# Bounding the Probabilities of Benefit and Harm Through Sensitivity Parameters and Proxies

arXiv: https://arxiv.org/abs/2303.05396 · HTML: https://mlsanity.com/paper/2303.05396/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 8 Mar 2023.

## Builds on (most cited first, 7 of 7)

- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Causes of Effects: Learning individual responses from population data](https://mlsanity.com/paper/2104.13730/) (2021)
- [Personalized Decision Making -- A Conceptual Introduction](https://mlsanity.com/paper/2208.09558/) (2022)
- [Probabilities of Causation with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09568/) (2022)
- [Unit Selection with Causal Diagram](https://mlsanity.com/paper/2109.07556/) (2021)
- [On the Monotonicity of a Nondifferentially Mismeasured Binary Confounder](https://mlsanity.com/paper/2005.13245/) (2020)
- [Simple yet Sharp Sensitivity Analysis for Unmeasured Confounding](https://mlsanity.com/paper/2104.13020/) (2021)

## Built on by (most cited first, 3 of 3)

- [On the Probability of Immunity](https://mlsanity.com/paper/2309.11942/) (2023)
- [Path-specific harm decomposition: A partial identification framework](https://mlsanity.com/paper/2609.29938/) (2026)
- [Same Predictions, Different Harms: Causal Auditing of Patient World Models](https://mlsanity.com/paper/2610.05198/) (2026)

## Abstract (arXiv)

We present two methods for bounding the probabilities of benefit and harm under unmeasured confounding. The first method computes the (upper or lower) bound of either probability as a function of the observed data distribution and two intuitive sensitivity parameters which, then, can be presented to the analyst as a 2-D plot to assist her in decision making. The second method assumes the existence of a measured nondifferential proxy (i.e., direct effect) of the unmeasured confounder. Using this proxy, tighter bounds than the existing ones can be derived from just the observed data distribution.