# Sharpening the Rosenbaum Sensitivity Bounds to Address Concerns About Interactions Between Observed and Unobserved Covariates

arXiv: https://arxiv.org/abs/2004.00766 · HTML: https://mlsanity.com/paper/2004.00766/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2020.

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

- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Estimating and Improving Dynamic Treatment Regimes With a Time-Varying Instrumental Variable](https://mlsanity.com/paper/2104.07822/) (2021)
- [Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring](https://mlsanity.com/paper/2510.13397/) (2025)

## Abstract (arXiv)

In observational studies, it is typically unrealistic to assume that treatments are randomly assigned, even conditional on adjusting for all observed covariates. Therefore, a sensitivity analysis is often needed to examine how hidden biases due to unobserved covariates would affect inferences on treatment effects. In matched observational studies where each treated unit is matched to one or multiple untreated controls for observed covariates, the Rosenbaum bounds sensitivity analysis is one of the most popular sensitivity analysis models. In this paper, we show that in the presence of interactions between observed and unobserved covariates, directly applying the Rosenbaum bounds will almost inevitably exaggerate the report of sensitivity of causal conclusions to hidden bias. We give sharper odds ratio bounds to fix this deficiency. We illustrate our new method through studying the effect of anger/hostility tendency on the risk of having heart problems.