[Paper Review] MetaStan: An R package for Bayesian (model-based) meta-analysis using Stan

Burak Kürsad Günhan, Christian Röver+1 more|arXiv (Cornell University)|Feb 1, 2022

Meta-analysis and systematic reviews4 citations

TL;DR

MetaStan is an R package that enables Bayesian (model-based) meta-analysis using Stan's efficient Hamiltonian Monte Carlo sampling. It supports pairwise meta-analysis, meta-regression, and model-based meta-analysis for continuous, binary, and count outcomes via a generalized linear mixed model framework with flexible prior distributions and convergence diagnostics.

ABSTRACT

Meta-analysis methods are used to combine evidence from multiple studies. Meta-regression as well as model-based meta-analysis are extensions of standard pairwise meta-analysis in which information about study-level covariates and (arm-level) dosing amount or exposure may be taken into account. A Bayesian approach to inference is very attractive in this context, especially when a meta-analysis is based on few studies only or rare events. In this article, we present the R package MetaStan which implements a wide range of pairwise and model-based meta-analysis models. A generalised linear mixed model (GLMM) framework is used to describe the pairwise meta-analysis, meta-regression and model-based meta-analysis models. Within the GLMM framework, the likelihood and link functions are adapted to reflect the nature of the data. For example, a binomial likelihood with a logit link is used to perform a meta-analysis based on datasets with dichotomous endpoints. Bayesian computations are conducted using Stan via the rstan interface. Stan uses a Hamiltonian Monte Carlo sampler which belongs to the family of Markov chain Monte Carlo methods. Stan implementations are done by using suitable parametrizations to ease computations. The user-friendly R package MetaStan, available on CRAN, supports a wide range of pairwise and model-based meta-analysis models. MetaStan provides fitting functions for pairwise meta-analysis with the option of including covariates and model-based meta-analysis. The supported outcome types are continuous, binary, and count. Forest plots for the pairwise meta-analysis and dose-response plots for the model-based meta-analysis can be obtained from the package. The use of MetaStan is demonstrated through clinical examples.

Motivation & Objective

• To provide a user-friendly R package for Bayesian meta-analysis that supports a wide range of models including pairwise meta-analysis, meta-regression, and model-based meta-analysis.
• To implement efficient Bayesian inference using Stan’s Hamiltonian Monte Carlo sampler, improving computational performance over older MCMC methods.
• To address challenges in sparse data or few-study meta-analyses by incorporating weakly informative priors and non-centered parameterization.
• To enable visualization of results through forest plots (pairwise) and dose-response plots (model-based meta-analysis).
• To offer a flexible, extensible framework for meta-analysis with support for various likelihood and link functions across different outcome types.

Proposed method

• Uses a generalized linear mixed model (GLMM) framework to model pairwise meta-analysis, meta-regression, and model-based meta-analysis.
• Employs Stan’s Hamiltonian Monte Carlo (HMC) sampler via the rstan interface for efficient posterior computation.
• Applies non-centered parameterization by default in sparse settings (e.g., few studies) to improve MCMC mixing and convergence.
• Supports multiple likelihood functions: binomial (logit link) for binary outcomes, normal (identity link) for continuous, and Poisson (log link) for count data.
• Allows specification of weakly informative priors for fixed effects (normal) and heterogeneity (half-normal, Cauchy, uniform) to stabilize inference.
• Provides built-in functions for convergence diagnostics (e.g., R-hat, effective sample size) and visualization (forest_plot, dose-response plots).

Experimental results

Research questions

• RQ1 How can Bayesian meta-analysis be efficiently implemented for diverse outcome types (continuous, binary, count) using modern MCMC sampling?
• RQ2 What impact does non-centered parameterization have on MCMC convergence in low-sample-size meta-analyses?
• RQ3 How do weakly informative priors improve estimation stability in sparse or rare-event settings?
• RQ4 Can a unified R package effectively support both standard pairwise meta-analysis and model-based meta-analysis with dose-response modeling?
• RQ5 How does the performance of Stan-based HMC compare to Gibbs or Metropolis-Hastings samplers in complex meta-analytic models?

Key findings

• MetaStan successfully implements Bayesian pairwise meta-analysis, meta-regression, and model-based meta-analysis using Stan’s HMC sampler with high computational efficiency.
• The use of non-centered parameterization in the topiramate dataset (6 studies) improved MCMC convergence, with R-hat values close to 1 and effective sample sizes exceeding 3,200.
• Posterior estimates for the log-odds ratio (θ) had a mean of 2.65 with a 95% credible interval of [2.15, 3.14], indicating a strong treatment effect.
• Heterogeneity standard deviation (τ) had a posterior mean of 0.26 and a 95% credible interval of [0.21, 0.66], suggesting moderate between-study variability.
• The package provides reliable convergence diagnostics, including R-hat < 1.05 and effective sample sizes > 3,200, supporting robust inference.
• Forest plots and dose-response visualizations generated by MetaStan effectively summarize results, enhancing interpretability for clinical and methodological applications.