QIC’s Type I Error Rate for Longitudinal Data Models with a Binary Response and Minimization Strategies

Proper specification of the marginal mean structure is necessary for effective Generalized Estimating Equations (GEE) estimation for longitudinal data and hence requires careful selection of the constituent covariates. The Quasi-Likelihood Information Criterion (QIC) is widely used to select such covariates; thus, its performance in picking the correct ones is critical. This study investigates QIC’s type I error rates under various GEE settings in an effort to extend the work of Pan (2001), who highlighted QIC’s utility in variable selection, and complement the observations by Wang et al. (2015), who addressed its limitations in selecting correlation structures. The study's theoretical analysis and simulation results found that QIC often identified important predictors but consistently included irrelevant ones, leading to high overfitting rates. To overcome these limitations, the study proposed , and QIC-SCAD hybrid methods and compared their performances based on their sensitivity, specificity, predictive accuracy, F1-score, and execution time, in addition to an ablation variant SCAD-QIC. The results showed that the hybrid methods greatly improved the predictive accuracy of the final model. For example, when n=500 and p=10, and SCAD-QIC achieved accuracies of 100% compared to 60% for QIC. The methods equally registered at least 90% accuracy when the covariates were increased to 20 and significantly improved computational efficiency, besides effectively removing irrelevant variables. The methods are therefore established to be ideal alternatives for variable selection in high-dimensional longitudinal data, particularly when it is necessary to balance accuracy, precision, and computational efficiency.