Meta‐analyses of a treatment's effect compared with a control frequently calculate the meta‐effect from standardized mean differences (SMDs). SMDs are usually estimated by Cohen's d or Hedges' g. Cohen's d divides the difference between sample means of a continuous response by the pooled standard deviation, but is subject to nonnegligible bias for small sample sizes. Hedges' g removes this bias with a correction factor. The current literature (including meta‐analysis books and software packages) is confusingly inconsistent about methods for synthesizing SMDs, potentially making reproducibility a problem. Using conventional methods, the variance estimate of SMD is associated with the point estimate of SMD, so Hedges' g is not guaranteed to be unbiased in meta‐analyses. This article comprehensively reviews and evaluates available methods for synthesizing SMDs. Their performance is compared using extensive simulation studies and analyses of actual datasets. We find that because of the intrinsic association between point estimates and standard errors, the usual version of Hedges' g can result in more biased meta‐estimation than Cohen's d. We recommend using average‐adjusted variance estimators to obtain an unbiased meta‐estimate, and the Hartung‐Knapp‐Sidik‐Jonkman method for accurate estimation of its confidence interval.

中文翻译：

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荟萃分析中标准化均差的各种估计量的评估


与对照相比，治疗效果的荟萃分析经常根据标准化平均差（SMD）计算荟萃效应。 SMD 通常通过 Cohen's d或 Hedges' g来估计。 Cohen's d将连续响应的样本均值之间的差异除以汇总标准差，但对于小样本量会存在不可忽略的偏差。 Hedges' g通过修正因子消除了这种偏差。目前的文献（包括荟萃分析书籍和软件包）对于合成 SMD 的方法不一致，令人困惑，这可能会导致重现性成为问题。使用传统方法，SMD 的方差估计与 SMD 的点估计相关，因此 Hedges' g在荟萃分析中不能保证无偏。本文全面回顾和评估了合成 SMD 的可用方法。通过广泛的模拟研究和实际数据集的分析来比较它们的性能。我们发现，由于点估计和标准误差之间的内在关联，Hedges g的通常版本可能会比 Cohen d产生更多有偏差的元估计。我们建议使用平均调整方差估计来获得无偏元估计，并使用 Hartung-Knapp-Sidik-Jonkman 方法来准确估计其置信区间。