  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.
