A comparison of methods to detect publication bias in meta-analysis

Meta-analyses are subject to bias for many of reasons, including publication bias. Asymmetry in a funnel plot of study size against treatment effect is often used to identify such bias. We compare the performance of three simple methods of testing for bias: the rank correlation method; a simple linear regression of the standardized estimate of treatment effect on the precision of the estimate; and a regression of the treatment effect on sample size. The tests are applied to simulated meta-analyses in the presence and absence of publication bias. Both one-sided and two-sided censoring of studies based on statistical significance was used. The results indicate that none of the tests performs consistently well. Test performance varied with the magnitude of the true treatment effect, distribution of study size and whether a one- or two-tailed significance test was employed. Overall, the power of the tests was low when the number of studies per meta-analysis was close to that often observed in practice. Tests that showed the highest power also had type I error rates higher than the nominal level. Based on the empirical type I error rates, a regression of treatment effect on sample size, weighted by the inverse of the variance of the logit of the pooled proportion (using the marginal total) is the preferred method.