Abstract
BackgroundThe 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.MethodsWe 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.ResultsThe 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.ConclusionsSeveral 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.
Highlights
The tendency towards publication bias is greater for observational studies than for randomized clinical trials [4]
We develop new regression methods that use a smoothed variance as the precision scale of an individual study to test the asymmetry of funnel plots
We observed that the type I error rates of the three rank correlation tests and the other four regression tests diverged from the nominal level as the heterogeneity or number of included studies increased
Summary
The tendency towards publication bias is greater for observational studies than for randomized clinical trials. Rank correlation-based tests have been criticized for their low power, and most regressions exhibit high type I error rates [5,11,12,13] These tests assume that, under the null hypothesis of no publication bias, there is no association between effect size and precision. This is plausible when the outcome is quantitative, because the assumption of normality implies that the sample mean is statistically independent of the sample variance. The principle behind recently developed methods (such as funnel plot regression [11], Harbord’s score test [14], Peters’ test [12,17], and Rucker’s arcsine transformed tests [15]) is a reduction in the intrinsic association between the estimated effect size and its estimated asymptotic variance. In Berkey’s study, the smoothed estimator of the within-study variance was used in the random effect regression model for meta-analysis to estimate less biased regression coefficients [18]
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