Regularized principal spline functions to mitigate spatial confounding.

IF 1.4 4区 数学 Q3 BIOLOGY
Biometrics Pub Date : 2025-04-02 DOI:10.1093/biomtc/ujaf076
Carlo Zaccardi, Pasquale Valentini, Luigi Ippoliti, Alexandra M Schmidt
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引用次数: 0

Abstract

This paper proposes a new approach to address the problem of unmeasured confounding in spatial designs. Spatial confounding occurs when some confounding variables are unobserved and not included in the model, leading to distorted inferential results about the effect of an exposure on an outcome. We show the relationship existing between the confounding bias of a non-spatial model and that of a semi-parametric model that includes a basis matrix to represent the unmeasured confounder conditional on the exposure. This relationship holds for any basis expansion; however, it is shown that using the semi-parametric approach guarantees a reduction in the confounding bias only under certain circumstances, which are related to the spatial structures of the exposure and the unmeasured confounder, the type of basis expansion utilized, and the regularization mechanism. To adjust for spatial confounding, and therefore try to recover the effect of interest, we propose a Bayesian semi-parametric regression model, where an expansion matrix of principal spline basis functions is used to approximate the unobserved factor, and spike-and-slab priors are imposed on the respective expansion coefficients in order to select the most important bases. From the results of an extensive simulation study, we conclude that our proposal is able to reduce the confounding bias more than competing approaches, and it also seems more robust to bias amplification.

正则化主样条函数以减轻空间混淆。
本文提出了一种解决空间设计中不可测量混淆问题的新方法。当一些混淆变量未被观察到且未包含在模型中时,就会发生空间混淆,从而导致有关暴露对结果影响的扭曲推断结果。我们展示了非空间模型的混杂偏差与半参数模型的混杂偏差之间存在的关系,其中包括一个基矩阵来表示未测量的混杂因素,条件是暴露。这个关系适用于任何基展开;然而,研究表明,使用半参数方法只能在某些情况下保证减少混杂偏差,这些情况与暴露和未测量混杂因素的空间结构、所使用的基展开类型和正则化机制有关。为了调整空间混淆,从而试图恢复兴趣的影响,我们提出了一个贝叶斯半参数回归模型,其中使用主样条基函数的展开矩阵来近似未观察到的因子,并对各自的扩展系数施加spike和slab先验,以选择最重要的基。从广泛的模拟研究结果中,我们得出结论,我们的建议能够比竞争方法更有效地减少混杂偏差,并且对偏差放大似乎也更稳健。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Biometrics
Biometrics 生物-生物学
CiteScore
2.70
自引率
5.30%
发文量
178
审稿时长
4-8 weeks
期刊介绍: The International Biometric Society is an international society promoting the development and application of statistical and mathematical theory and methods in the biosciences, including agriculture, biomedical science and public health, ecology, environmental sciences, forestry, and allied disciplines. The Society welcomes as members statisticians, mathematicians, biological scientists, and others devoted to interdisciplinary efforts in advancing the collection and interpretation of information in the biosciences. The Society sponsors the biennial International Biometric Conference, held in sites throughout the world; through its National Groups and Regions, it also Society sponsors regional and local meetings.
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