Adaptive Proximal Causal Inference with Some Invalid Proxies

TL;DR

This paper develops a new adaptive LASSO-based method for causal inference using proxies, capable of handling invalid proxies and providing valid confidence intervals under certain conditions.

Contribution

It introduces necessary and sufficient conditions for identifying causal effects with many proxies, and proposes an adaptive LASSO estimator that selects valid proxies and estimates causal effects with theoretical guarantees.

Findings

The adaptive LASSO estimator is root-n consistent.

The method provides valid confidence intervals when a valid outcome proxy exists.

Simulations and real data demonstrate the effectiveness of the approach.

Abstract

Proximal causal inference (PCI) is a recently proposed framework to identify and estimate the causal effect of an exposure on an outcome in the presence of hidden confounders, using observed proxies. Specifically, PCI relies on two types of proxies: a treatment-inducing confounding proxy, related to the outcome only through its association with unmeasured confounders (given treatment and covariates), and an outcome-inducing confounding proxy, related to the treatment only through such association (given covariates). These proxies must satisfy stringent exclusion restrictions - namely, the treatment proxy must not affect the outcome, and the outcome proxy must not be affected by the treatment. To improve identification and potentially efficiency, multiple proxies are often used, raising concerns about bias from exclusion violations. To address this, we introduce necessary and sufficient conditions for identifying causal effects in the presence of many proxies, some potentially invalid. Under a canonical proximal linear structural equations model, we propose a LASSO-based median estimator that jointly selects valid proxies and estimates the causal effect, with theoretical guarantees. Recognizing LASSO's limitations in consistently selecting valid treatment proxies, we develop an adaptive LASSO-based estimator with differential penalization. We show that it is root-n consistent and yields valid confidence intervals when a valid outcome proxy is available. We also extend the approach to settings with many potentially invalid outcome proxies. Theoretical results are supported by simulations and an application assessing the effect of right heart catheterization on 30-day survival in ICU patient.