Environmental epidemiology has traditionally examined single exposure one at a time. Advances in exposure assessment and statistical methods now enable studies of multiple exposures and their combined health impacts. Bayesian Kernel Machine Regression (BKMR) is a widely used approach to flexibly estimates joint, nonlinear effects of multiple exposures. But BMKR is computationally intensive for large datasets, as repeated kernel inversion in Markov chain Monte Carlo (MCMC) can be time-consuming and often infeasible in practice. To address this issue, we propose using supervised random Fourier basis functions to replace the Gaussian process random effects. This re-frames the kernel machine regression into a linear mixed-effect model that facilitates computationally efficient estimation and prediction. Bayesian inference is conducted using MCMC with Hamiltonian Monte Carlo algorithms. Simulation studies demonstrate that our method yields results comparable to BKMR while significantly reduces the computation time. Our approach outperforms BKMR when the exposure-response surface has stronger dependency and when using predictive process as an alternative approximation method. Finally, we applied this approach to analyze over 270,000 birth records, examining associations between multiple ambient air pollutants and birthweight in Georgia.

翻译：环境流行病学传统上每次仅考察单一暴露。暴露评估与统计方法的进步，使得研究多种暴露及其联合健康影响成为可能。贝叶斯核机器回归（BKMR）是一种广泛使用的方法，能够灵活估计多种暴露的联合非线性效应。然而，对于大型数据集，BKMR的计算量很大，因为马尔可夫链蒙特卡洛（MCMC）中重复的核矩阵求逆可能非常耗时，且在实践中往往不可行。为解决这一问题，我们提出使用有监督的随机傅里叶基函数来替代高斯过程随机效应。这将核机器回归重新表述为一个线性混合效应模型，从而有助于实现计算高效的估计与预测。贝叶斯推断使用结合哈密顿蒙特卡洛算法的MCMC进行。模拟研究表明，我们的方法得到的结果与BKMR相当，同时显著减少了计算时间。当暴露-反应曲面具有更强的依赖性，以及使用预测过程作为替代近似方法时，我们的方法优于BKMR。最后，我们将此方法应用于分析超过27万份出生记录，以考察佐治亚州多种环境空气污染物与出生体重之间的关联。