The median and the mode as robust meta-analysis estimators in the presence of small-study effects and outliers

Meta-analyses based on systematic literature reviews are commonly used to obtain a quantitative summary of the available evidence on a given topic. However, the reliability of any meta-analysis is constrained by that of its constituent studies. One major limitation is the possibility of small study effects, when estimates from smaller and larger studies differ systematically. Small study effects may result from reporting biases (i.e., publication bias), from inadequacies of the included studies that are related to study size, or from reasons unrelated to bias. We propose two estimators based on the median and mode to increase the reliability of findings in a meta-analysis by mitigating the influence of small study effects. By re-examining data from published meta-analyses and by conducting a simulation study, we show that these estimators offer robustness to a range of plausible bias mechanisms, without making explicit modelling assumptions. They are also robust to outlying studies without explicitly removing such studies from the analysis. When meta-analyses are suspected to be at risk of bias because of small study effects, we recommend reporting the mean, median and modal pooled estimates.