The DerSimonian-Laird (DL) weighted average method has been widely used for estimation of a pooled effect size from an aggregated data meta-analysis study. It is mainly criticized for its underestimation of the standard error of the pooled effect size in the presence of heterogeneous study effect sizes. The uncertainty in the estimation of the between-study variance is not accounted for in the calculation of this standard error. Due to this negative property, many alternative estimation approaches have been proposed in literature. One approach was developed by Hardy and Thompson (HT), who implemented a profile likelihood approach instead of the moment-based approach of DL. Others have further extended the likelihood approach and proposed higher-order likelihood inferences (e.g., Bartlett-type corrections). Likelihood-based methods better address the uncertainty in estimating the between-study variance than the DL method, but all these methods assume that the within-study standard deviations are known and equal to the observed standard error of the study effect sizes. Here we treat the observed standard errors as estimators for the within-study variability and we propose a bivariate likelihood approach that jointly estimates the pooled effect size, the between-study variance, and the potentially heteroscedastic within-study variances. We study the performance of the proposed method by means of simulation, and compare it to DL, HT, and the higher-order likelihood methods. Our proposed approach appears to be less sensitive to the number of studies, and less biased in case of heteroscedasticity.
翻译:DerSimonian-Laird(DL)加权平均法被广泛用于估算综合数据元分析研究的综合数据元分析研究得出的集合效应规模。主要批评该方法在差异研究影响规模存在的情况下低估了集合效应规模的标准误差(例如,Bartlett-类型更正)。在计算这一标准错误时,没有考虑到研究差异的不确定性。由于这一负面属性,文献中提出了许多替代估算方法。Hardy和Thompson(HT)开发了一种方法,采用了剖面可能性方法,而不是DL基于时间的方法。其他人进一步扩展了可能性方法,并提出了更高排序的可能性推断(例如,Bartlett-类型更正 ) 。基于可能性的方法更好地解决了估算研究差异的不确定性,而不是DL方法,但所有这些方法都假定研究内部标准偏差是已知的,与所观察到的研究影响规模的标准误差相等。在这里,我们把观察到的标准差作为内部研究变异性的估测度,我们建议采用比差率方法,我们提议采用联合估算了差异分析方法,我们的拟议变异性研究方法,我们的拟议性变差方法与可能采用。