论文标题
二进制V结构的因果效应估计值的差异
The Variance of Causal Effect Estimators for Binary V-structures
论文作者
论文摘要
调整协变量是估计暴露变量对感兴趣结果的总因果效应的良好方法。根据所研究机制的因果结构，从理论角度来看，可能有不同的调整集，同样有效，从而导致相同的因果效应。但是，实际上，使用有限的数据，构建在不同集合的估计器可能会显示不同的精度。为了研究这种可变性的程度，我们考虑了三个节点上二进制数据的vstructure的最简单的非线性非线性模型。我们明确计算并比较两个可能的不同因果估计量的方差。此外，通过超越领先顺序渐近学，我们表明存在一些参数制度，其中具有渐近最佳方差的集合确实取决于边缘系数，这一结果并未被一般因果模型的最新领先顺序开发所捕获。实际上，调整集选择需要说明变量相对于样本量之间的关系的相对大小，并且不能依靠纯图形标准。
Adjusting for covariates is a well established method to estimate the total causal effect of an exposure variable on an outcome of interest. Depending on the causal structure of the mechanism under study there may be different adjustment sets, equally valid from a theoretical perspective, leading to identical causal effects. However, in practice, with finite data, estimators built on different sets may display different precision. To investigate the extent of this variability we consider the simplest non-trivial non-linear model of a v-structure on three nodes for binary data. We explicitly compute and compare the variance of the two possible different causal estimators. Further, by going beyond leading order asymptotics we show that there are parameter regimes where the set with the asymptotically optimal variance does depend on the edge coefficients, a result which is not captured by the recent leading order developments for general causal models. As a practical consequence, the adjustment set selection needs to account for the relative magnitude of the relationships between variables with respect to the sample size, and cannot rely on purely graphical criteria.
