🤖 AI Summary
Unmeasured confounding frequently biases causal inference in observational studies, while existing sensitivity analyses often rely on strong parametric modeling assumptions. To assess the robustness of the average causal effect (ACE), this paper proposes the first sensitivity analysis framework grounded in semiparametric efficient influence functions: it constructs a model-free, truncated first-order estimator that avoids explicit parametric modeling of sensitivity parameters. Theoretically, the estimator is shown to be √n-consistent and semiparametrically efficient. Simulation studies demonstrate its superior performance over mainstream methods under diverse confounding structures. An empirical application to the effect of maternal smoking during pregnancy on newborn birth weight validates its practical robustness. The core contribution lies in systematically integrating semiparametric efficiency theory into sensitivity analysis—yielding a model-agnostic, statistically efficient, and interpretable quantification of causal robustness.
📝 Abstract
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.
