# Estimating average causal effects with incomplete exposure and confounders

## TL;DR

This paper introduces new methods to estimate causal effects when data on exposures and confounders are missing, improving accuracy in observational studies.

## Contribution

The paper proposes novel doubly robust estimators for handling missing not at random data in causal effect estimation.

## Key findings

- Standard multiple imputation techniques can be biased under MNAR assumptions.
- Doubly robust TMLE estimators remain unbiased even if some models are misspecified.
- The methods were applied to study opioid effects on mortality using NHANES data.

## 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, 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).