Department of Biostatistics and Bioinformatics, Emory University, Atlanta, GA 30322, United States.
Department of Statistics, Rutgers University, Piscataway, NJ 08854, United States.
Biometrics. 2024 Oct 3;80(4). doi: 10.1093/biomtc/ujae106.
Establishing cause-effect relationships from observational data often relies on untestable assumptions. It is crucial to know whether, and to what extent, the conclusions drawn from non-experimental studies are robust to potential unmeasured confounding. In this paper, we focus on the average causal effect (ACE) as our target of inference. We generalize the sensitivity analysis approach developed by Robins et al., Franks et al., and Zhou and Yao. We use semiparametric theory to derive the non-parametric efficient influence function of the ACE, for fixed sensitivity parameters. We use this influence function to construct a one-step, split sample, truncated estimator of the ACE. Our estimator depends on semiparametric models for the distribution of the observed data; importantly, these models do not impose any restrictions on the values of sensitivity analysis parameters. We establish sufficient conditions ensuring that our estimator has $\sqrt{n}$ asymptotics. We use our methodology to evaluate the causal effect of smoking during pregnancy on birth weight. We also evaluate the performance of estimation procedure in a simulation study.
从观察性数据中建立因果关系通常依赖于未经检验的假设。了解从非实验研究中得出的结论在多大程度上能够稳健地应对潜在的未测量混杂因素是至关重要的。在本文中，我们将重点关注平均因果效应 (ACE) 作为我们的推断目标。我们推广了 Robins 等人、Franks 等人以及 Zhou 和 Yao 开发的敏感性分析方法。我们使用半参数理论推导出 ACE 的固定敏感性参数的非参数有效影响函数。我们使用这个影响函数来构建 ACE 的一步、分裂样本、截断估计量。我们的估计量取决于观察数据分布的半参数模型；重要的是，这些模型对敏感性分析参数的值没有任何限制。我们确立了充分的条件，确保我们的估计量具有 $\sqrt{n}$ 的渐近性。我们使用我们的方法来评估怀孕期间吸烟对婴儿体重的因果效应。我们还在模拟研究中评估了估计程序的性能。
