  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 build on the work of Franks et al.
(2019)and Robins (2000) by specifying non-identified sensitivity parameters
that govern a contrast between the conditional (on measured covariates)
distributions of the outcome under treatment (control) between treated and
untreated individuals. 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.
