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

Jovana Dedeić, Jelena Ivetić, Srđan Milićević, Katarina Vidojević, Marija Delić

Abstract

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.

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

Abstract

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.
Paper Structure (19 sections, 29 equations, 5 figures, 4 tables)

This paper contains 19 sections, 29 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Random-Effects Model (REM)
  4. Extreme Value Theory
  5. Novel Modeling Framework XT-REM
  6. Model Formulation
  7. Parameter Estimation
  8. Identifiability of the model
  9. Consistency of the maximum likelihood estimators
  10. Simulation Study Design
  11. Simulation Design
  12. Simulation Results
  13. Additional Simulation Scenario
  14. Real Data Study
  15. Data Description
  16. ...and 4 more sections

Figures (5)

  • Figure 1: Average AIC values and aggregated proportion estimates obtained across simulation scenarios with increasing percentages of extreme studies. The left panel presents the mean AIC values for the REM and XT-REM models, while the right panel shows the estimated aggregated proportions. The dashed horizontal line indicates the true proportion used in the simulation.
  • Figure 2: Distribution of aggregated proportion estimates across Monte Carlo replications. The dashed horizontal line indicates the true proportion used in the simulation. The XT-REM model produces estimates that are more concentrated around the true value, whereas the classical REM model exhibits larger variability and systematic upward bias.
  • Figure 3: Separation of central and extreme observations within the XT-REM framework. Each point represents the observed proportion in a simulated study. Observations below the threshold $u$ are modeled using the REM component, whereas observations exceeding the threshold are treated as extreme values and modeled using the EVT component. The dotted line indicates the REM estimate of the aggregated proportion, and the dash--dot line represents the estimated $99\%$ EVT quantile describing the upper tail behavior.
  • Figure 4: Distribution of observed pneumonitis proportions across studies.
  • Figure 5: Fitted GPD for exceedances of pneumonitis proportions above the selected threshold. The histogram shows observed exceedances and the curve represents the fitted GPD density.