Funnel plots and publication bias: Does asymmetry means a bad meta-model? I have done a multi-level meta analysis with R, using metafor package. My questions relates to funnel plot asymmetry. 
(1) If a regression test suggested funnel asymmetry (i.e. suggested a publication bias is present), Does this mean that my meta-analysis model is bad? and my results of meta-analysis are bad?
(2) What are other possible reasons, besides publication bias, that could lead to asymmetry in the funnel plots? 
 A: There are several things that can lead to an asymmetric funnel plot (and I doubt my list is complete - there are presumably other reasons, too):


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*Publication bias in its various forms (selective publication of studies, journals being more interested in significant results, less impressive results ending up in hard to find obscure journals, selective publication of results from a study etc.)

*Related but not quite the same: when analyses are not fully pre-specified the various choices made during analyses, which may bias results one way or another ("garden of forking paths")

*Within study biases (e.g. you look at the odds ratio for people having a medical event, but one treatment group had fewer drop-outs and thus, longer follow-up than the other one)

*The choice of effect scale (e.g. plotting odds/risk/hazard ratios on a linear scale instead of a log-scale could make things look asymmetric, using odds ratios across studies of different length when there is a constant hazard ratio etc.)

*Chance (there are so many meta-analyses done that some will show some asymmetry just by chance - and this is to some extent part of the scientific process: things that work well - even if this is by chance - continue to be studied)

*When none of the above apply (which we cannot really know for sure): if you are plotting estimates from a model, then an asymmetry could still arise due to an issue with the model (as you mention).

