# To Impute or not to Impute? Missing Data in Treatment Effect Estimation

arXiv: https://arxiv.org/abs/2202.02096 · HTML: https://mlsanity.com/paper/2202.02096/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 79 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 15 of 15)

- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [Causal Inference with Noisy and Missing Covariates via Matrix Factorization](https://mlsanity.com/paper/1806.00811/) (2018)
- [SurvITE: Learning Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2110.14001/) (2021)
- [Doubly robust treatment effect estimation with missing attributes](https://mlsanity.com/paper/1910.10624/) (2019)
- [MissDeepCausal: Causal Inference from Incomplete Data Using Deep Latent Variable Models](https://mlsanity.com/paper/2002.10837/) (2020)
- [Identifiable Energy-based Representations: An Application to Estimating Heterogeneous Causal Effects](https://mlsanity.com/paper/2108.03039/) (2021)
- [Accounting for interactions and complex inter-subject dependency in estimating treatment effect in cluster randomized trials with missing outcomes](https://mlsanity.com/paper/1507.01822/) (2015)
- [To adjust or not to adjust? Estimating the average treatment effect in randomized experiments with missing covariates](https://mlsanity.com/paper/2108.00152/) (2021)

## Built on by (most cited first, 9 of 9)

- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Time](https://mlsanity.com/paper/2306.04255/) (2023)
- [Dynamic Inter-treatment Information Sharing for Individualized Treatment Effects Estimation](https://mlsanity.com/paper/2305.15984/) (2023)
- [PIE: Simulating Disease Progression via Progressive Image Editing](https://mlsanity.com/paper/2309.11745/) (2023)
- [How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputation](https://mlsanity.com/paper/2407.08442/) (2024)
- [Causal machine learning for heterogeneous treatment effects in the presence of missing outcome data](https://mlsanity.com/paper/2412.19711/) (2024)
- [Variational Counterfactual Prediction under Runtime Domain Corruption](https://mlsanity.com/paper/2306.13271/) (2023)
- [Accounting for Missing Covariates in Heterogeneous Treatment Estimation](https://mlsanity.com/paper/2410.15655/) (2024)

## Abstract (arXiv)

Missing data is a systemic problem in practical scenarios that causes noise and bias when estimating treatment effects. This makes treatment effect estimation from data with missingness a particularly tricky endeavour. A key reason for this is that standard assumptions on missingness are rendered insufficient due to the presence of an additional variable, treatment, besides the input (e.g. an individual) and the label (e.g. an outcome). The treatment variable introduces additional complexity with respect to why some variables are missing that is not fully explored by previous work. In our work we introduce mixed confounded missingness (MCM), a new missingness mechanism where some missingness determines treatment selection and other missingness is determined by treatment selection. Given MCM, we show that naively imputing all data leads to poor performing treatment effects models, as the act of imputation effectively removes information necessary to provide unbiased estimates. However, no imputation at all also leads to biased estimates, as missingness determined by treatment introduces bias in covariates. Our solution is selective imputation, where we use insights from MCM to inform precisely which variables should be imputed and which should not. We empirically demonstrate how various learners benefit from selective imputation compared to other solutions for missing data. We highlight that our experiments encompass both average treatment effects and conditional average treatment effects.