Center for Evidence-based Medicine, Brown University, Providence, RI 02912, USA.
Clin Trials. 2012 Oct;9(5):610-20. doi: 10.1177/1740774512453218. Epub 2012 Aug 7.
Many comparative studies report results at multiple time points. Such data are correlated because they pertain to the same patients, but are typically meta-analyzed as separate quantitative syntheses at each time point, ignoring the correlations between time points.
To develop a meta-analytic approach that estimates treatment effects at successive time points and takes account of the stochastic dependencies of those effects.
We present both fixed and random effects methods for multivariate meta-analysis of effect sizes reported at multiple time points. We provide formulas for calculating the covariance (and correlations) of the effect sizes at successive time points for four common metrics (log odds ratio, log risk ratio, risk difference, and arcsine difference) based on data reported in the primary studies. We work through an example of a meta-analysis of 17 randomized trials of radiotherapy and chemotherapy versus radiotherapy alone for the postoperative treatment of patients with malignant gliomas, where in each trial survival is assessed at 6, 12, 18, and 24 months post randomization. We also provide software code for the main analyses described in the article.
We discuss the estimation of fixed and random effects models and explore five options for the structure of the covariance matrix of the random effects. In the example, we compare separate (univariate) meta-analyses at each of the four time points with joint analyses across all four time points using the proposed methods. Although results of univariate and multivariate analyses are generally similar in the example, there are small differences in the magnitude of the effect sizes and the corresponding standard errors. We also discuss conditional multivariate analyses where one compares treatment effects at later time points given observed data at earlier time points.
Simulation and empirical studies are needed to clarify the gains of multivariate analyses compared with separate meta-analyses under a variety of conditions.
Data reported at multiple time points are multivariate in nature and are efficiently analyzed using multivariate methods. The latter are an attractive alternative or complement to performing separate meta-analyses.
许多比较研究报告了多个时间点的结果。这些数据是相关的，因为它们与同一患者有关，但通常在每个时间点作为单独的定量综合进行荟萃分析，忽略了时间点之间的相关性。
开发一种荟萃分析方法，该方法可以估计连续时间点的治疗效果，并考虑这些效果的随机依赖性。
我们提出了用于分析多个时间点报告的效应大小的多元荟萃分析的固定效应和随机效应方法。我们提供了基于主要研究中报告的数据，计算四个常见指标（对数优势比、对数风险比、风险差和反正弦差）在连续时间点的效应大小的协方差（和相关系数）的公式。我们通过对 17 项随机对照试验的荟萃分析来举例说明，这些试验研究了放化疗与单纯放疗治疗恶性胶质瘤患者术后的效果，在每个试验中，生存情况在随机分组后 6、12、18 和 24 个月进行评估。我们还为本文中描述的主要分析提供了软件代码。
我们讨论了固定效应和随机效应模型的估计，并探索了随机效应协方差矩阵结构的五种选择。在这个例子中，我们比较了在四个时间点中的每一个时间点进行的单独（单变量）荟萃分析，以及使用提出的方法在所有四个时间点上进行的联合分析。尽管在这个例子中，单变量和多变量分析的结果通常是相似的，但效应大小和相应的标准误差的大小有很小的差异。我们还讨论了条件多变量分析，其中一种方法是比较在早期观察数据的基础上，在后期时间点的治疗效果。
需要进行模拟和实证研究，以明确在各种条件下，与单独的荟萃分析相比，多变量分析的优势。
在多个时间点报告的数据在本质上是多元的，使用多元方法进行分析是有效的。与单独进行荟萃分析相比，后者是一种有吸引力的替代或补充方法。
