Hardy R J, Thompson S G
Medical Statistics Unit, London School of Hygiene and Tropical Medicine, U.K.
Stat Med. 1996 Mar 30;15(6):619-29. doi: 10.1002/(SICI)1097-0258(19960330)15:6<619::AID-SIM188>3.0.CO;2-A.
In a meta-analysis of a set of clinical trials, a crucial but problematic component is providing an estimate and confidence interval for the overall treatment effect theta. Since in the presence of heterogeneity a fixed effect approach yields an artificially narrow confidence interval for theta, the random effects method of DerSimonian and Laird, which incorporates a moment estimator of the between-trial components of variance sigma B2, has been advocated. With the additional distributional assumptions of normality, a confidence interval for theta may be obtained. However, this method does not provide a confidence interval for sigma B2, nor a confidence interval for theta which takes account of the fact that sigma B2 has to be estimated from the data. We show how a likelihood based method can be used to overcome these problems, and use profile likelihoods to construct likelihood based confidence intervals. This approach yields an appropriately widened confidence interval compared with the standard random effects method. Examples of application to a published meta-analysis and a multicentre clinical trial are discussed. It is concluded that likelihood based methods are preferred to the standard method in undertaking random effects meta-analysis when the value of sigma B2 has an important effect on the overall estimated treatment effect.
在一组临床试验的荟萃分析中，一个关键但存在问题的部分是为总体治疗效果θ提供估计值和置信区间。由于在存在异质性的情况下，固定效应方法会产生一个人为缩小的θ置信区间，因此提倡采用DerSimonian和Laird的随机效应方法，该方法纳入了试验间方差σB2成分的矩估计量。在正态性的额外分布假设下，可以获得θ的置信区间。然而，该方法没有提供σB2的置信区间，也没有提供考虑到σB2必须从数据中估计这一事实的θ置信区间。我们展示了如何使用基于似然的方法来克服这些问题，并使用轮廓似然性来构建基于似然的置信区间。与标准随机效应方法相比，这种方法产生了一个适当加宽的置信区间。讨论了应用于已发表的荟萃分析和多中心临床试验的示例。得出的结论是，当σB2的值对总体估计治疗效果有重要影响时，在进行随机效应荟萃分析时，基于似然的方法优于标准方法。
