Chung Yeojin, Rabe-Hesketh Sophia, Choi In-Hee
School of Business Administration, Kookmin University, Seoul, Korea.
Stat Med. 2013 Oct 15;32(23):4071-89. doi: 10.1002/sim.5821. Epub 2013 May 13.
Fixed-effects meta-analysis has been criticized because the assumption of homogeneity is often unrealistic and can result in underestimation of parameter uncertainty. Random-effects meta-analysis and meta-regression are therefore typically used to accommodate explained and unexplained between-study variability. However, it is not unusual to obtain a boundary estimate of zero for the (residual) between-study standard deviation, resulting in fixed-effects estimates of the other parameters and their standard errors. To avoid such boundary estimates, we suggest using Bayes modal (BM) estimation with a gamma prior on the between-study standard deviation. When no prior information is available regarding the magnitude of the between-study standard deviation, a weakly informative default prior can be used (with shape parameter 2 and rate parameter close to 0) that produces positive estimates but does not overrule the data, leading to only a small decrease in the log likelihood from its maximum. We review the most commonly used estimation methods for meta-analysis and meta-regression including classical and Bayesian methods and apply these methods, as well as our BM estimator, to real datasets. We then perform simulations to compare BM estimation with the other methods and find that BM estimation performs well by (i) avoiding boundary estimates; (ii) having smaller root mean squared error for the between-study standard deviation; and (iii) better coverage for the overall effects than the other methods when the true model has at least a small or moderate amount of unexplained heterogeneity.
固定效应荟萃分析受到批评，因为同质性假设往往不现实，可能导致参数不确定性的低估。因此，随机效应荟萃分析和荟萃回归通常用于处理研究间已解释和未解释的变异性。然而，研究间（残差）标准差的边界估计为零的情况并不少见，这会导致其他参数的固定效应估计及其标准误。为避免此类边界估计，我们建议对研究间标准差使用具有伽马先验的贝叶斯模态（BM）估计。当没有关于研究间标准差大小的先验信息时，可以使用弱信息默认先验（形状参数为2，速率参数接近0），该先验会产生正估计，但不会否决数据，只会使对数似然从其最大值略有下降。我们回顾了荟萃分析和荟萃回归中最常用的估计方法，包括经典方法和贝叶斯方法，并将这些方法以及我们的BM估计器应用于实际数据集。然后，我们进行模拟，将BM估计与其他方法进行比较，发现BM估计表现良好，具体表现为：（i）避免边界估计；（ii）研究间标准差的均方根误差较小；（iii）当真实模型至少有少量或中等程度的未解释异质性时，总体效应的覆盖范围比其他方法更好。
