Random effects meta-analysis is widely used for synthesizing studies under the assumption that underlying effects come from a normal distribution. However, under certain conditions the use of alternative distributions might be more appropriate. We conducted a systematic review to identify articles introducing alternative meta-analysis models assuming non-normal between-study distributions. We identified 27 eligible articles suggesting 24 alternative meta-analysis models based on long-tail and skewed distributions, on mixtures of distributions, and on Dirichlet process priors. Subsequently, we performed a simulation study to evaluate the performance of these models and to compare them with the standard normal model. We considered 22 scenarios varying the amount of between-study variance, the shape of the true distribution, and the number of included studies. We compared 15 models implemented in the Frequentist or in the Bayesian framework. We found small differences with respect to bias between the different models but larger differences in the level of coverage probability. In scenarios with large between-study variance, all models were substantially biased in the estimation of the mean treatment effect. This implies that focusing only on the mean treatment effect of random effects meta-analysis can be misleading when substantial heterogeneity is suspected or outliers are present.

翻译：随机效应元分析被广泛应用于综合研究，其假设基础效应来自正态分布。然而，在某些条件下，使用替代分布可能更为合适。我们进行了一项系统综述，以识别引入假设研究间分布为非正态的替代元分析模型的文章。我们确定了27篇符合条件的文章，提出了24种基于长尾与偏态分布、混合分布以及狄利克雷过程先验的替代元分析模型。随后，我们开展了一项模拟研究，以评估这些模型的性能，并将其与标准正态模型进行比较。我们考虑了22种情景，这些情景在研究间方差量、真实分布形态以及纳入研究数量方面各不相同。我们比较了在频率主义或贝叶斯框架下实现的15种模型。我们发现不同模型在偏差方面差异较小，但在覆盖概率水平上存在较大差异。在研究间方差较大的情景中，所有模型在估计平均处理效应时均存在显著偏差。这意味着，当怀疑存在显著异质性或存在异常值时，仅关注随机效应元分析的平均处理效应可能会产生误导。