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

Meta-analyses based on systematic literature reviews are commonly used to obtain a quantitative summary of the available evidence on a given topic. Despite its attractive simplicity, and its established position at the summit of the evidence-based medicine hierarchy, the reliability of any meta-analysis is largely constrained by the quality of its constituent studies. One major limitation is small study effects, whose presence can often easily be detected, but not so easily adjusted for. Here, robust methods of estimation based on the median and mode are proposed as tools to increase the reliability of findings in a meta-analysis. By re-examining data from published meta-analyses, and by conducting a detailed simulation study, we show that these two simple methods offer notable robustness to a range of plausible bias mechanisms, without making any explicit modelling assumptions. In conclusion, when performing a meta-analysis with suspected small study effects, we recommend reporting the mean, median and modal pooled estimates as a simple but informative sensitivity analyses.