On efficient adjustment in causal graphs
On efficient adjustment in causal graphs
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DOI：
10.3929/ethz-b-000459196
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发表时间：
2020-02
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影响因子：
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通讯作者：
Jan-Jelle Witte;Leonard Henckel;M. Maathuis;V. Didelez
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文献类型：
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作者：
Jan-Jelle Witte;Leonard Henckel;M. Maathuis;V. Didelez
我们考虑通过协变量调整来估计观测数据的总因果效应。理想情况下，调整集是根据给定的因果图选择的，反映了对潜在因果结构的了解。然而，有效的调整集并不是唯一的。最近的研究引入了一个“最优”有效调整集（o集）的图形准则。对于给定的图，与某些参数和非参数模型中的其他调整集相比，o集的调整产生最小的渐近方差。本文给出了关于o集的三个新结果。首先，我们给出了一个新颖的、更直观的图形表征：我们证明了o集是一个合适的潜在投影图（我们称之为禁止投影）中结果节点的父集。一个重要的特性是，禁止投影通过协变量调整保留了与总因果效应估计相关的所有信息，使其本身成为一个有用的方法工具。其次，我们将现有的IDA算法扩展为使用o集，并论证了该算法仍然是半局部的。这是在r包程序中实现的。第三，我们提出了一些假设，在这些假设下，o集可以被视为流行的非图形变量选择算法（如逐步向后选择）的目标集。
We consider estimation of a total causal effect from observational data via covariate adjustment. Ideally, adjustment sets are selected based on a given causal graph, reflecting knowledge of the underlying causal structure. Valid adjustment sets are, however, not unique. Recent research has introduced a graphical criterion for an 'optimal' valid adjustment set (O-set). For a given graph, adjustment by the O-set yields the smallest asymptotic variance compared to other adjustment sets in certain parametric and non-parametric models. In this paper, we provide three new results on the O-set. First, we give a novel, more intuitive graphical characterisation: We show that the O-set is the parent set of the outcome node(s) in a suitable latent projection graph, which we call the forbidden projection. An important property is that the forbidden projection preserves all information relevant to total causal effect estimation via covariate adjustment, making it a useful methodological tool in its own right. Second, we extend the existing IDA algorithm to use the O-set, and argue that the algorithm remains semi-local. This is implemented in the R-package pcalg. Third, we present assumptions under which the O-set can be viewed as the target set of popular non-graphical variable selection algorithms such as stepwise backward selection.