Causal Inference on Missing Exposure via Robust Estimation

TL;DR

This paper introduces a robust inverse probability weighting estimator for causal inference with missing exposure data, addressing issues of model misspecification and extreme weights, and demonstrating superior performance over existing methods.

Contribution

It proposes a novel weighted estimating equation approach with triple robustness for handling missing exposure in causal studies, improving bias and variability.

Findings

WEE methods outperform imputation approaches in simulations.

The proposed estimators are asymptotically normal and consistent.

Application to COVID-19 data illustrates practical utility.

Abstract

How to deal with missing data in observational studies is a common concern for causal inference. When the covariates are missing at random (MAR), multiple approaches have been provided to help solve the issue. However, if the exposure is MAR, few approaches are available and careful adjustments on both missingness and confounding issues are required to ensure a consistent estimate of the true causal effect on the response. In this article, a new inverse probability weighting (IPW) estimator based on weighted estimating equations (WEE) is proposed to incorporate weights from both the missingness and propensity score (PS) models, which can reduce the joint effect of extreme weights in finite samples. Additionally, we develop a triple robust (TR) estimator via WEE to further protect against the misspecification of the missingness model. The asymptotic properties of WEE estimators are proved using properties of estimating equations. Based on the simulation studies, WEE methods outperform others including imputation-based approaches in terms of bias and variability. Finally, an application study is conducted to identify the causal effect of the presence of cardiovascular disease on mortality for COVID-19 patients.