Methods for meta-analysis and meta-regression of binomial data: concepts and tutorial with Stata command metapreg.

Background: Despite the widespread interest in meta-analysis of proportions, its rationale, certain theoretical and methodological concepts are poorly understood. The generalized linear models framework is well-established and provides a natural and optimal model for meta-analysis, network meta-analysis, and meta-regression of proportions. Nonetheless, generic methods for meta-analysis of proportions based on the approximation to the normal distribution continue to dominate.

Methods: We developed metapreg, a tool with advanced statistical procedures to perform a meta-analysis, network meta-analysis, and meta-regression of binomial proportions in Stata using binomial, logistic and logistic-normal models. First, we explain the rationale and concepts essential in understanding statistical methods for meta-analysis of binomial proportions and describe the models implemented in metapreg. We then describe and demonstrate the models in metapreg using data from seven published meta-analyses. We also conducted a simulation study to compare the performance of metapreg estimators with the existing estimators of the population-averaged proportion in metaprop and metan under a broad range of conditions including, high over-dispersion and small meta-analysis.

Conclusion: metapreg is a flexible, robust and user-friendly tool employing a rigorous approach to evidence synthesis of binomial data that makes the most efficient use of all available data and does not require ad-hoc continuity correction or data imputation. We expect its use to yield higher-quality meta-analysis of binomial proportions.