Department of Mathematics, College of Science and Arts, Najran University, Najran 55461, Saudi Arabia.
Department of Statistics, Florida State University, Tallahassee, FL 32306, USA.
Int J Environ Res Public Health. 2021 Mar 27;18(7):3492. doi: 10.3390/ijerph18073492.
Bayesian methods are an important set of tools for performing meta-analyses. They avoid some potentially unrealistic assumptions that are required by conventional frequentist methods. More importantly, meta-analysts can incorporate prior information from many sources, including experts' opinions and prior meta-analyses. Nevertheless, Bayesian methods are used less frequently than conventional frequentist methods, primarily because of the need for nontrivial statistical coding, while frequentist approaches can be implemented via many user-friendly software packages. This article aims at providing a practical review of implementations for Bayesian meta-analyses with various prior distributions. We present Bayesian methods for meta-analyses with the focus on odds ratio for binary outcomes. We summarize various commonly used prior distribution choices for the between-studies heterogeneity variance, a critical parameter in meta-analyses. They include the inverse-gamma, uniform, and half-normal distributions, as well as evidence-based informative log-normal priors. Five real-world examples are presented to illustrate their performance. We provide all of the statistical code for future use by practitioners. Under certain circumstances, Bayesian methods can produce markedly different results from those by frequentist methods, including a change in decision on statistical significance. When data information is limited, the choice of priors may have a large impact on meta-analytic results, in which case sensitivity analyses are recommended. Moreover, the algorithm for implementing Bayesian analyses may not converge for extremely sparse data; caution is needed in interpreting respective results. As such, convergence should be routinely examined. When select statistical assumptions that are made by conventional frequentist methods are violated, Bayesian methods provide a reliable alternative to perform a meta-analysis.
贝叶斯方法是进行荟萃分析的一组重要工具。它们避免了传统频率派方法所需的一些潜在不切实际的假设。更重要的是，荟萃分析人员可以从许多来源（包括专家意见和先前的荟萃分析）纳入先验信息。然而，贝叶斯方法的使用频率低于传统的频率派方法，主要是因为需要进行非平凡的统计编码，而频率派方法可以通过许多用户友好的软件包来实现。本文旨在提供对具有各种先验分布的贝叶斯荟萃分析实现的实用综述。我们介绍了荟萃分析的贝叶斯方法，重点是二分类结局的优势比。我们总结了各种常用的先验分布选择，用于研究间异质性方差，这是荟萃分析中的关键参数。它们包括逆伽马、均匀和半正态分布，以及基于证据的信息对数正态先验。提出了五个真实世界的例子来说明它们的性能。我们提供了所有的统计代码，以供将来的从业者使用。在某些情况下，贝叶斯方法可能会产生与频率派方法明显不同的结果，包括对统计显著性的决策改变。当数据信息量有限时，先验的选择可能会对荟萃分析结果产生重大影响，在这种情况下，建议进行敏感性分析。此外，实施贝叶斯分析的算法可能不会在数据极其稀疏的情况下收敛；在解释各自的结果时需要谨慎。因此，应定期检查收敛性。当传统频率派方法所做的统计假设被违反时，贝叶斯方法提供了一种可靠的替代方法来进行荟萃分析。
