Publication bias arises when the availability of studies depends on the results, such as their significance, magnitude or direction. A meta-analysis of the available studies can then differ systematically from one including all eligible evidence. Funnel plot asymmetry can motivate investigation but does not establish this mechanism; heterogeneity and other small-study effects can also cause asymmetry.
A selection model combines a distribution for all study results with a probability that a result becomes available. The observed distribution is reweighted by this probability and renormalized. Assumed or estimated selection mechanisms permit sensitivity analysis of a meta-analysis, but unavailable results generally prevent a fully assumption-free correction.
Trim and fill estimates missing studies from funnel plot asymmetry by trimming extreme studies to locate a centre and filling in counterparts on the less represented side. The adjusted meta-analysis includes these imputed estimates. Its interpretation depends on a symmetry model for missing evidence; it is not a guarantee that genuine publication bias has been removed.
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