A finite mixture method for outlier detection and robustness in meta-analysis

When performing a meta-analysis unexplained variation above that predicted by within study variation is usually modeled by a random effect. However, in some cases, this is not sufficient to explain all the variation because of outlier or unusual studies. A previously described method is to define an outlier as a study requiring a higher random effects variance and testing each study sequentially. An extension is described where the studies are considered to be a finite mixture of outliers and non-outliers, allowing any number of outlier studies and the use of standard mixture model techniques. The bootstrap likelihood ratio test is used to determine if there are any outliers present by comparing models with and without outliers, and the outlier studies are identified using posterior predicted probabilities. The estimation of the overall treatment effect is then determined including all observations but with the outliers down-weighted. This has the advantage that studies that are marginal outliers are still included in the meta-analysis but with an appropriate weighting. The method is applied to examples from meta-analysis and meta-regression.