Robust estimation and confidence interval in meta-regression models

Meta-analysis provides a quantitative method for combining results from independent studies with the same treatment. However, existing estimation methods are sensitive to the presence of outliers in the datasets. In this paper we study the robust estimation for the parameters in meta-regression, including the between-study variance and regression parameters. Huber's rho function and Tukey's biweight function are adopted to derive the formulae of robust maximum likelihood (ML) estimators. The corresponding algorithms are developed. The asymptotic confidence interval and second-order-corrected confidence interval are investigated. Extensive simulation studies are conducted to assess the performance of the proposed methodology, and our results show that the robust estimators are promising and outperform the conventional ML and restricted maximum likelihood estimators when outliers exist in the dataset. The proposed methods are applied in three case studies and the results further support the eligibility of our methods in practical situations.