Estimating Average Causal Effects with Incomplete Exposure and Confounders

TL;DR

This paper develops methods for estimating average causal effects in observational studies with missing exposure and confounder data, addressing both MAR and MNAR scenarios, and demonstrates their effectiveness through simulations and real data application.

Contribution

It introduces doubly robust targeted maximum likelihood estimators for causal effects under MNAR assumptions, extending existing methods to handle incomplete data more reliably.

Findings

Standard imputation is unbiased under MAR but biased under MNAR.

Proposed estimators are doubly robust and flexible for various outcome types.

Application to NHANES data illustrates practical utility.

Abstract

Standard methods for estimating average causal effects require complete observations of the exposure and confounders. In observational studies, however, missing data are ubiquitous. Motivated by a study on the effect of prescription opioids on mortality, we propose methods for estimating average causal effects when exposures and potential confounders may be missing. We consider missingness at random and additionally propose several specific missing not at random (MNAR) assumptions. Under our proposed MNAR assumptions, we show that the average causal effects are identified from the observed data and derive corresponding influence functions in a nonparametric model, which form the basis of our proposed estimators. Our simulations show that standard multiple imputation techniques paired with a complete data estimator is unbiased when data are missing at random (MAR) but can be biased otherwise. For each of the MNAR assumptions, we instead propose doubly robust targeted maximum likelihood estimators (TMLE), allowing misspecification of either (i) the outcome models or (ii) the exposure and missingness models. The proposed methods are suitable for any outcome types, and we apply them to a motivating study that examines the effect of prescription opioid usage on all-cause mortality using data from the National Health and Nutrition Examination Survey (NHANES).