Automatic Variable Selection for Longitudinal Quantile Regression With Application to Alzheimer's Disease Progression

Modern biomedical research increasingly relies on longitudinal studies with repeated measurements and complex within‐subject dependence. In this paper, we develop a new framework for automatic variable selection in longitudinal quantile regression, motivated in part by applications to Alzheimer's disease research. Our approach combines the quadratic inference function (QIF) methodology with smooth‐threshold estimating equations (SEEs) to accommodate within‐subject correlation while enabling computationally efficient estimation and automatic variable selection in settings where the number of covariates may diverge. We establish variable selection consistency of the proposed method and show that the Bayesian information criterion can be used to select tuning parameters in a principled manner. Simulation studies demonstrate strong performance in both estimation accuracy and selection reliability. Finally, we apply the proposed procedure to data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), identifying biomarkers and risk factors associated with extreme cognitive decline.