Dynamic treatment effects: high-dimensional inference under model misspecification

TL;DR

This paper introduces a novel sequential model doubly robust estimator for dynamic treatment effects, enabling accurate causal inference in high-dimensional settings despite model misspecification.

Contribution

It develops a new estimator with novel moment-targeting estimates that achieve root-N inference under high-dimensional confounding, even when nuisance models are misspecified.

Findings

Achieves root-N inference with at least one correctly specified nuisance model.

Develops novel loss functions that ensure robust inference under model misspecification.

Addresses challenges of high-dimensional confounding in dynamic treatment effect estimation.

Abstract

Estimating dynamic treatment effects is crucial across various disciplines, providing insights into the time-dependent causal impact of interventions. However, this estimation poses challenges due to time-varying confounding, leading to potentially biased estimates. Furthermore, accurately specifying the growing number of treatment assignments and outcome models with multiple exposures appears increasingly challenging to accomplish. Double robustness, which permits model misspecification, holds great value in addressing these challenges. This paper introduces a novel "sequential model doubly robust" estimator. We develop novel moment-targeting estimates to account for confounding effects and establish that root-$N$ inference can be achieved as long as at least one nuisance model is correctly specified at each exposure time, despite the presence of high-dimensional covariates. Although the nuisance estimates themselves do not achieve root-$N$ rates, the carefully designed loss functions in our framework ensure final root-$N$ inference for the causal parameter of interest. Unlike off-the-shelf high-dimensional methods, which fail to deliver robust inference under model misspecification even within the doubly robust framework, our newly developed loss functions address this limitation effectively.