= Solution
One method is <trim and fill>. Estimate the direction and extent of funnel asymmetry, temporarily trim the extreme studies on the overrepresented side to estimate a centre, and fill in mirror-image studies on the underrepresented side. Recompute the pooled effect using the observed and imputed studies. This estimates what the summary might be under a symmetry-based missing-study model. It can move an exaggerated effect towards the null, but genuine heterogeneity can violate its symmetry assumptions.
A second method is a <selection model for publication bias>. Specify how the <probability> of a result being available depends on quantities such as its $P$ value, direction or precision, and combine that mechanism with a model for the underlying study effects. If a study estimate has density $f(y)$ and availability <probability> $\pi(y)$, its observed density is proportional to $f(y)\pi(y)$, with a normalizing factor accounting for unobserved results. Fit the model, or vary the selection <probabilities> over plausible scenarios, to obtain selection-adjusted effects. Such models make assumptions about evidence that is missing, so their results are particularly useful as <sensitivity analyses>. \b[Neither method removes <publication bias> without assumptions about the missing studies.]
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