This manuscript presents a novel Bayesian varying coefficient quantile regression (BVCQR) model designed to assess the longitudinal effects of chemical exposure mixtures on children's neurodevelopment. Recognizing the complexity and high-dimensionality of environmental exposures, the proposed approach addresses critical gaps in existing research by offering a method that can manage the sparsity of data and provide interpretable results. The proposed BVCQR model estimates the effects of mixtures on neurodevelopmental outcomes at specific ages, leveraging a horseshoe prior for sparsity and utilizing a Bayesian method for uncertainty quantification. Our simulations demonstrate the model's robustness and effectiveness in handling high-dimensional data, offering significant improvements over traditional models. The model's application to the Health Outcomes and Measures of the Environment (HOME) Study further illustrates its utility in identifying significant chemical exposures affecting children's growth and development. The findings underscore the potential of BVCQR in environmental health research, providing a sophisticated tool for analyzing the longitudinal impact of complex chemical mixtures, with implications for future studies aimed at understanding and mitigating environmental risks to child health.

翻译：本文提出了一种新颖的贝叶斯变系数分位数回归（BVCQR）模型，旨在评估化学暴露混合物对儿童神经发育的纵向效应。针对环境暴露的复杂性和高维性特征，该方法通过处理数据稀疏性并提供可解释结果，填补了现有研究的空白。所提出的BVCQR模型利用马蹄先验处理稀疏性，并结合贝叶斯方法进行不确定性量化，能够估计特定年龄段混合物对神经发育结果的影响。模拟实验证明了该模型在处理高维数据时的稳健性和有效性，相较于传统模型具有显著改进。将该模型应用于健康结果与环境测量（HOME）研究，进一步展示了其在识别影响儿童生长发育的关键化学暴露因素方面的实用价值。研究结果突出了BVCQR在环境健康研究中的潜力，为分析复杂化学混合物的纵向影响提供了精密工具，对旨在理解和降低环境因素对儿童健康风险的未来研究具有重要启示。