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.
翻译:调整共变值是一种既定的方法,用以估计接触变量对利益结果的总因果关系。根据所研究机制的因果结构,可能存在不同的调整组,从理论角度看同样有效,导致相同的因果效应。然而,在实践上,根据有限数据,不同组的估算器可能显示不同的精确度。为了调查这种变异的程度,我们考虑了二进制数据三个节点上最简单的非三进制非线性反线模型。我们明确计算并比较了两种可能不同的因果估测器的差异。此外,我们超越了主要顺序的假设,表明存在一些参数制度,在这种参数下,与非现时最佳差异有关的设定取决于边际系数,而一般因果模型最近的先导顺序发展没有抓住这一结果。作为实际结果,调整后确定选择需要考虑到变量与样本大小的关系的相对规模,不能依靠纯粹的图形标准。