Unmeasured, spatially structured factors can confound associations between spatial environmental exposures and health outcomes. Adding flexible splines to a regression model is a simple approach for spatial confounding adjustment, but the spline degrees of freedom do not provide an easily interpretable spatial scale. We describe a method for quantifying the extent of spatial confounding adjustment in terms of the Euclidean distance at which variation is removed. We develop this approach for confounding adjustment with splines and using Fourier and wavelet filtering. We demonstrate differences in the spatial scales that these bases can represent and provide a comparison of methods for selecting the amount of confounding adjustment. We find the best performance for selecting the amount of adjustment by using an information criterion evaluated on an outcome model without exposure. We apply this method to spatial adjustment in an analysis of fine particulate matter and blood pressure in a cohort of US women.

中文翻译：

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选择尺度以进行空间混淆调整

无法衡量的，空间结构化的因素会混淆空间环境暴露与健康结果之间的关联。在回归模型中添加灵活的样条曲线是进行空间混杂调整的简单方法，但是样条曲线的自由度无法提供易于解释的空间比例。我们描述了一种方法，该方法可以根据变化被消除的欧几里得距离来量化空间混杂调整的程度。我们开发了这种方法，用于混淆样条曲线的调整以及使用傅立叶和小波滤波。我们证明了这些基础可以代表的空间尺度差异，并提供了选择混淆调整量的方法的比较。我们通过使用在没有暴露的结果模型上评估的信息标准来找到选择调整量的最佳性能。我们将这一方法应用于空间调整，以分析美国女性队列中的细颗粒物和血压。