The identification theory for causal effects in directed acyclic graphs (DAGs) with hidden variables is well established, but methods for estimating and inferring functionals that extend beyond the g-formula remain underdeveloped. Previous studies have introduced semiparametric estimators for such functionals in a broad class of DAGs with hidden variables. While these estimators exhibit desirable statistical properties such as double robustness in certain cases, they also face significant limitations. Notably, they encounter substantial computational challenges, particularly involving density estimation and numerical integration for continuous variables, and their estimates may fall outside the parameter space of the target estimand. Additionally, the asymptotic properties of these estimators is underexplored, especially when integrating flexible statistical and machine learning models for nuisance functional estimations. This paper addresses these challenges by introducing novel one-step corrected plug-in and targeted minimum loss-based estimators of causal effects for a class of hidden variable DAGs that go beyond classical back-door and front-door criteria (known as the treatment primal fixability criterion in prior literature). These estimators leverage data-adaptive machine learning algorithms to minimize modeling assumptions while ensuring key statistical properties including double robustness, efficiency, boundedness within the target parameter space, and asymptotic linearity under $L^2(P)$-rate conditions for nuisance functional estimates that yield root-n consistent causal effect estimates. To ensure our estimation methods are accessible in practice, we provide the flexCausal package in R.

翻译：在有向无环图（DAG）中，含隐变量的因果效应识别理论已较为完善，但针对超越g-公式的泛函的估计与推断方法仍显不足。先前的研究已针对一大类含隐变量的DAG引入了此类泛函的半参数估计量。尽管这些估计量在某些情况下展现出诸如双重稳健性等理想的统计性质，但它们也面临显著的局限性。值得注意的是，它们存在巨大的计算挑战，特别是涉及连续变量的密度估计与数值积分，且其估计值可能落在目标估计量的参数空间之外。此外，这些估计量的渐近性质尚未得到充分探索，尤其是在使用灵活的统计与机器学习模型进行干扰泛函估计时。本文通过引入一类超越经典后门与前门准则（在先前文献中称为处理原始可固定性准则）的含隐变量DAG的因果效应的新型一步校正插件估计量及基于目标最小损失的估计量，以应对这些挑战。这些估计量利用数据自适应的机器学习算法，以最小化建模假设，同时确保关键的统计性质，包括双重稳健性、有效性、在目标参数空间内的有界性，以及在干扰泛函估计满足$L^2(P)$-速率条件（该条件可产生根号n一致的因果效应估计）下的渐近线性。为确保我们的估计方法在实践中易于使用，我们提供了R语言软件包flexCausal。