A robust test for multivariate publication bias in meta-analysis

Abstract

A rank regression based procedure for testing for the existence of publication bias in meta-analysis is proposed. The method is designed to possess the robustness of the Begg rank correlation test for publication bias and the efficiency of Egger’s regression approach. The procedure uses the Jaeckel rank-regression framework along with a rank prediction protocol for estimating the intercept term of Egger-type regression models for a robust and efficient test of publication bias in univariate meta-analysis. Application on several real-life meta-analyses studies demonstrate the use of the proposed proce dure. This approach of using the Jaeckel rank-regression with rank prediction protocol is extended to the nested mixed model framework to develop a robust and efficient test for publication bias in multivariate meta-analyses. Commonly used statistical methods detect publication bias in univariate meta-analysis. This procedure is compared to the only other existing test for publication bias in multivariate meta-analysis, Hong’s composite pseudo likelihood test, using simulation experiments. It is shown that the proposed method is better at maintaining the nominal size of the test and more power ful than the existing test especially in meta analyses that contain studies with possibly outlying effect sizes.