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Publication bias is a major problem, perhaps the major problem, in meta-analysis (or systematic reviews). Small studies are more likely to be published if their results are 'significant' than if their results are negative or inconclusive, and so the studies available for review are biased in favour of those with positive outcomes. Correcting for this bias is not possible without making untestable assumptions. In this paper, a sensitivity analysis is suggested which is based on fitting a model to the funnel plot. Some examples are discussed.
J. B. Copas (Fri,) studied this question.
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