A researcher collecting data from a randomized controlled trial (RCT) often has access to an auxiliary observational dataset that may be confounded or otherwise biased for estimating causal effects. Common modeling assumptions impose restrictions on the outcome mean function - the conditional expectation of the outcome of interest given observed covariates - in the two datasets. Running examples from the literature include settings where the observational dataset is subject to outcome-mediated selection bias or to confounding bias taking an assumed parametric form. We propose a succinct framework to derive the efficient influence function for any identifiable pathwise differentiable estimand under a general class of restrictions on the outcome mean function. This uncovers surprising results that with homoskedastic outcomes and a constant propensity score in the RCT, even strong parametric assumptions cannot improve the semiparametric lower bound for estimating various average treatment effects. We then leverage double machine learning to construct a one-step estimator that achieves the semiparametric efficiency bound even in cases when the outcome mean function and other nuisance parameters are estimated nonparametrically. The goal is to empower a researcher with custom, previously unstudied modeling restrictions on the outcome mean function to systematically construct causal estimators that maximially leverage their assumptions for variance reduction. We demonstrate the finite sample precision gains of our estimator over existing approaches in extensions of various numerical studies and data examples from the literature.

翻译：研究者从随机对照试验(RCT)收集数据时，常可获得辅助性观测数据集，但该数据集可能存在混杂偏倚或其它导致因果效应估计偏差的问题。常见的建模假设会对两个数据集中的结果均值函数——即给定观测协变量时感兴趣结果的条件期望——施加约束。文献中的典型案例如下：观测数据集受到结果中介选择偏倚的影响，或存在假定参数形式的混杂偏倚。我们提出了一个简洁框架，用于在结果均值函数的一般约束类别下，推导任何可识别路径可微分估计量的高效影响函数。这揭示了令人惊讶的结果：在结果同方差且RCT中倾向得分恒定的条件下，即使采用强参数假设也无法改进估计各类平均处理效应的半参数下界。随后，我们利用双重机器学习构建了一步估计量，即使在结果均值函数和其他干扰参数通过非参数方式估计的情况下，该估计量仍能达到半参数效率界。本研究旨在使研究者能够针对结果均值函数定制先前未被研究的建模约束，从而系统化构建能最大限度利用假设以实现方差缩减的因果估计量。通过对文献中多种数值研究和数据案例的扩展分析，我们证明了所提估计量相较于现有方法在有限样本精度上的提升。