XT-REM: A Two-Component Model for Meta-Analysis of Extreme Event Proportions

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.