Meta-analysis of proportions using generalized linear mixed models

Epidemiologic research often involves meta-analyses of proportions. Conventional two-step methods first transform each study's proportion and subsequently perform a meta-analysis on the transformed scale. They suffer from several important limitations: the log and logit transformations impractically treat within-study variances as fixed, known values and require ad hoc corrections for zero counts; the results from arcsine-based transformations may lack interpretability. Generalized linear mixed models (GLMMs) have been recommended in meta-analyses as a one-step approach to fully accounting for within-study uncertainties. However, they are seldom used in current practice to synthesize proportions. This article summarizes various methods for meta-analyses of proportions, illustrates their implementations, and explores their performance using real and simulated datasets. In general, GLMMs led to smaller biases and mean squared errors and higher coverage probabilities than two-step methods. Many software programs are readily available to implement these methods.