Van Lissa Caspar J, van Erp Sara, Clapper Eli-Boaz
Dept. Methodology & Statistics, Tilburg University, The Netherlands.
Dept. Methodology & Statistics, Utrecht University, The Netherlands.
Res Synth Methods. 2023 Mar;14(2):301-322. doi: 10.1002/jrsm.1628. Epub 2023 Mar 1.
When meta-analyzing heterogeneous bodies of literature, meta-regression can be used to account for potentially relevant between-studies differences. A key challenge is that the number of candidate moderators is often high relative to the number of studies. This introduces risks of overfitting, spurious results, and model non-convergence. To overcome these challenges, we introduce Bayesian Regularized Meta-Analysis (BRMA), which selects relevant moderators from a larger set of candidates by shrinking small regression coefficients towards zero with regularizing (LASSO or horseshoe) priors. This method is suitable when there are many potential moderators, but it is not known beforehand which of them are relevant. A simulation study compared BRMA against state-of-the-art random effects meta-regression using restricted maximum likelihood (RMA). Results indicated that BRMA outperformed RMA on three metrics: BRMA had superior predictive performance, which means that the results generalized better; BRMA was better at rejecting irrelevant moderators, and worse at detecting true effects of relevant moderators, while the overall proportion of Type I and Type II errors was equivalent to RMA. BRMA regression coefficients were slightly biased towards zero (by design), but its residual heterogeneity estimates were less biased than those of RMA. BRMA performed well with as few as 20 studies, suggesting its suitability as a small sample solution. We present free open source software implementations in the R-package pema (for penalized meta-analysis) and in the stand-alone statistical program JASP. An applied example demonstrates the use of the R-package.
在对异质性文献进行Meta分析时，Meta回归可用于解释研究间潜在的相关差异。一个关键挑战在于，相对于研究数量而言，候选调节变量的数量往往较多。这带来了过度拟合、虚假结果和模型不收敛的风险。为了克服这些挑战，我们引入了贝叶斯正则化Meta分析（BRMA），它通过使用正则化（LASSO或马蹄形）先验将小回归系数向零收缩，从更大的候选变量集中选择相关调节变量。当存在许多潜在调节变量，但事先不知道哪些变量相关时，这种方法很适用。一项模拟研究将BRMA与使用限制最大似然法（RMA）的最新随机效应Meta回归进行了比较。结果表明，BRMA在三个指标上优于RMA：BRMA具有更好的预测性能，这意味着结果的泛化性更好；BRMA在拒绝无关调节变量方面表现更好，而在检测相关调节变量的真实效应方面表现较差，同时I型和II型错误的总体比例与RMA相当。BRMA回归系数（按设计）略微偏向零，但其残差异质性估计比RMA的偏差更小。BRMA在仅有20项研究时也表现良好，表明它适合作为小样本解决方案。我们在R包pema（用于惩罚性Meta分析）和独立统计程序JASP中提供了免费的开源软件实现。一个应用示例展示了R包的使用。
