School of Social Work & Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina.
Department of Statistics, University of Pretoria, South Africa.
Biometrics. 2020 Dec;76(4):1319-1329. doi: 10.1111/biom.13238. Epub 2020 Mar 3.
Meta-analysis is a statistical methodology for combining information from diverse sources so that a more reliable and efficient conclusion can be reached. It can be conducted by either synthesizing study-level summary statistics or drawing inference from an overarching model for individual participant data (IPD) if available. The latter is often viewed as the "gold standard." For random-effects models, however, it remains not fully understood whether the use of IPD indeed gains efficiency over summary statistics. In this paper, we examine the relative efficiency of the two methods under a general likelihood inference setting. We show theoretically and numerically that summary-statistics-based analysis is at most as efficient as IPD analysis, provided that the random effects follow the Gaussian distribution, and maximum likelihood estimation is used to obtain summary statistics. More specifically, (i) the two methods are equivalent in an asymptotic sense; and (ii) summary-statistics-based inference can incur an appreciable loss of efficiency if the sample sizes are not sufficiently large. Our results are established under the assumption that the between-study heterogeneity parameter remains constant regardless of the sample sizes, which is different from a previous study. Our findings are confirmed by the analyses of simulated data sets and a real-world study of alcohol interventions.
荟萃分析是一种将不同来源的信息综合起来以得出更可靠和有效的结论的统计方法。它可以通过综合研究水平的汇总统计数据或从可用的个体参与者数据（IPD）的总体模型中进行推断来进行。后者通常被视为“金标准”。然而，对于随机效应模型，仍然不完全清楚使用 IPD 是否确实比汇总统计数据更有效率。在本文中，我们在一般似然推理设置下检查了这两种方法的相对效率。我们从理论和数值上表明，只要随机效应服从正态分布并且使用最大似然估计来获取汇总统计数据，基于汇总统计数据的分析最多与 IPD 分析一样有效。更具体地说，（i）在渐近意义上，这两种方法是等效的；（ii）如果样本量不够大，基于汇总统计数据的推断可能会导致效率的显著损失。我们的结果是在假设研究间异质性参数保持不变而与样本量无关的情况下得出的，这与之前的一项研究不同。我们的发现通过对模拟数据集和酒精干预的实际研究的分析得到了证实。
