Graphical augmentations to sample-size-based funnel plot in meta-analysis.

Assessing publication bias is a critical procedure in meta-analyses for rating the synthesized overall evidence. Because statistical tests for publication bias are usually not powerful and only give P values that inform either the presence or absence of the bias, examining the asymmetry of funnel plots has been popular to investigate potentially missing studies and the direction of the bias. Most funnel plots present treatment effects against their standard errors, and the contours depicting studies' significance levels have been used in the plots to distinguish publication bias from other factors (such as heterogeneity and subgroup effects) that may cause the plots' asymmetry. However, treatment effects and their standard errors are frequently associated even if no publication bias exists (eg, both variables depend on the four data cells in a 2 × 2 table for the odds ratio), so standard-error-based funnel plots may lead to false positive conclusions when such association may not be negligible. In addition, the missingness of studies may relate to their sample sizes besides P values (which are partly determined by standard errors); studies with more samples are more likely published. Therefore, funnel plots based on sample sizes can be an alternative tool. However, the contours for standard-error-based funnel plots cannot be directly applied to sample-size-based ones. This article introduces contours for sample-size-based funnel plots of various effect sizes, which may help meta-analysts properly interpret such plots' asymmetry. We provide five examples to illustrate the use of the proposed contours.