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. (2000), Franks et al. (2020) and Zhou and Yao (2023. 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 bias-corrected 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 root-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.

翻译：从观察性数据确立因果关系往往依赖于不可验证的假设。了解基于非实验研究得出的结论对潜在未测量混杂因素的稳健性程度至关重要。本文以平均因果效应（ACE）作为推断目标，推广了Robins等人（2000）、Franks等人（2020）以及Zhou与Yao（2023）提出的敏感性分析方法。我们运用半参数理论推导了固定敏感性参数下ACE的非参数有效影响函数，并利用该影响函数构建ACE的一步偏差校正估计量。该估计量依赖于观测数据分布的半参数模型——关键在于这些模型未对敏感性分析参数的取值施加任何约束。我们建立了确保估计量具有根号n渐近性的充分条件，并应用该方法评估孕期吸烟对新生儿出生体重的因果效应，同时通过模拟研究验证了估计流程的性能。