Outlier detection and accommodation in meta-regression models

This article studies outlier detection and accommodation under mean-shift model in random effect meta-regression model. We present two approaches for multiple outliers detection in terms of well known mean-shift model. One use traditional way as in classical regression model to derive the test statistic in which the heterogeneity variance parameter is fixed first and then replaced by its estimator under the null model; this method is called as one-step approximation. However, this one-step approximation ignores the impact of heterogeneity variance estimation if the outliers detected are highly influential on estimating heterogeneity variance. Therefore, we propose a new approximate method to derive test statistic of multiple outliers in meta-regression model, in which the effects of estimating heterogeneity variance are taken into consideration. The formulae based on MLE and REMLE are both considered. The power performance of test statistics are examined and compared via simulation studies and we find our approximate method is more effective to identifying outliers in meta-regression models. In addition, we propose a modified model to accommodate outliers in meta-regression model. Two examples are analyzed for illustration.