Treatment-effect estimates adjusted for small-study effects via a limit meta-analysis

Statistical heterogeneity and small-study effects are 2 major issues affecting the validity of meta-analysis.In this article, we introduce the concept of a limit meta-analysis, which leads to shrunken, empirical Bayes estimates of study effects after allowing for small-study effects.This in turn leads to 3 model-based adjusted pooled treatment-effect estimators and associated confidence intervals.We show how visualizing our estimators using the radial plot indicates how they can be calculated using existing software.The concept of limit meta-analysis also gives rise to a new measure of heterogeneity, termed G2, for heterogeneity that remains after small-study effects are accounted for.In a simulation study with binary data and small-study effects, we compared our proposed estimators with those currently used together with a recent proposal by Moreno and others.Our criteria were bias, mean squared error (MSE), variance, and coverage of 95% confidence intervals.Only the estimators arising from the limit meta-analysis produced approximately unbiased treatment-effect estimates in the presence of small-study effects, while the MSE was acceptably small, provided that the number of studies in the meta-analysis was not less than 10.These limit meta-analysis estimators were also relatively robust against heterogeneity and one of them had a relatively small coverage error.