Analytic Bounds on Causal Risk Differences in Directed Acyclic Graphs Involving Three Observed Binary Variables.
Analytic Bounds on Causal Risk Differences in Directed Acyclic Graphs Involving Three Observed Binary Variables.
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DOI：
10.1016/j.jspi.2009.03.024
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发表时间：
2009-10-01
影响因子：
0.9
通讯作者：
MacLehose, Richard F.
中科院分区：
文献类型：
--
作者：
Kaufman, Sol;Kaufman, Jay S.;MacLehose, Richard F.
关键词：
本文采用线性规划方法，将因果风险差（RDC）作为目标函数，并给出了RDC在任何一组潜在响应类型分布的线性约束下所能达到的最小值和最大值。我们考虑了涉及二元暴露X、协变量Z和结果y的两种情况。在第一种情况下，Z不受X的影响，并且是X对y的因果效应的潜在混杂因素。在第二种情况下，Z受到X的影响，并且在X和y之间的因果路径中处于中间位置。对于每种情况，我们考虑了与相关有向无环图（DAG）中弧的存在或不存在相对应的各种线性约束，单调性假设，以及加性尺度相互作用的存在与否。当Z是一个潜在的效应测量修饰符时，我们还估计了Z层特定的边界，当Z受X影响时，我们估计了受控和自然直接效应的边界。在没有任何来自背景知识的额外约束的情况下，我们重复了众所周知的RDc边界：−Pr(Y≠X)≤RDc≤Pr（Y=X）。这些边界具有单位宽度，但可以通过基于背景知识的假设来缩小。我们提供并比较了两种情况下各种假设组合的边界和边界宽度，并将这些边界应用于两项研究的实际数据。
We apply a linear programming approach which uses the causal risk difference (RDC) as the objective function and provides minimum and maximum values that RDC can achieve under any set of linear constraints on the potential response type distribution. We consider two scenarios involving binary exposure X, covariate Z and outcome Y. In the first, Z is not affected by X, and is a potential confounder of the causal effect of X on Y. In the second, Z is affected by X and intermediate in the causal pathway between X and Y. For each scenario we consider various linear constraints corresponding to the presence or absence of arcs in the associated directed acyclic graph (DAG), monotonicity assumptions, and presence or absence of additive-scale interactions. We also estimate Z-stratum-specific bounds when Z is a potential effect measure modifier and bounds for both controlled and natural direct effects when Z is affected by X. In the absence of any additional constraints deriving from background knowledge, the well-known bounds on RDc are duplicated: −Pr(Y≠X) ≤ RDC ≤ Pr(Y=X). These bounds have unit width, but can be narrowed by background knowledge-based assumptions. We provide and compare bounds and bound widths for various combinations of assumptions in the two scenarios and apply these bounds to real data from two studies.
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