New models for describing outliers in meta‐analysis

An unobserved random effect is often used to describe the between-study variation that is apparent in meta-analysis datasets. A normally distributed random effect is conventionally used for this purpose. When outliers or other unusual estimates are included in the analysis, the use of alternative random effect distributions has previously been proposed. Instead of adopting the usual hierarchical approach to modelling between-study variation, and so directly modelling the study specific true underling effects, we propose two new marginal distributions for modelling heterogeneous datasets. These two distributions are suggested because numerical integration is not needed to evaluate the likelihood. This makes the computation required when fitting our models much more robust. The properties of the new distributions are described, and the methodology is exemplified by fitting models to four datasets.