A correction to Begg's test for publication bias

Begg and Mazumdar proposed using a rank correlation test to test for publication bias when carrying out meta-analyses. The asymptotic variance of the rank correlation test statistic was derived under assumptions unmet by this application, often resulting in a loss of power. Low power when Begg's test is used to screen for publication bias may lead to false positives in a subsequent meta-analysis. We obtain the asymptotic bias under the common conditionally normal model as a function of the distribution of primary study variances. In simulations, we consider the performance of Begg's test using an approximation to the correct asymptotic variance. We consider this performance under the common fixed effects and random effects frameworks. We then examine several meta-analyses drawn from the literature where the standard and bias-corrected versions of Begg's test lead to different conclusions.