Dataset for: Clinical heterogeneity in random-effect meta-analysis: an adjusted maximum likelihood approach for solving a between-study boundary estimate problem

Random-effect meta-analysis is commonly applied to estimate overall effects with unexplained heterogeneity across studies. However, standard methods, including (restricted) maximum likelihood (ML or REML), frequently produce (near) zero estimates for between-study variance parameters. Consequently, these methods are reduced to simple and unrealistic fixed-effect models, resulting in an ignorance of the substantial clinical heterogeneity and sometimes leading to incorrect conclusions. To solve the boundary estimate problem, we propose 1) an adjusted maximum likelihood method for the between-study variance that maximizes a likelihood defined as a product of a standard likelihood and a Gaussian class of adjustment factor and 2) a framework using sensitivity analysis by developing a new criterion to check for the occurrence of the boundary estimate. Although the adjustment introduces bias to the overall effects to ensure strictly positive estimates of the between-study variance when the number of studies K is small, the bias asymptotically approaches zero, resulting in the same estimates derived from the REML method. Also, the adjusted maximum likelihood estimator of the between-study variance is consistent for large K, and interestingly, the REML method and our method are equivalent in terms of mean squared error criterion, up to O(K). We illustrate our approach with a motivating example to examine the controversial result of a meta-analysis for 24 randomized controlled trials of human albumin. Numerical evaluations show that our approach produces no boundary estimates but similar synthesized results with the standard maximum likelihood methods as those produced by conventional methods, especially with a small number of studies.

随机效应Meta分析（Random-effect meta-analysis）常被用于估计各研究间存在未解释异质性时的总体效应。然而，包括最大似然法（Maximum Likelihood，ML）与受限最大似然法（Restricted Maximum Likelihood，REML）在内的标准方法，常会得到研究间方差参数的（近似）零估计值。由此，此类方法便会退化为简单且脱离实际的固定效应模型，进而忽视了显著的临床异质性，有时甚至会得出错误结论。为解决这一边界估计问题，本文提出两类方案：一是针对研究间方差的校正最大似然法，该方法最大化由标准似然与高斯类校正因子的乘积所定义的似然函数；二是构建基于敏感性分析的框架，通过制定新准则以检测边界估计的发生。尽管当研究数量K较小时，该校正会对总体效应引入偏差，以确保研究间方差获得严格正的估计值，但该偏差会渐近趋近于0，最终得到与REML法一致的估计结果。此外，研究间方差的校正最大似然估计量在K较大时具有一致性；且有趣的是，REML法与本文所提方法在均方误差准则下至多相差O(K)阶项。本文通过一则实证示例阐释所提方法，该示例用于检验一项纳入24项人血白蛋白随机对照试验（Randomized Controlled Trials, RCTs）的Meta分析所存在的争议性结果。数值模拟评估表明，本文方法不会产生边界估计，且得到的合成结果与常规标准最大似然法的结果相近，尤其在研究数量较少时表现更优。