Meta-analysis with glmmTMB: simulation study and illustrative examples

This repository contains the code, simulated data, results and worked examples supporting the manuscript “Meta-analysis with the glmmTMB R package”.

Supplementary webpage: https://coraliewilliams.github.io/equalto_sim_study/webpage.html

Repository structure

equalto_sim_study/
├── R/
│   ├── 01_sim_params.R      # Defines simulation conditions
│   ├── 02_functions.R       # Simulation functions
│   ├── 03_run_sims.R        # Runs simulations and fits models
│   ├── 04_sim_results.R     # Summarises results and produces figures
│   └── ...                  # Additional example and simulation scripts
├── data/                    # Simulation parameter grids
├── results/
│   ├── raw/                 # Raw simulation and model outputs
│   └── figures/             # Figures generated from the results
├── docs/
│   ├── webpage.qmd          # Source for the supplementary webpage
│   ├── webpage.html         # Rendered webpage
│   └── felix_data/          # Data used in the phylogenetic example
└── equalto_sim_study.Rproj

Simulation study overview

The simulation study evaluates the equalto covariance structure in glmmTMB, which allows a known sampling-error variance–covariance matrix to be incorporated directly into a model.

Results from glmmTMB are compared with equivalent models fitted using metafor.

Four effect-size measures are considered:

Effect-size measure	Outcome type	Main models compared
Standardised mean difference	Continuous	metafor::rma.uni() and Gaussian glmmTMB with equalto
Log response ratio	Continuous	metafor::rma.uni() and Gaussian glmmTMB with equalto
Log odds ratio	Binary	Two-stage models and binomial GLMMs
Log incidence rate ratio	Count/rate	Two-stage models and Poisson GLMMs

The full design includes 20 studies per meta-analysis, null and moderate overall effects, three heterogeneity levels, moderate and rare event settings, and 1,000 repetitions per condition.

Performance is assessed using convergence, computation time, bias, root mean squared error, confidence-interval width, coverage, Type I error and power.

Worked examples

The supplementary webpage includes examples of:

• multilevel meta-analysis with correlated sampling errors;
• bivariate meta-analysis;
• network meta-analysis;
• phylogenetic meta-analysis; and
• location–scale meta-analysis.

Where possible, equivalent models are fitted with metafor for comparison.

R package requirements

The main packages required to run and analyse the simulations are the following:

install.packages(c( "glmmTMB", "metafor", "tidyverse", "furrr", "progressr", "data.table" ))

Reproducing the simulation study

Clone the repository:

git clone https://github.com/coraliewilliams/equalto_sim_study.git
cd equalto_sim_study

Run the scripts from the repository root in the following order:

source("R/01_sim_params.R")
source("R/03_run_sims.R")
source("R/04_sim_results.R")

03_run_sims.R automatically sources 02_functions.R.

The full simulation is computationally intensive. For a preliminary test, reduce the number of repetitions in 01_sim_params.R and adjust the number of parallel workers in 03_run_sims.R.

Supplementary webpage

The source file is:

docs/webpage.qmd

The rendered version is available at:

https://coraliewilliams.github.io/equalto_sim_study/webpage.html

Citation

Repository DOI hosted on Zenodo: https://doi.org/10.5281/zenodo.22742805

This repository supports the associated manuscript:

Williams, C. et al. Meta-analysis with the glmmTMB R package. Citation details and DOI will be added following publication.

Contact

Coralie Williams Email: coralie.williams@outlook.com