In this paper, we introduce a novel model for the meta-analysis of proportions that integrates the standard random-effects model (REM) with an extreme value theory (EVT)-based component. The proposed model, named XT-REM (Extreme-Tail Random Effects Model), extends the classical REM framework by explicitly accounting for extreme proportions through a partial segmentation of the study set based on a predefined threshold. While the majority of proportions are modeled using REM, proportions exceeding the threshold are analyzed using the Generalized Pareto Distribution (GPD). This formulation enables a dual interpretation of meta-analytic results, providing both an aggregate estimate for the central bulk of studies and a separate characterization of tail behavior. The XT-REM framework accommodates heteroskedastic variance structures inherent to proportion data, while preserving identifiability and consistency. Using real-world data on immunotherapy-related adverse events, together with simulation studies calibrated to empirical settings, we demonstrate that XT-REM yields a comparable central estimate while enabling a more explicit assessment of tail behavior, including high-percentile extreme proportions. Compared with the classical REM, XT-REM achieves higher log-likelihood values and lower AIC, in the considered scenarios, indicating a better fit within this modeling framework. In summary, XT-REM offers a theoretically grounded and practically useful extension of random-effects meta-analysis, with potential relevance to clinical contexts in which extreme event rates carry important implications for risk assessment.

翻译：本文提出了一种用于比例元分析的新模型，该模型将标准随机效应模型与基于极值理论的分量相结合。所提出的模型名为XT-REM（极尾随机效应模型），通过基于预定义阈值对研究集进行部分分割，明确考虑极端比例，从而扩展了经典REM框架。多数比例采用REM建模，而超过阈值的比例则使用广义帕累托分布进行分析。该公式实现了元分析结果的双重解释，既提供研究中心主体部分的聚合估计，又提供尾部行为的独立特征。XT-REM框架能够适应比例数据固有的异方差方差结构，同时保持可识别性和一致性。利用免疫治疗相关不良事件的真实数据，以及根据经验设置校准的模拟研究，我们证明XT-REM在提供可比的中心估计的同时，能够更明确地评估尾部行为，包括高百分位极端比例。与经典REM相比，在考虑的场景下，XT-REM实现了更高的对数似然值和更低的AIC，表明该建模框架内拟合效果更优。总之，XT-REM为随机效应元分析提供了理论扎实且实用的扩展，在极端事件发生率对风险评估具有重要影响的临床背景下具有潜在适用性。