A statistical method for synthesizing meta-analyses

Multiple meta-analyses may use similar search criteria and focus on the same topic of interest, but they may yield different or sometimes discordant results. The lack of statistical methods for synthesizing these findings makes it challenging to properly interpret the results from multiple meta-analyses, especially when their results are conflicting. In this paper, we first introduce a method to synthesize the meta-analytic results when multiple meta-analyses use the same type of summary effect estimates. When meta-analyses use different types of effect sizes, the meta-analysis results cannot be directly combined. We propose a two-step frequentist procedure to first convert the effect size estimates to the same metric and then summarize them with a weighted mean estimate. Our proposed method offers several advantages over existing methods by Hemming et al. (2012). First, different types of summary effect sizes are considered. Second, our method provides the same overall effect size as conducting a meta-analysis on all individual studies from multiple meta-analyses. We illustrate the application of the proposed methods in two examples and discuss their implications for the field of meta-analysis.