Continuous aerobic exercise and atherosclerosis-related vascular indices in overweight and obese adults: a Bayesian three-level meta-analysis of randomized controlled trials

Figures

• 

  Figure 1. Flow diagram of study selection for trials included in the systematic review.

• 

  Figure 2. Quality evaluation of each study. D1, randomization process; D2, deviations from intended interventions; D3, missing outcome data; D4, measurement of the outcome; D5, selection of the reported result; D6, overall.

• 

  Figure 3. Bayesian three-level random-effects meta-analysis of CET versus control on FMD. Left: study-specific SMDs, standardized mean differences and pooled estimate. Right: posterior distributions for the overall mean effect (μ) and heterogeneity components (τ_within and τ_between); bars indicate 95% CrI, credible intervals.

• 

  Figure 4. Bayesian three-level random-effects meta-analysis of CET versus control on PWV. Left: study-specific SMDs, standardized mean differences and pooled estimate. Right: posterior distributions for the overall mean effect (μ) and heterogeneity components (τ_within and τ_between); bars indicate 95% CrI, credible intervals.

• 

  Figure 5. Bayesian three-level random-effects meta-analysis of CET versus control on CIMT Left: study-specific SMDs, standardized mean differences and pooled estimate. Right: posterior distributions for the overall mean effect (μ) and heterogeneity components (τ_within and τ_between); bars indicate 95% CrI, credible intervals.

• 

  Figure 6. MCMC diagnostics for the Bayesian three-level meta-analytic models. Trace plots are shown for the pooled mean effect (μ), within-study heterogeneity (τ_within), and between-study heterogeneity (τ_between) for FMD, PWV, and CIMT. Summary statistics for each parameter, including R-hat and ESS, effective sample size, are presented on the right; divergences indicate the number of divergent transitions during sampling.

• 

  Figure 7. Posterior predictive checks for the Bayesian three-level meta-analytic models. For each outcome (FMD, PWV, and CIMT), the observed effect-size density is shown as a thick blue curve, whereas posterior predictive densities simulated from the fitted model are shown as colored thin curves; dashed vertical lines indicate the null effect (SMD = 0).

• 

  Figure 8. Exploratory meta-regression analyses of CET prescription characteristics and vascular outcomes. Panels show study-level SMDs, standardized mean differences plotted against intervention duration (weeks) and training frequency (sessions/week) for FMD, CIMT, and PWV. Solid blue lines indicate the estimated meta-regression slopes, and shaded areas indicate 95% credible intervals. Points represent study-level effect sizes; color scales indicate the alternate prescription characteristic (frequency for duration models and duration for frequency models).

• 

  Figure 9. Leave-one-out sensitivity analyses for the Bayesian three-level meta-analytic models. For each outcome (FMD, PWV, and CIMT), the pooled effect estimate was recalculated after omitting one study at a time to evaluate the influence of individual trials on the overall result.

• 

  Figure 10. Funnel plots for assessment of small-study effects and potential publication bias. Separate funnel plots are shown for FMD, PWV, and CIMT. Each point represents one study-level effect size plotted against its standard error; the vertical line indicates the pooled effect estimate, and diagonal lines indicate pseudo 95% confidence limits.