# Sensitivity analysis via the proportion of unmeasured confounding

arXiv: https://arxiv.org/abs/1912.02793 · HTML: https://mlsanity.com/paper/1912.02793/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 13 of 13)

- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [Long Story Short: Omitted Variable Bias in Causal Machine Learning](https://mlsanity.com/paper/2112.13398/) (2021)
- [What's the Harm? Sharp Bounds on the Fraction Negatively Affected by Treatment](https://mlsanity.com/paper/2205.10327/) (2022)
- [Estimating and Improving Dynamic Treatment Regimes With a Time-Varying Instrumental Variable](https://mlsanity.com/paper/2104.07822/) (2021)
- [FADE: FAir Double Ensemble Learning for Observable and Counterfactual Outcomes](https://mlsanity.com/paper/2109.00173/) (2021)
- [Robust Fitted-Q-Evaluation and Iteration under Sequentially Exogenous Unobserved Confounders](https://mlsanity.com/paper/2302.00662/) (2023)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [Reinforcement Learning with Continuous Actions Under Unmeasured Confounding](https://mlsanity.com/paper/2505.00304/) (2025)
- [A Causal Research Pipeline and Tutorial for Psychologists and Social Scientists](https://mlsanity.com/paper/2206.05175/) (2022)
- [Counterfactually Comparing Abstaining Classifiers](https://mlsanity.com/paper/2305.10564/) (2023)
- [Data-Driven Influence Functions for Optimization-Based Causal Inference](https://mlsanity.com/paper/2208.13701/) (2022)
- [Valid causal inference with unobserved confounding in high-dimensional settings](https://mlsanity.com/paper/2401.06564/) (2024)
- [Weighted Spline-Expanded Networks with Distributional Balancing for Continuous Treatment Effects](https://mlsanity.com/paper/2609.33740/) (2026)

## Abstract (arXiv)

In observational studies, identification of ATEs is generally achieved by assuming that the correct set of confounders has been measured and properly included in the relevant models. Because this assumption is both strong and untestable, a sensitivity analysis should be performed. Common approaches include modeling the bias directly or varying the propensity scores to probe the effects of a potential unmeasured confounder. In this paper, we take a novel approach whereby the sensitivity parameter is the "proportion of unmeasured confounding:" the proportion of units for whom the treatment is not as good as randomized even after conditioning on the observed covariates. We consider different assumptions on the probability of a unit being unconfounded. In each case, we derive sharp bounds on the average treatment effect as a function of the sensitivity parameter and propose nonparametric estimators that allow flexible covariate adjustment. We also introduce a one-number summary of a study's robustness to the number of confounded units. Finally, we explore finite-sample properties via simulation, and apply the methods to an observational database used to assess the effects of right heart catheterization.