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.

翻译：已知健康结局（如体重指数和胆固醇水平）随年龄变化，且其与相关风险因素的关联效应亦呈动态变化。本文提出一种新型动态建模框架，通过K近邻融合LASSO实现变系数区域分位数回归，以刻画健康结局与风险因素间随年龄变化的时变关联。该方法具备强理论性质，包括紧致的估计误差界以及在特定正则条件下检测精确聚类模式的能力。为高效求解该优化问题，我们开发了交替方向乘子法算法。实证结果表明，所提方法能有效捕捉健康结局与其风险因素间复杂的年龄依赖关联。