Gjerdevik Miriam, Heuch Ivar
Department of Mathematics, University of Bergen, P, O, Box 7800, N-5020 Bergen, Norway.
BMC Med Res Methodol. 2014 Sep 22;14:109. doi: 10.1186/1471-2288-14-109.
The rank correlation test introduced by Begg and Mazumdar is extensively used in meta-analysis to test for publication bias in clinical and epidemiological studies. It is based on correlating the standardized treatment effect with the variance of the treatment effect using Kendall's tau as the measure of association. To our knowledge, the operational characteristics regarding the significance level of the test have not, however, been fully assessed.
We propose an alternative rank correlation test to improve the error rates of the original Begg and Mazumdar test. This test is based on the simulated distribution of the estimated measure of association, conditional on sampling variances. Furthermore, Spearman's rho is suggested as an alternative rank correlation coefficient. The attained level and power of the tests are studied by simulations of meta-analyses assuming the fixed effects model.
The significance levels of the original Begg and Mazumdar test often deviate considerably from the nominal level, the null hypothesis being rejected too infrequently. It is proven mathematically that the assumptions for using the rank correlation test are not strictly satisfied. The pairs of variables fail to be independent, and there is a correlation between the standardized effect sizes and sampling variances under the null hypothesis of no publication bias. In the meta-analysis setting, the adverse consequences of a false negative test are more profound than the disadvantages of a false positive test. Our alternative test improves the error rates in fixed effects meta-analysis. Its significance level equals the nominal value, and the Type II error rate is reduced. In small data sets Spearman's rho should be preferred to Kendall's tau as the measure of association.
As the attained significance levels of the test introduced by Begg and Mazumdar often deviate greatly from the nominal level, modified rank correlation tests, improving the error rates, should be preferred when testing for publication bias assuming fixed effects meta-analysis.
Begg和Mazumdar提出的秩相关检验在荟萃分析中被广泛用于检验临床和流行病学研究中的发表偏倚。它基于使用肯德尔秩相关系数（Kendall's tau）作为关联度量，将标准化治疗效果与治疗效果的方差进行关联分析。然而，据我们所知，关于该检验显著性水平的操作特性尚未得到充分评估。
我们提出了一种替代的秩相关检验，以提高原始Begg和Mazumdar检验的错误率。该检验基于在抽样方差条件下估计关联度量的模拟分布。此外，建议使用斯皮尔曼等级相关系数（Spearman's rho）作为替代的秩相关系数。通过假设固定效应模型的荟萃分析模拟来研究检验的实际显著性水平和检验效能。
原始Begg和Mazumdar检验的显著性水平常常与名义水平有很大偏差，原假设被拒绝的频率过低。数学证明表明，使用秩相关检验的假设并未得到严格满足。变量对并非独立，并且在无发表偏倚的原假设下，标准化效应量与抽样方差之间存在相关性。在荟萃分析环境中，假阴性检验的不良后果比假阳性检验的缺点更为严重。我们的替代检验提高了固定效应荟萃分析中的错误率。其显著性水平等于名义值，且II型错误率降低。在小数据集中，应首选斯皮尔曼等级相关系数（Spearman's rho）而非肯德尔秩相关系数（Kendall's tau）作为关联度量。
由于Begg和Mazumdar提出的检验所达到的显著性水平常常与名义水平有很大偏差，在假设固定效应荟萃分析检验发表偏倚时，应首选改进错误率的修正秩相关检验。
