Semiparametric sensitivity analysis: unmeasured confounding in observational studies

TL;DR

This paper develops a semiparametric sensitivity analysis method for assessing the robustness of causal inferences to unmeasured confounding in observational studies, providing a new estimator with theoretical guarantees.

Contribution

It introduces a novel semiparametric approach to sensitivity analysis for the average causal effect, deriving an efficient influence function and constructing a robust estimator.

Findings

Estimator achieves root-n asymptotics under certain conditions

Method applied to assess smoking's effect on birth weight

Simulation study confirms estimator's good performance

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. (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, 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 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.