Correcting for Primary Study Misspecifications in Meta-Analysis

In non-experimental sciences the errors associated with model misspecifications in primarystudies carry over to meta-analysis. We use Monte Carlo simulations to analyse the effects ofthese misspecifications on results of a meta-analysis using a meta-estimator that calculates asimple average effect and a meta-estimator that includes dummy variables to control forprimary study misspecification. The results show that using the dummy variable model goes along way in mitigating the negative effects of error propagation on the bias and mean squarederror of the meta-estimator, and the size and the power of statistical tests. Although primarystudy misspecifications can usually be observed and controlled for in a meta-analysis, themore complex interactions between these observed characteristics are far more difficult tocontrol for in practice. Our results show that these interactions may, however, substantiallyaffect the outcomes of a meta-analysis. When meta-analysis is used to look for a ‘true’ effectrather than for analysing variation in outcomes, our results provide an argument for studyselection on model quality to avoid the impact of error propagation in meta-analysis.