用于选择条件仪表组的图形工具

IF 2.4 2区 数学 Q2 BIOLOGY
Biometrika Pub Date : 2023-11-03 DOI:10.1093/biomet/asad066
Henckel, Leonard, Buttenschön, Martin, Maathuis, Marloes H.
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引用次数: 0

摘要

我们考虑使用条件工具集在未测量的混杂存在下对总因果效应的有效估计。具体地说,我们考虑了与已知无环有向混合图相容的具有相关误差的线性结构方程模型的两阶段最小二乘估计。为了为我们的结果奠定基础,我们描述了一类线性有效的条件工具集,这些工具集对目标总效应产生一致的两阶段最小二乘估计,并为这些估计量导出了一个新的渐近方差公式。根据这些结果,我们提供了三种图形工具来选择更有效的线性有效条件工具集。首先,对于某些线性有效条件工具集对,一个图形准则确定两个相应的估计量中哪一个具有较小的渐近方差。其次,一种贪婪地添加协变量的算法,这些协变量可以减少给定线性有效条件工具集的渐近方差。第三,一个线性有效的条件工具集,其对应的估计量具有最小的渐近方差,可以用图形准则来保证。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Graphical tools for selecting conditional instrumental sets
Summary We consider the efficient estimation of total causal effects in the presence of unmeasured confounding using conditional instrumental sets. Specifically, we consider the two-stage least squares estimator in the setting of a linear structural equation model with correlated errors that is compatible with a known acyclic directed mixed graph. To set the stage for our results, we characterize the class of linearly valid conditional instrumental sets that yield consistent two-stage least squares estimators for the target total effect and derive a new asymptotic variance formula for these estimators. Equipped with these results, we provide three graphical tools for selecting more efficient linearly valid conditional instrumental sets. First, a graphical criterion that for certain pairs of linearly valid conditional instrumental sets identifies which of the two corresponding estimators has the smaller asymptotic variance. Second, an algorithm that greedily adds covariates that reduce the asymptotic variance to a given linearly valid conditional instrumental set. Third, a linearly valid conditional instrumental set for which the corresponding estimator has the smallest asymptotic variance that can be ensured with a graphical criterion.
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来源期刊
Biometrika
Biometrika 生物-生物学
CiteScore
5.50
自引率
3.70%
发文量
56
审稿时长
6-12 weeks
期刊介绍: Biometrika is primarily a journal of statistics in which emphasis is placed on papers containing original theoretical contributions of direct or potential value in applications. From time to time, papers in bordering fields are also published.
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