Reporting checklist

Introduction

Transparent reporting of Bayesian meta-analyses enables readers to evaluate the appropriateness of modelling choices, assess robustness, and reproduce results. This checklist covers the minimum reporting requirements for a bayesma analysis intended for publication.

The checklist is structured to follow the order in which items typically appear in a methods or results section.

Checklist

Data and eligibility

• Eligibility criteria for studies, populations, interventions, comparators, and outcomes.
• Databases searched, date range, and search strategy.
• Number of studies identified, screened, assessed for eligibility, and included (PRISMA flow diagram).
• Pre-registration identifier (PROSPERO or equivalent).

Effect size computation

• Effect measure used (OR, RR, HR, SMD, MD, etc.) and justification.
• For two-stage analysis: software and method used to compute $(y_i, s_i)$.
• For one-stage analysis: raw cell counts or means and SDs used directly.
• Treatment of multi-arm studies (if applicable).

Model specification

• Model type: common-effect or random-effects; one-stage or two-stage.
• Random-effects distribution: Gaussian, Student-$t$, skew-normal, or mixture.
• Prior distributions for all parameters, with justification.
• Source of any informative priors (e.g., Turner et al. 2015 for $\tau$).
• Software: bayesma, version, and Stan backend (cmdstanr version).

MCMC settings

• Number of chains, warmup iterations, and sampling iterations.
• adapt_delta value.
• Random seed (for reproducibility).

Convergence diagnostics

• Maximum $\hat{R}$ across all parameters (target: $< 1.01$).
• Minimum bulk and tail ESS (target: $> 400$).
• Number of divergent transitions (target: 0).
• Any parameters that required intervention and the resolution.

Primary results

• Posterior median and 95% credible interval for the pooled effect $\mu$.
• Posterior median and 95% credible interval for between-study heterogeneity $\tau$.
• Prediction interval for the effect in a new study.
• Back-transformation to natural scale (OR, RR, etc.) where applicable.

Publication bias assessment

• Method used (Egger, PET-PEESE, selection model, BC-BNP, mixture, none).
• Justification for method choice.
• Bias-adjusted pooled estimate and comparison to unadjusted estimate.
• Bayes factor or posterior probability for presence of bias (where applicable).

Sensitivity analysis

• Prior sensitivity: range of $\tau$ priors tested and whether conclusions changed.
• Study-level influence: any studies with substantial influence on the pooled estimate.
• Model comparison: criteria used and whether a different model was preferred.
• Bias assumption sensitivity (for selection models: sensitivity to selection mechanism).

Heterogeneity interpretation

• Estimated $\tau$ and its uncertainty.
• $I^2$ (if reported) with accompanying $\tau$ and 95% CrI rather than as a standalone measure.
• Prediction interval for a new study (more informative than $I^2$ alone).

Subgroup and moderation analysis

• Moderators tested, with justification.
• Posterior for each moderator coefficient and Bayes factor against the null.
• All tested moderators reported, not only those with significant results.

Software citation

• R citation: citation().
• bayesma citation: citation("bayesma").
• cmdstanr and Stan citations.
• Any additional packages used for visualisation or reporting.

Automated report generation

bayesma can produce a fully formatted publication report with all key results, plots, and tables via bayesma_report(). See report-generation.qmd for the full workflow.

bayesma_report(
  fit,
  output_file = "meta_analysis_report.qmd",
  title       = "Bayesian meta-analysis of ...",
  author      = "Author Name"
)

GRADE assessment

The GRADE framework (Grading of Recommendations Assessment, Development and Evaluation) assesses the overall certainty of the evidence. Key domains affected by modelling choices:

• Inconsistency: assessed via $\tau$ and the prediction interval.
• Publication bias: assessed via selection models and Egger’s test.
• Imprecision: assessed via the width of the 95% credible interval.

Certainty ratings should be applied after bias assessment and sensitivity analysis, not before.