The power functions of Begg's and Egger's tests for publication bias

Publication bias undermines the results of meta‐analyses and other systematic reviews. Applying a formal test for publication bias is therefore a part of many protocols for conducting a meta‐analysis. To be effective in this role, the tests must have good power to detect the presence of publication bias. We derive the local limiting power functions and study the Pitman relative efficiency for two popular tests, Begg's and Egger's tests. The analysis suggests that the differences between the two arise out of built‐in robustness properties of Begg's test. These work to its detriment in the commonly used Gaussian model, but leave it with better efficiency when study effects are heavy‐tailed or skew.