Hybrid test for publication bias in meta-analysis

Publication bias frequently appears in meta-analyses when the included studies' results (e.g., p-values) influence the studies' publication processes. Some unfavorable studies may be suppressed from publication, so the meta-analytic results may be biased toward an artificially favorable direction. Many statistical tests have been proposed to detect publication bias in recent two decades. However, they often make dramatically different assumptions about the cause of publication bias; therefore, they are usually powerful only in certain cases that support their particular assumptions, while their powers may be fairly low in many other cases. Although several simulation studies have been carried out to compare different tests' powers under various situations, it is typically infeasible to justify the exact mechanism of publication bias in a real-world meta-analysis and thus select the corresponding optimal publication bias test. We introduce a hybrid test for publication bias by synthesizing various tests and incorporating their benefits, so that it maintains relatively high powers across various mechanisms of publication bias. The superior performance of the proposed hybrid test is illustrated using simulation studies and three real-world meta-analyses with different effect sizes. It is compared with many existing methods, including the commonly used regression and rank tests, and the trim-and-fill method.