title: Treatment-effect estimates adjusted for small-study effects via a limit meta-analysis.
abstract: 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 G(2), 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.
authors.affiliation: Institute of Medical Biometry and Medical Informatics, University Medical Center, 79104 Freiburg, Germany. ruecker@imbi.uni-freiburg.de
authors.forename: Gerta
authors.initials: G
authors.lastname: Rücker
authors.forename: Guido
authors.initials: G
authors.lastname: Schwarzer
authors.forename: James R
authors.initials: JR
authors.lastname: Carpenter
authors.forename: Harald
authors.initials: H
authors.lastname: Binder
authors.forename: Martin
authors.initials: M
authors.lastname: Schumacher
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D006801:Humans; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D018401:Sample Size; D016896:Treatment Outcome