# Sensitivity to Unobserved Confounding in Studies with Factor-structured Outcomes

arXiv: https://arxiv.org/abs/2208.06552 · HTML: https://mlsanity.com/paper/2208.06552/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2022.

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

- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [ρ-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows](https://mlsanity.com/paper/2209.07111/) (2022)
- [Sensitivity Analysis to Unobserved Confounding with Copula-based Normalizing Flows](https://mlsanity.com/paper/2508.08752/) (2025)
- [Segment Discovery: Enhancing E-commerce Targeting](https://mlsanity.com/paper/2409.13847/) (2024)
- [How Wrong Can Your Counterfactual Be? Quantifying Confounding Bias for Continuous Treatments without a Control Group](https://mlsanity.com/paper/2603.07438/) (2026)

## Abstract (arXiv)

In this work, we propose an approach for assessing sensitivity to unobserved confounding in studies with multiple outcomes. We demonstrate how prior knowledge unique to the multi-outcome setting can be leveraged to strengthen causal conclusions beyond what can be achieved from analyzing individual outcomes in isolation. We argue that it is often reasonable to make a shared confounding assumption, under which residual dependence amongst outcomes can be used to simplify and sharpen sensitivity analyses. We focus on a class of factor models for which we can bound the causal effects for all outcomes conditional on a single sensitivity parameter that represents the fraction of treatment variance explained by unobserved confounders. We characterize how causal ignorance regions shrink under additional prior assumptions about the presence of null control outcomes, and provide new approaches for quantifying the robustness of causal effect estimates. Finally, we illustrate our sensitivity analysis workflow in practice, in an analysis of both simulated data and a case study with data from the National Health and Nutrition Examination Survey (NHANES).