Institute for Research in Operative Medicine, Witten/Herdecke University, Ostmerheimer Str 200, Building 38, 51109, Cologne, Germany.
Institute of Medical Biometry and Informatics, University of Heidelberg, Heidelberg, Germany.
Res Synth Methods. 2018 Sep;9(3):366-381. doi: 10.1002/jrsm.1296. Epub 2018 Apr 26.
Meta-analyses often include only a small number of studies (≤5). Estimating between-study heterogeneity is difficult in this situation. An inaccurate estimation of heterogeneity can result in biased effect estimates and too narrow confidence intervals. The beta-binominal model has shown good statistical properties for meta-analysis of sparse data. We compare the beta-binominal model with different inverse variance random (eg, DerSimonian-Laird, modified Hartung-Knapp, and Paule-Mandel) and fixed effects methods (Mantel-Haenszel and Peto) in a simulation study. The underlying true parameters were obtained from empirical data of actually performed meta-analyses to best mirror real-life situations. We show that valid methods for meta-analysis of a small number of studies are available. In fixed effects situations, the Mantel-Haenszel and Peto methods performed best. In random effects situations, the beta-binominal model performed best for meta-analysis of few studies considering the balance between coverage probability and power. We recommended the beta-binominal model for practical application. If very strong evidence is needed, using the Paule-Mandel heterogeneity variance estimator combined with modified Hartung-Knapp confidence intervals might be useful to confirm the results. Notable most inverse variance random effects models showed unsatisfactory statistical properties also if more studies (10-50) were included in the meta-analysis.
荟萃分析通常仅包括少数研究（≤5）。在这种情况下，估计研究间异质性很困难。异质性的不准确估计可能导致有偏差的效应估计和过窄的置信区间。贝塔二项式模型在稀疏数据分析的荟萃分析中表现出良好的统计特性。我们在模拟研究中比较了贝塔二项式模型与不同的逆方差随机（例如，DerSimonian-Laird、改良的Hartung-Knapp 和 Paule-Mandel）和固定效应方法（Mantel-Haenszel 和 Peto）。基础真实参数是从实际进行的荟萃分析的经验数据中获得的，以最佳反映现实生活情况。我们表明，对于少数研究的荟萃分析，有有效的方法可用。在固定效应情况下，Mantel-Haenszel 和 Peto 方法表现最好。在随机效应情况下，贝塔二项式模型在考虑覆盖率概率和功效之间的平衡时，对少数研究的荟萃分析表现最佳。我们建议在实际应用中使用贝塔二项式模型。如果需要非常有力的证据，使用 Paule-Mandel 异质性方差估计器结合改良的 Hartung-Knapp 置信区间可能有助于确认结果。值得注意的是，如果荟萃分析中包含更多的研究（10-50），大多数逆方差随机效应模型的统计特性也不理想。
