Liu Dungang, Liu Regina, Xie Minge
Department of Biostatistics, Yale University School of Public Health, New Haven, CT 06511, USA.
Department of Statistics and Biostatistics, Rutgers University, New Brunswick, NJ 08854, USA.
J Am Stat Assoc. 2015;110(509):326-340. doi: 10.1080/01621459.2014.899235.
Meta-analysis has been widely used to synthesize evidence from multiple studies for common hypotheses or parameters of interest. However, it has not yet been fully developed for incorporating heterogeneous studies, which arise often in applications due to different study designs, populations or outcomes. For heterogeneous studies, the parameter of interest may not be estimable for certain studies, and in such a case, these studies are typically excluded from conventional meta-analysis. The exclusion of part of the studies can lead to a non-negligible loss of information. This paper introduces a metaanalysis for heterogeneous studies by combining the derived from the summary statistics of individual studies, hence referred to as the CD approach. It includes all the studies in the analysis and makes use of all information, direct as well as indirect. Under a general likelihood inference framework, this new approach is shown to have several desirable properties, including: i) it is asymptotically as efficient as the maximum likelihood approach using individual participant data (IPD) from all studies; ii) unlike the IPD analysis, it suffices to use summary statistics to carry out the CD approach. Individual-level data are not required; and iii) it is robust against misspecification of the working covariance structure of the parameter estimates. Besides its own theoretical significance, the last property also substantially broadens the applicability of the CD approach. All the properties of the CD approach are further confirmed by data simulated from a randomized clinical trials setting as well as by real data on aircraft landing performance. Overall, one obtains an unifying approach for combining summary statistics, subsuming many of the existing meta-analysis methods as special cases.
荟萃分析已被广泛用于综合多项研究的证据，以探讨常见假设或感兴趣的参数。然而，在纳入异质性研究方面，该方法尚未得到充分发展，而异质性研究在实际应用中经常出现，原因包括不同的研究设计、研究人群或研究结果。对于异质性研究，某些研究中感兴趣的参数可能无法估计，在这种情况下，这些研究通常会被排除在传统的荟萃分析之外。排除部分研究会导致不可忽视的信息损失。本文通过结合从各个研究的汇总统计数据中推导出来的内容，介绍了一种针对异质性研究的荟萃分析方法，因此称为CD方法。它在分析中纳入了所有研究，并利用了所有信息，包括直接信息和间接信息。在一般的似然推断框架下，这种新方法被证明具有几个理想的特性，包括：i）它在渐近意义上与使用所有研究的个体参与者数据（IPD）的最大似然方法一样有效；ii）与IPD分析不同，使用汇总统计数据就足以进行CD方法。不需要个体层面的数据；iii）它对参数估计的工作协方差结构的错误设定具有稳健性。除了其自身的理论意义外，最后一个特性还大大拓宽了CD方法的适用性。CD方法的所有特性都通过随机临床试验设置模拟的数据以及飞机着陆性能的实际数据得到了进一步证实。总体而言，我们得到了一种统一的方法来组合汇总统计数据，将许多现有的荟萃分析方法作为特殊情况包含在内。
