# Simple yet Sharp Sensitivity Analysis for Unmeasured Confounding

arXiv: https://arxiv.org/abs/2104.13020 · HTML: https://mlsanity.com/paper/2104.13020/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 15 references that are in the map.
- First posted on arXiv 27 Apr 2021.

## Builds on (most cited first, 2 of 2)

- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Sharp sensitivity bounds for mediation under unmeasured mediator-outcome confounding](https://mlsanity.com/paper/1601.05155/) (2016)

## Built on by (most cited first, 5 of 5)

- [Bounding the Probabilities of Benefit and Harm Through Sensitivity Parameters and Proxies](https://mlsanity.com/paper/2303.05396/) (2023)
- [ρ-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows](https://mlsanity.com/paper/2209.07111/) (2022)
- [A Consistent Estimator for Confounding Strength](https://mlsanity.com/paper/2211.01903/) (2022)
- [Sensitivity Analysis to Unobserved Confounding with Copula-based Normalizing Flows](https://mlsanity.com/paper/2508.08752/) (2025)
- [Simple yet Sharp Sensitivity Analysis for Any Contrast Under Unmeasured Confounding](https://mlsanity.com/paper/2406.07940/) (2024)

## Abstract (arXiv)

We present a method for assessing the sensitivity of the true causal effect to unmeasured confounding. The method requires the analyst to set two intuitive parameters. Otherwise, the method is assumption-free. The method returns an interval that contains the true causal effect, and whose bounds are arbitrarily sharp, i.e. practically attainable. We show experimentally that our bounds can be tighter than those obtained by the method of Ding and VanderWeele (2016a) which, moreover, requires to set one more parameter than our method. Finally, we extend our method to bound the natural direct and indirect effects when there are measured mediators and unmeasured exposure-outcome confounding.