Using selection models to assess sensitivity to publication bias: A tutorial and call for more routine use

In meta-analyses, it is critical to assess the extent to which publication bias might have compromised the results. Classical methods based on the funnel plot, including Egger's test and Trim-and-Fill, have become the de facto default methods to do so, with a large majority of recent meta-analyses in top medical journals (85%) assessing for publication bias exclusively using these methods. However, these classical funnel plot methods have important limitations when used as the sole means of assessing publication bias: they essentially assume that the publication process favors large point estimates for small studies and does not affect the largest studies, and they can perform poorly when effects are heterogeneous. In light of these limitations, we recommend that meta-analyses routinely apply other publication bias methods in addition to or instead of classical funnel plot methods. To this end, we describe how to use and interpret selection models. These methods make the often more realistic assumption that publication bias favors "statistically significant" results, and the methods also directly accommodate effect heterogeneity. Selection models have been established for decades in the statistics literature and are supported by user-friendly software, yet remain rarely reported in many disciplines. We use a previously published meta-analysis to demonstrate that selection models can yield insights that extend beyond those provided by funnel plot methods, suggesting the importance of establishing more comprehensive reporting practices for publication bias assessment.