Varying‐coefficients for regional quantile via KNN‐based LASSO with applications to health outcome study

Health outcomes, such as body mass index and cholesterol levels, are known to be dependent on age and exhibit varying effects with their associated risk factors. In this paper, we propose a novel framework for dynamic modeling of the associations between health outcomes and risk factors using varying-coefficients (VC) regional quantile regression via K-nearest neighbors (KNN) fused Lasso, which captures the time-varying effects of age. The proposed method has strong theoretical properties, including a tight estimation error bound and the ability to detect exact clustered patterns under certain regularity conditions. To efficiently solve the resulting optimization problem, we develop an alternating direction method of multipliers (ADMM) algorithm. Our empirical results demonstrate the efficacy of the proposed method in capturing the complex age-dependent associations between health outcomes and their risk factors.