Simulation models for aggregated data meta-analysis: Evaluation of pooling effect sizes and publication biases

Simulation studies are commonly used to evaluate the performance of newly developed meta-analysis methods. For methodology that is developed for an aggregated data meta-analysis, researchers often resort to simulation of the aggregated data directly, instead of simulating individual participant data from which the aggregated data would be calculated in reality. Clearly, distributional characteristics of the aggregated data statistics may be derived from distributional assumptions of the underlying individual data, but they are often not made explicit in publications. This article provides the distribution of the aggregated data statistics that were derived from a heteroscedastic mixed effects model for continuous individual data and a procedure for directly simulating the aggregated data statistics. We also compare our simulation approach with other simulation approaches used in literature. We describe their theoretical differences and conduct a simulation study for three meta-analysis methods: DerSimonian and Laird method for pooling aggregated study effect sizes and the Trim & Fill and precision-effect test and precision-effect estimate with standard errors method for adjustment of publication bias. We demonstrate that the choice of simulation model for aggregated data may have an impact on (the conclusions of) the performance of the meta-analysis method. We recommend the use of multiple aggregated data simulation models to investigate the sensitivity in the performance of the meta-analysis method. Additionally, we recommend that researchers try to make the individual participant data model explicit and derive from this model the distributional consequences of the aggregated statistics to help select appropriate aggregated data simulation models.