A modified regression method to test publication bias in meta-analyses with binary outcomes

Background: The tendency towards publication bias is greater for observational studies than for randomized clinical trials. Several statistical methods have been developed to test the publication bias. However, almost all existing methods exhibit rather low power or have inappropriate type I error rates. Methods: We propose a modified regression method, which used a smoothed variance to estimate the precision of a study, to test for publication bias in meta-analyses of observational studies. A comprehensive simulation study is carried out, and a real-world example is considered. Results: The simulation results indicate that the performance of tests varies with the number of included studies, level of heterogeneity, event rates, and sample size ratio between two groups. Neither the existing tests nor the newly developed method is particularly powerful in all simulation scenarios. However, our proposed method has a more robust performance across different settings. In the presence of heterogeneity, the arcsine-Thompson test is a suitable alternative, and Peters' test can be considered as a complementary method when mild or no heterogeneity is present. Conclusions: Several factors should be taken into consideration when employing asymmetry tests for publication bias. Based on our simulation results, we provide a concise table to show the appropriate use of regression methods to test for publication bias based on our simulation results.