Statistics Department, Colorado State University, 1877 Campus Delivery, Fort Collins, CO, USA 80523.
Biostatistics. 2022 Jul 18;23(3):754-771. doi: 10.1093/biostatistics/kxaa051.
In studies of maternal exposure to air pollution, a children's health outcome is regressed on exposures observed during pregnancy. The distributed lag nonlinear model (DLNM) is a statistical method commonly implemented to estimate an exposure-time-response function when it is postulated the exposure effect is nonlinear. Previous implementations of the DLNM estimate an exposure-time-response surface parameterized with a bivariate basis expansion. However, basis functions such as splines assume smoothness across the entire exposure-time-response surface, which may be unrealistic in settings where the exposure is associated with the outcome only in a specific time window. We propose a framework for estimating the DLNM based on Bayesian additive regression trees. Our method operates using a set of regression trees that each assume piecewise constant relationships across the exposure-time space. In a simulation, we show that our model outperforms spline-based models when the exposure-time surface is not smooth, while both methods perform similarly in settings where the true surface is smooth. Importantly, the proposed approach is lower variance and more precisely identifies critical windows during which exposure is associated with a future health outcome. We apply our method to estimate the association between maternal exposures to PM$_{2.5}$ and birth weight in a Colorado, USA birth cohort.
在研究母亲暴露于空气污染的情况时，会将儿童健康结果回归到怀孕期间观察到的暴露情况。分布式滞后非线性模型（DLNM）是一种常用的统计方法，用于估计暴露-时间-反应函数，当假设暴露效应是非线性时。DLNM 的先前实现使用双变量基扩展参数化的暴露-时间-反应曲面进行估计。然而，样条等基函数假设整个暴露-时间-反应表面是平滑的，这在暴露仅与特定时间窗口中的结果相关的情况下可能不切实际。我们提出了一种基于贝叶斯加法回归树的估计 DLNM 的框架。我们的方法使用一组回归树进行操作，每个回归树都假设在暴露-时间空间中存在分段常数关系。在模拟中，我们表明，当暴露-时间表面不光滑时，我们的模型优于基于样条的模型，而在真实表面光滑的情况下，两种方法的性能相似。重要的是，所提出的方法方差更低，并且更准确地确定了暴露与未来健康结果相关的关键窗口。我们将我们的方法应用于估计美国科罗拉多州出生队列中母亲暴露于 PM$_{2.5}$与出生体重之间的关联。
