A new improved graphical and quantitative method for detecting bias in meta-analysis

Detection of publication and related biases remains suboptimal and threatens the validity and interpretation of meta-analytical findings. When bias is present, it usually differentially affects small and large studies manifesting as an association between precision and effect size and therefore visual asymmetry of conventional funnel plots. This asymmetry can be quantified and Egger's regression is, by far, the most widely used statistical measure for quantifying funnel plot asymmetry. However, concerns have been raised about both the visual appearance of funnel plots and the sensitivity of Egger's regression to detect such asymmetry, particularly when the number of studies is small. In this article, we propose a new graphical method, the Doi plot, to visualize asymmetry and also a new measure, the LFK index, to detect and quantify asymmetry of study effects in Doi plots. We demonstrate that the visual representation of asymmetry was better for the Doi plot when compared with the funnel plot. We also show that the diagnostic accuracy of the LFK index in discriminating between asymmetry due to simulated publication bias versus chance or no asymmetry was also better with the LFK index which had areas under the receiver operating characteristic curve of 0.74-0.88 with simulations of meta-analyses with five, 10, 15, and 20 studies. The Egger's regression result had lower areas under the receiver operating characteristic curve values of 0.58-0.75 across the same simulations. The LFK index also had a higher sensitivity (71.3-72.1%) than the Egger's regression result (18.5-43.0%). We conclude that the methods proposed in this article can markedly improve the ability of researchers to detect bias in meta-analysis.