Criteria for identifying optimal adjustment sets (i.e., yielding a consistent estimator with minimal asymptotic variance) for estimating average treatment effects in parametric and nonparametric models have recently been established. In a single treatment time point setting, it has been shown that the optimal adjustment set can be identified based on a causal directed acyclic graph alone. In a longitudinal treatment setting, previous work has established graphical rules to compare the asymptotic variance of estimators based on nested time-dependent adjustment sets. However, these rules do not always permit the identification of an optimal time-dependent adjustment set based on a causal graph alone. In this paper, we extend previous results by exploiting conditional independencies that can be read from the graph. We demonstrate theoretically and empirically that our results can yield estimators with even lower asymptotic variance than those allowed by previous results. We conjecture that our new results may even allow the identification of an optimal time-dependent adjustment set based on the causal graph and provide numerical examples supporting this conjecture.

翻译：最近，针对参数和非参数模型中估计平均处理效应的最优调整集（即能够产生具有最小渐近方差的一致估计量）的识别准则已经建立。在单次处理时间点设定下，已证明最优调整集可以仅基于因果有向无环图进行识别。在纵向处理设定中，先前研究已建立了基于嵌套时间依赖调整集的估计量渐近方差比较的图规则。然而，这些规则并不总能允许仅基于因果图识别最优时间依赖调整集。本文通过利用可从图中读取的条件独立性，扩展了先前的研究结果。我们从理论和实证上证明，我们的结果能够产生比先前结果所允许的估计量具有更低渐近方差的估计量。我们推测，我们的新结果甚至可能允许基于因果图识别最优时间依赖调整集，并提供了支持这一猜想的数值示例。