Fortified Proximal Causal Inference with Many Invalid Proxies

TL;DR

This paper introduces a semiparametric method for causal inference that remains valid even when many proxies used for confounding adjustment are potentially invalid, by leveraging a new class of fortified confounding bridge functions.

Contribution

It develops a novel fortified confounding bridge function framework and provides estimators that are robust to invalid proxies without knowing which proxies are valid.

Findings

Method achieves nonparametric identification of ATE with invalid proxies.

Estimators are multiply robust and locally efficient.

Simulation and real data demonstrate effectiveness.

Abstract

Causal inference from observational data often relies on the assumption of no unmeasured confounding, an assumption frequently violated in practice due to unobserved or poorly measured covariates. Proximal causal inference (PCI) offers a promising framework for addressing unmeasured confounding using a pair of outcome and treatment confounding proxies. However, existing PCI methods typically assume all specified proxies are valid, which may be unrealistic and is untestable without extra assumptions. In this paper, we develop a semiparametric approach for a many-proxy PCI setting that accommodates potentially invalid treatment confounding proxies. We introduce a new class of fortified confounding bridge functions and establish nonparametric identification of the population average treatment effect (ATE) under the assumption that at least $\gamma$ out of $K$ candidate treatment confounding proxies are valid, for any $\gamma \leq K$ set by the analyst without requiring knowledge of which proxies are valid. We establish a local semiparametric efficiency bound and develop a class of multiply robust, locally efficient estimators for the ATE. These estimators are thus simultaneously robust to invalid treatment confounding proxies and model misspecification of nuisance parameters. The proposed methods are evaluated through simulation and applied to assess the effect of right heart catheterization in critically ill patients.