Egger M, Davey Smith G, Schneider M, Minder C
Department of Social Medicine, University of Bristol.
BMJ. 1997 Sep 13;315(7109):629-34. doi: 10.1136/bmj.315.7109.629.
Funnel plots (plots of effect estimates against sample size) may be useful to detect bias in meta-analyses that were later contradicted by large trials. We examined whether a simple test of asymmetry of funnel plots predicts discordance of results when meta-analyses are compared to large trials, and we assessed the prevalence of bias in published meta-analyses.
Medline search to identify pairs consisting of a meta-analysis and a single large trial (concordance of results was assumed if effects were in the same direction and the meta-analytic estimate was within 30% of the trial); analysis of funnel plots from 37 meta-analyses identified from a hand search of four leading general medicine journals 1993-6 and 38 meta-analyses from the second 1996 issue of the Cochrane Database of Systematic Reviews.
Degree of funnel plot asymmetry as measured by the intercept from regression of standard normal deviates against precision.
In the eight pairs of meta-analysis and large trial that were identified (five from cardiovascular medicine, one from diabetic medicine, one from geriatric medicine, one from perinatal medicine) there were four concordant and four discordant pairs. In all cases discordance was due to meta-analyses showing larger effects. Funnel plot asymmetry was present in three out of four discordant pairs but in none of concordant pairs. In 14 (38%) journal meta-analyses and 5 (13%) Cochrane reviews, funnel plot asymmetry indicated that there was bias.
A simple analysis of funnel plots provides a useful test for the likely presence of bias in meta-analyses, but as the capacity to detect bias will be limited when meta-analyses are based on a limited number of small trials the results from such analyses should be treated with considerable caution.
漏斗图（效应估计值与样本量的关系图）可能有助于检测荟萃分析中的偏倚，而这些偏倚后来可能会被大型试验所推翻。我们研究了漏斗图的简单不对称性检验能否预测荟萃分析与大型试验结果的不一致性，并评估了已发表的荟萃分析中偏倚的发生率。
通过医学文献数据库检索，找出由一项荟萃分析和一项大型试验组成的配对（如果效应方向相同且荟萃分析估计值在试验值的30%以内，则假设结果一致）；对从1993 - 1996年四种主要综合医学杂志的手工检索中识别出的37项荟萃分析以及1996年第二期Cochrane系统评价数据库中的38项荟萃分析的漏斗图进行分析。
通过标准正态偏差对精度的回归截距来衡量漏斗图的不对称程度。
在识别出的8对荟萃分析和大型试验中（5对来自心血管医学，1对来自糖尿病医学，1对来自老年医学，1对来自围产期医学），有4对结果一致，4对结果不一致。在所有不一致的情况中，都是因为荟萃分析显示出更大的效应。在4对不一致的配对中有3对存在漏斗图不对称，但在所有一致的配对中均未出现。在14项（38%）杂志荟萃分析和5项（13%）Cochrane综述中，漏斗图不对称表明存在偏倚。
对漏斗图进行简单分析可为荟萃分析中可能存在偏倚提供有用的检验，但由于当荟萃分析基于有限数量的小型试验时，检测偏倚的能力将受到限制，因此对此类分析的结果应极为谨慎地对待。
