Coralie Williams | Searcharxiv

arXiv2026

Meta-analysis with the glmmTMB R package

Two common formulations of meta-analytical models include the standard two-stage normal-normal models, which synthesise estimated effect sizes, and the one-stage generalised linear mixed model (GLMM), which directly model the underlying outcome data across studies. The general-purpose glmmTMB R package provides flexible response distributions and random-effect covariance structures through Template Model Builder (TMB). Its existing functionality can fit one-stage meta-analytic GLMM specifications. However, incorporating known sampling variances and covariances in the conventional two-stage inverse-variance formulation of meta-analysis was previously not easily accomplished in glmmTMB. Here, we introduce equalto, a new covariance structure in glmmTMB that allows users to supply a known sampling error variance-covariance matrix when fitting meta-analytic models. This enables explicit modelling of heteroscedasticity and dependence among sampling errors. Using simulations, we show that glmmTMB produces estimates identical to those from the corresponding metafor package functions for normal-normal models and similar estimates for GLMM specifications. We illustrate these models using published meta-analysis datasets in medicine, evolutionary ecology, and the social sciences. With the addition of the equalto covariance structure, glmmTMB now provides a unified and flexible framework for fitting two-stage normal-normal models and one-stage meta-analytic GLMMs, including multivariate specifications. These models can be fitted using the same glmmTMB() function, expanding the R toolkit available for evidence synthesis.

stat.CO↗

arXiv2025

Mastering an Accurate and Generalizable Simulation-Based Method to Obtain Bias-corrected Point Estimates and Sampling Variance for Any Effect Sizes

Meta-analyses require an effect-size estimate and its corresponding sampling variance from primary studies. In some cases, estimators for the sampling variance of a given effect size statistic may not exist, necessitating the derivation of a new formula for sampling variance. Traditionally, sampling variance formulas are obtained via hand-derived Taylor expansions (the delta method), though this procedure can be challenging for non-statisticians. Building on the idea of single-fit parametric resampling, we introduce SAFE bootstrap: a Single-fit, Accurate, Fast, and Easy simulation recipe that replaces potentially complex algebra with four intuitive steps: fit, draw, transform, and summarise. In a unified framework, the SAFE bootstrap yields bias-corrected point estimates and standard errors for any effect size statistic, regardless of whether the outcome is continuous or discrete. SAFE bootstrapping works by drawing once from a simple sampling model (normal, binomial, etc.), converting each replicate into any effect size of interest and then calculating the bias and sampling variance from simulated data. We demonstrate how to implement the SAFE bootstrap for a simple example first, and then for common effect sizes, such as the standardised mean difference and log odds ratio, as well as for less common effect sizes. With some additional coding, SAFE can also handle zero values and small sample sizes. Our tutorial, with R code supplements, should not only enhance understanding of sampling variance for effect sizes, but also serve as an introduction to the power of simulation-based methods for deriving any effect size with bias correction and its associated sampling variance.

stat.ME↗