A Simulation-Based Evaluation of the DR-GEE Approach Based on Flexible Cluster-Size Weighting Under Hybrid Informative Cluster Size Structures

This study evaluates a DR-GEE approach based on Doubly Robust Generalized Estimating Equations for marginal inference under a hybrid informative cluster size structure. Hybrid informative cluster size refers to situations where cluster size can be related to both the marginal response variable and the distribution of covariates associated with the response. The proposed approach aims to achieve a cluster-balanced marginal estimator designed to mitigate the excessive influence of cluster sizes. To this end, the method combines a flexible cluster-size weighting component, defined by the α adjustment parameter, with an augmentation term derived from the study’s outcome model. Thus, both the direct cluster size–outcome relationship and the imbalance in the distribution of covariates are taken into account. A comprehensive Monte Carlo simulation evaluated performance under varying informativeness levels (γ = 0.1, 0.5, 1.0) and average cluster sizes (λ = 3, 5, 8). DR-GEE was compared with standard GEE, CWGEE, WCR, and DWGEE across different tuning parameters (α = 0.25, 0.50, 1.0). The results show that DR-GEE with α = 1 generally achieved the most favorable performance under hybrid ICS conditions. For example, when γ = 1 and λ = 5, GEE exhibited substantial bias (0.538) and high RMSE (0.566), whereas DR-GEE (α = 1) markedly reduced bias (0.076) and RMSE (0.224). Unlike CWGEE and DWGEE, which address only one dimension of informativeness, DR-GEE balances both cluster size–outcome dependence and covariate information.