Meta-analysis is a key statistical tool for synthesizing clinical trial data to evaluate treatment effects, yet traditional methods like fixed and random-effects models often fail to handle heterogeneity, study-level covariates, or hierarchical structures effectively. To overcome these limitations, we developed a Bayesian hierarchical meta-analysis framework for robust parameter estimation on small samples and utilized analytical integration for efficient inference. Simulation studies indicated robust estimation of the proposed model. We applied it to the safety profiles of Oxcarbazepine (OXC) and Carbamazepine (CBZ) in epilepsy treatment. The results indicated that OXC was significantly associated with a lower risk of side effects than CBZ. The code and relevant data used in this study are openly available on GitHub at: https://github.com/xsjk/HierarchicalMetaAnalysis.

翻译：元分析是整合临床试验数据以评估治疗效果的关键统计工具，但传统方法如固定效应模型和随机效应模型在处理异质性、研究层面协变量或分层结构时往往存在局限性。为克服这些局限，我们开发了一种贝叶斯分层元分析框架，用于在样本量较小时实现稳健参数估计，并采用解析积分进行高效推断。模拟研究证明了所提出模型的稳健性。我们将该模型应用于奥卡西平（OXC）和卡马西平（CBZ）治疗癫痫的安全性特征分析。结果表明，OXC的不良反应风险显著低于CBZ。本研究所用代码及相关数据已公开发布于GitHub平台（https://github.com/xsjk/HierarchicalMetaAnalysis）。