studies were identified according to the search strategy. After eliminating 277 duplicates, 982 records underwent screening based on title and abstract, resulting in the exclusion of 923 records. Out of the remaining 59 studies eligible for full text, 48 studies were excluded based on predetermined inclusion and exclusion criteria. Ultimately, 11 randomized controlled trials were included in this study ^,,,,,,,,,, .

PRISMA Flow diagram of the search process for studies.

3.2

As shown in Table 1 , these studies included 401 HV patients from 6 countries. Six types of interventions were reported: placebo, active exercises (e.g., toe-spread-out exercises, short-foot exercises, resisted foot exercises), passive exercises (e.g., joint mobilizations, stretching/manual therapy), active exercises combined with passive exercises, exercise combined with taping, and exercise combined with orthoses. The average age of participants ranged from 21 to 66 years old, with a diverse distribution across groups and the majority being females. All were mild-to-moderate HV cases (HVA 15°–40°). Exercise programs were mainly supervised, with some home-based instructions. Certain studies incorporated kinesiology taping or orthoses in addition to exercise to enhance treatment outcomes. Most supervised training programs typically lasted 4–12 weeks, with sessions ranging from twice weekly to 2–3 times daily. Assessments were conducted at baseline (pre) and post-treatment phases. The most commonly measured outcomes included HVA and visual analog scale/numeric rating scale (VAS/NRS). No adverse events were reported.

3.3

The risk-of-bias results are shown in Fig. 2 , and Table 2 lists the risk of bias across individual studies by domain. All included studies used simple randomization, but only four reported the details. Since most studies involved treatments such as supervised exercise, blinding of treatment outcomes appeared challenging. In the overall bias examination, 8 RCTs were classified as some concerns, while 3 RCTs were classified as high risk.

(A) Risk of bias graph (B) Risk of bias summary.

3.4

3.4.1

Network Meta-analysis and Sensitivity analysis

Fig. 3 illustrates the network for HVA, which included 11 studies with 393 participants. Compared with the adjusted placebo, exercise combined with taping was identified as the most effective intervention (MD: −6.72, 95 % CI: −9.34 to −4.11; 89.5 %), followed by exercise combined with orthoses (MD: −6.67, 95 % CI: −9.70 to −3.64; 85.6 %), as shown in Table 3 and Fig. 4 . The funnel plots ( Fig. 5 ) indicate general symmetry and no significant publication bias. As shown in Table 4 , the NMA showed clinical heterogeneity (τ² = 2.12), with no overall inconsistency according to the node-splitting method and the global inconsistency test (p = 0.22), while the sensitivity analysis excluding studies of high risk of bias revealed low heterogeneity (τ² < 0.01). Fig. 6 shows the sensitivity analysis of NMA, which included 8 studies with 233 participants, and Fig. 7 shows the ranking of interventions. Table 3 shows that, versus adjusted placebo, exercise combined with orthoses was the most effective intervention (MD: −8.9, 95 % CI: −10.73 to −7.07; 99.6 %), followed by exercise combined with taping (MD: −5.66, 95 % CI: −8.27 to −3.05; 79.3 %).

Network meta-analysis plot for the assessment of HVA.

Table 3

Main estimate and sensitivity analyses of HVA.

	Main estimate	Sensitivity analyses
AC	−3.19 (−5.43, −0.95)	−1.95 (−3.72, −0.18)
PA	−3.50 (−7.08, −0.08)	−3.04 (−5.26, −0.81)
CO	−4.42 (−6.43, −2.41)	−3.47 (−4.97, −1.98)
TA	−6.72 (−9.34, −4.11)	−5.66 (−8.27, −3.05)
OR	−6.67 (−9.70, −3.32)	−8.9 (−10.73, −7.07)

OR: exercise combined with orthoses; TA: exercise combined with taping; CO: active exercise combined with passive exercise; PA: passive exercise; AC: active exercise; PLA: the adjusted placebo;

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