Quadruply robust methods for causal mediation analysis

TL;DR

This paper introduces a quadruply robust framework for causal mediation analysis, expanding the model class for unbiased effect estimation and supporting machine learning and high-dimensional data.

Contribution

It develops a new quadruply robust approach that generalizes existing triply robust methods, including nonparametric and high-dimensional modeling strategies.

Findings

The QR estimator performs well in simulations.

The MQR estimator is effective in high-dimensional settings.

Real data application confirms practical utility.

Abstract

Estimating natural effects is a core task in causal mediation analysis. Existing triply robust (TR) frameworks (Tchetgen Tchetgen & Shpitser 2012) and their extensions have been developed to estimate the natural effects. In this work, we introduce a new quadruply robust (QR) framework that enlarges the model class for unbiased identification. We study two modeling strategies. The first is a nonparametric modeling approach, under which we propose a general QR estimator that supports the use of machine learning methods for nuisance estimation. We also study high-dimensional settings, where the dimensions of covariates and mediators may both be large. In these settings, we adopt a parametric modeling strategy and develop a model quadruply robust (MQR) estimator to limit the impact of model misspecification. Simulation studies and a real data application demonstrate the finite-sample performance of the proposed methods.