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Innovative statistical method for longitudinal and hierarchical data modeling: the GMEXGBoost method.

Fariba Asadi1,2, Reza Homayounfar3,4, Yaser Mehrali5

  • 1Ferdows Faculty of Medical Sciences, Birjand University of Medical Sciences, Birjand, Iran.

BMC Medical Research Methodology
|January 7, 2026
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Summary

A new algorithm, GMEXGBoost, improves analysis of complex healthcare data by combining generalized mixed-effects models and XGBoost. It offers superior stability and accuracy for hierarchical and longitudinal datasets with strong correlations.

Keywords:
Boosted treeGeneralized linear mixed modelLongitudinal and hierarchical data

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Area of Science:

  • * Computational statistics and machine learning.
  • * Biostatistics and health data science.

Background:

  • * Exponential data growth in healthcare necessitates advanced analytical methods beyond conventional machine learning.
  • * Traditional algorithms struggle with correlated, longitudinal, and hierarchical data common in healthcare.
  • * Generalized mixed-effects models (GLMMs) and XGBoost have limitations when used independently for complex data structures.

Purpose of the Study:

  • * Introduce GMEXGBoost, a novel algorithm extending GLMMs with XGBoost's boosting framework.
  • * Develop a method that explicitly incorporates data correlations while retaining predictive power.
  • * Evaluate GMEXGBoost's performance against existing models in simulations and real-world data.

Main Methods:

  • * Developed GMEXGBoost by integrating GLMM fixed-effect estimation with XGBoost's boosting and random-effect accounting.
  • * Evaluated performance using simulations with varying effect structures and a real-world cohort study.
  • * Benchmarked against GLMM, GLMMTree, GMERF, and XGBoost using metrics like PMAD, PMCR, sensitivity, specificity, accuracy, and AUC in RStudio.

Main Results:

  • * XGBoost showed the lowest average errors in most scenarios.
  • * GMEXGBoost demonstrated superior stability and accuracy with large random-effect variances or strong correlations.
  • * GMEXGBoost outperformed other models on real-world data across key performance metrics.

Conclusions:

  • * GMEXGBoost effectively combines GLMM and XGBoost capabilities for improved performance on complex problems.
  • * The algorithm offers clear advantages for analyzing hierarchical and longitudinal datasets with strong correlations.
  • * GMEXGBoost is a valuable tool for decision-making in healthcare and other fields with structured data.