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Abstract:
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Publication bias (PB) is a major threat to the validity of meta-analyses. Funnel plots have been a popular tool for assessing PB. They usually present treatment effects against their standard errors (SEs), and the contours of different significance levels have been used to distinguish PB from other factors that may cause the plots’ asymmetry. However, treatment effects and their SEs may be associated even if no PB exists, so SE-based funnel plots may lead to false positive conclusions. Also, the missingness of studies may relate to their sample sizes. Therefore, funnel plots based on sample sizes (N-based) can be an alternative. We derive contours for N-based funnel plots, which help meta-analysts properly interpret such plots’ asymmetry. In addition, we introduce six measures to quantify the magnitude of PB. Currently, no guides are available for judging whether the PB is minimal or substantial. Based on the measures’ empirical distributions among a large collection of meta-analyses, we propose cutoffs that categorize the magnitude of PB as unimportant, moderate, substantial, and considerable. They help evidence users grade the certainty in evidence impacted by PB.
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