A new approach to outliers in meta-analysis

The synthesis of evidence from trials and medical studies using meta-analysis is essential for Evidence Based Medicine. However, problematical outlying results often occur even under the random-effects model. We propose a model that allows a long-tailed distribution for the random effect, which removes the necessity for an arbitrary decision to include or exclude outliers. In this approach, they are included, but with a reduced weight. We also introduce a modification of the forest plot to show the downweighting of outliers. We illustrate the methodology and its usefulness by carrying out both frequentist and Bayesian meta-analyses using data sets from the Cochrane Collaboration.