# Efficient nonparametric causal inference with missing exposure information

arXiv: https://arxiv.org/abs/1802.08952 · HTML: https://mlsanity.com/paper/1802.08952/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2018.

## Built on by (most cited first, 10 of 10)

- [Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Time](https://mlsanity.com/paper/2306.04255/) (2023)
- [Estimating Conditional Average Treatment Effects with Missing Treatment Information](https://mlsanity.com/paper/2203.01422/) (2022)
- [Estimation of Local Average Treatment Effect by Data Combination](https://mlsanity.com/paper/2109.05175/) (2021)
- [Estimating treatment effects from single-arm trials via latent-variable modeling](https://mlsanity.com/paper/2311.03002/) (2023)
- [Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inference](https://mlsanity.com/paper/2511.08303/) (2025)
- [Orthogonal Series Estimation for the Ratio of Conditional Expectation Functions](https://mlsanity.com/paper/2212.13145/) (2022)
- [Causal inference for the expected number of recurrent events in the presence of a terminal event](https://mlsanity.com/paper/2306.16571/) (2023)
- [Heterogeneous Treatment Effect Estimation under Noncompliance in the Illinois Workplace Wellness Study with Bayesian Tree Ensembles](https://mlsanity.com/paper/2408.07765/) (2024)
- [Debiased Machine Learning for Conformal Prediction of Counterfactual Outcomes Under Runtime Confounding](https://mlsanity.com/paper/2604.03772/) (2026)
- [Learning Who to Treat When Treatment is Missing](https://mlsanity.com/paper/2607.14346/) (2026)

## Abstract (arXiv)

Missing exposure information is a very common feature of many observational studies. Here we study identifiability and efficient estimation of causal effects on vector outcomes, in such cases where treatment is unconfounded but partially missing. We consider a missing at random setting where missingness in treatment can depend not only on complex covariates, but also on post-treatment outcomes. We give a new identifying expression for average treatment effects in this setting, along with the efficient influence function for this parameter in a nonparametric model, which yields a nonparametric efficiency bound. We use this latter result to construct nonparametric estimators that are less sensitive to the curse of dimensionality than usual, e.g., by having faster rates of convergence than the complex nuisance estimators they rely on. Further we show that these estimators can be root-n consistent and asymptotically normal under weak nonparametric conditions, even when constructed using flexible machine learning. Finally we apply these results to the problem of causal inference with a partially missing instrumental variable.