Abstract
Regression based methods for the detection of publication bias in meta-analysis have been extensively evaluated in literature. When dealing with continuous outcomes, specific hidden factors (e.g., heteroscedasticity) may interfere with the test statistics. In this paper we investigate the influence of residual heteroscedasticity on the performance of four tests for publication bias: the Egger test, the Begg-Mazumdar test and two tests based on weighted regression. In the presence of heteroscedasticity, the Egger test and the weighted regression tests highly inflate the Type I error rate, while the Begg-Mazumdar test deflates the Type I error rate. Although all three tests already have low statistical power, heteroscedasticity typically reduces it further. Our results in combination with earlier discussions on publication bias tests lead us to conclude that application of these tests on continuous treatment effects is not warranted.
Highlights
In a meta-analysis, publication bias can lead to an incorrect pooled estimate of a treatment effect
In this paper we investigate the influence of residual heteroscedasticity on the performance of four tests for publication bias: the Egger test, the Begg-Mazumdar test and two tests based on weighted regression
The Type I error rate and the power of Egger’s test, the rank corre lation test (RC), the weighted DL and the weighted Restricted Maximum Likelihood (REML) test are presented in Table 1 and Table 2, respectively
Summary
In a meta-analysis, publication bias can lead to an incorrect pooled estimate of a treatment effect. Several methods have been proposed in literature to test for lack of this type of publication bias, e.g., the Egger test [1], the rank-correlation test [2], and several others [1,3,4,5,6,7,8,9] These tests allow for heteroscedastic residual variances of the study effect sizes, but when their performances were studied the underlying data models are typically homoscedastic if sample size differences and realization of standard errors are ignored. Studies may or may not follow the premises of the test statistics, but when the variance of the outcome is correlated with its mean the resulting treatment effect estimates will be correlated with its standard errors as well This may lead to the detection of artificial “publication bias” without the presence of a real publication bias process. It is crucial to better understand the performances of the publication bias test for aggregated data under heteroscedasticity
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