  Skepticism about the assumption of no unmeasured confounding, also known as
exchangeability, is often warranted in making causal inferences from
observational data; because exchangeability hinges on an investigator's ability
to accurately measure covariates that capture all potential sources of
confounding. In practice, the most one can hope for is that covariate
measurements are at best proxies of the true underlying confounding mechanism
operating in a given observational study. In this paper, we consider the
framework of proximal causal inference introduced by Miao et al. (2018);
Tchetgen Tchetgen et al. (2020), which while explicitly acknowledging covariate
measurements as imperfect proxies of confounding mechanisms, offers an
opportunity to learn about causal effects in settings where exchangeability on
the basis of measured covariates fails. We make a number of contributions to
proximal inference including (i) an alternative set of conditions for
nonparametric proximal identification of the average treatment effect; (ii)
general semiparametric theory for proximal estimation of the average treatment
effect including efficiency bounds for key semiparametric models of interest;
(iii) a characterization of proximal doubly robust and locally efficient
estimators of the average treatment effect. Moreover, we provide analogous
identification and efficiency results for the average treatment effect on the
treated. Our approach is illustrated via simulation studies and a data
application on evaluating the effectiveness of right heart catheterization in
the intensive care unit of critically ill patients.
