Department of Medical Biometry, Institute for Quality and Efficiency in Health Care (IQWiG), Im Mediapark 8, Cologne, 50670, Germany.
Syst Rev. 2012 Jul 28;1:34. doi: 10.1186/2046-4053-1-34.
Meta-analysis is used to combine the results of several related studies. Two different models are generally applied: the fixed-effect (FE) and random-effects (RE) models. Although the two approaches estimate different parameters (that is, the true effect versus the expected value of the distribution of true effects) in practice, the graphical presentation of results is the same for both models. This means that in forest plots of RE meta-analyses, no estimate of the between-study variation is usually given graphically, even though it provides important information about the heterogeneity between the study effect sizes.
In addition to the point estimate of the between-study variation, a prediction interval (PI) can be used to determine the degree of heterogeneity, as it provides a region in which about 95% of the true study effects are expected to be found. To distinguish between the confidence interval (CI) for the average effect and the PI, it may also be helpful to include the latter interval in forest plots. We propose a new graphical presentation of the PI; in our method, the summary statistics in forest plots of RE meta-analyses include an additional row, '95% prediction interval', and the PI itself is presented in the form of a rectangle below the usual diamond illustrating the estimated average effect and its CI. We then compare this new graphical presentation of PIs with previous proposals by other authors. The way the PI is presented in forest plots is crucial. In previous proposals, the distinction between the CI and the PI has not been made clear, as both intervals have been illustrated either by a diamond or by extra lines added to the diamond, which may result in misinterpretation.
To distinguish graphically between the results of an FE and those of an RE meta-analysis, it is helpful to extend forest plots of the latter approach by including the PI. Clear presentation of the PI is necessary to avoid confusion with the CI of the average effect estimate.
荟萃分析用于合并几项相关研究的结果。通常应用两种不同的模型：固定效应（FE）和随机效应（RE）模型。尽管这两种方法在实践中估计的参数不同（即真实效应与真实效应分布的期望值），但两种模型的结果图形表示是相同的。这意味着在 RE 荟萃分析的森林图中，通常不会直观地给出研究间变异的估计值，尽管它提供了关于研究效应大小之间异质性的重要信息。
除了研究间变异的点估计值外，还可以使用预测区间（PI）来确定异质性的程度，因为它提供了一个大约 95%的真实研究效应预计会找到的区域。为了区分平均效应的置信区间（CI）和 PI，可以将后者区间包含在森林图中。我们提出了一种新的 PI 图形表示方法；在我们的方法中，RE 荟萃分析的森林图中的汇总统计信息包括一个额外的行，“95%预测区间”，并且 PI 本身以矩形的形式呈现，位于通常表示估计平均效应及其 CI 的钻石下方。然后，我们将这种新的 PI 图形表示方法与其他作者之前的建议进行比较。PI 在森林图中的呈现方式至关重要。在之前的建议中，CI 和 PI 之间的区别没有明确说明，因为这两个区间都通过钻石或添加到钻石上的额外线来表示，这可能导致误解。
为了直观地区分 FE 和 RE 荟萃分析的结果，通过包含 PI 来扩展后者的森林图是有帮助的。PI 的清晰呈现对于避免与平均效应估计的 CI 混淆是必要的。
