Generalized linear mixed models in epidemiological data analysis: A systematic review of methodological developments

Generalized linear mixed models (GLMMs) have become a fundamental statistical framework for analyzing hierarchical and correlated data in epidemiology and related quantitative fields. By combining non-Gaussian response distributions with random effects and structured dependence, GLMMs allow researchers to represent complex data structures arising from spatial, temporal, and multilevel processes. Over the past two decades, numerous methodological extensions have been introduced, including developments in spatial modeling, hierarchical structures, and computational inference. Despite this growth, these contributions are often presented as separate methodological advances, making it difficult to understand how they relate within the broader architecture of the GLMM framework. This study addresses this issue through a systematic review of methodological developments in GLMM-based epidemiological research. Thirty-nine studies published between 2001 and 2025 were examined to identify recurring modeling patterns and structural extensions of the GLMM framework. Based on this synthesis, a four-layer mathematical taxonomy is proposed that organizes GLMM methodology according to probabilistic specification, hierarchical structure, structured dependence, and inferential strategy. The results indicate that most innovations arise from structural modifications within these layers rather than from entirely new modeling paradigms, providing a clearer perspective on methodological diversity in the GLMM literature.