Average Causal Effect Estimation in DAGs with Hidden Variables: Beyond Back-Door and Front-Door Criteria

TL;DR

This paper develops novel estimators for causal effects in DAGs with hidden variables, extending beyond traditional criteria, and provides practical implementation via an R package.

Contribution

It introduces one-step corrected and targeted estimators that handle complex DAGs with hidden variables, ensuring statistical robustness and practical usability.

Findings

Estimators achieve double robustness and efficiency.

Estimates remain within the parameter space of the target causal effect.

The methods are implemented in the flexCausal R package.

Abstract

The identification theory for causal effects in directed acyclic graphs (DAGs) with hidden variables is well established, but methods for estimating and inferring functionals that extend beyond the g-formula remain underdeveloped. Previous studies have introduced semiparametric estimators for such functionals in a broad class of DAGs with hidden variables. While these estimators exhibit desirable statistical properties such as double robustness in certain cases, they also face significant limitations. Notably, they encounter substantial computational challenges, particularly involving density estimation and numerical integration for continuous variables, and their estimates may fall outside the parameter space of the target estimand. Additionally, the asymptotic properties of these estimators is underexplored, especially when integrating flexible statistical and machine learning models for nuisance functional estimations. This paper addresses these challenges by introducing novel one-step corrected plug-in and targeted minimum loss-based estimators of causal effects for a class of hidden variable DAGs that go beyond classical back-door and front-door criteria (known as the treatment primal fixability criterion in prior literature). These estimators leverage data-adaptive machine learning algorithms to minimize modeling assumptions while ensuring key statistical properties including double robustness, efficiency, boundedness within the target parameter space, and asymptotic linearity under $L^2(P)$-rate conditions for nuisance functional estimates that yield root-n consistent causal effect estimates. To ensure our estimation methods are accessible in practice, we provide the flexCausal package in R.