# Flexible sensitivity analysis for observational studies without observable implications

arXiv: https://arxiv.org/abs/1809.00399 · HTML: https://mlsanity.com/paper/1809.00399/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2018.

## Built on by (most cited first, 18 of 18)

- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [Stochastic Causal Programming for Bounding Treatment Effects](https://mlsanity.com/paper/2202.10806/) (2022)
- [Long Story Short: Omitted Variable Bias in Causal Machine Learning](https://mlsanity.com/paper/2112.13398/) (2021)
- [Model-Free and Model-Based Policy Evaluation when Causality is Uncertain](https://mlsanity.com/paper/2204.00956/) (2022)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [Causal Fairness under Unobserved Confounding: A Neural Sensitivity Framework](https://mlsanity.com/paper/2311.18460/) (2023)
- [Robust Design and Evaluation of Predictive Algorithms under Unobserved Confounding](https://mlsanity.com/paper/2212.09844/) (2022)
- [SBI: A Simulation-Based Test of Identifiability for Bayesian Causal Inference](https://mlsanity.com/paper/2102.11761/) (2021)
- [IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learning](https://mlsanity.com/paper/2605.12924/) (2026)
- [H"older Bounds for Sensitivity Analysis in Causal Reasoning](https://mlsanity.com/paper/2107.04661/) (2021)
- [Prescriptive maintenance with causal machine learning](https://mlsanity.com/paper/2206.01562/) (2022)
- [Externally Valid Policy Evaluation Combining Trial and Observational Data](https://mlsanity.com/paper/2310.14763/) (2023)
- [Valid causal inference with unobserved confounding in high-dimensional settings](https://mlsanity.com/paper/2401.06564/) (2024)
- [Mitigating Hidden Confounding by Progressive Confounder Imputation via Large Language Models](https://mlsanity.com/paper/2507.02928/) (2025)
- [Data Fusion for High-Resolution Estimation](https://mlsanity.com/paper/2508.14858/) (2025)
- [Coupling Generative Modeling and an Autoencoder with the Causal Bridge](https://mlsanity.com/paper/2509.25599/) (2025)
- [Bayesian Sensitivity of Causal Inference Estimators under Evidence-Based Priors](https://mlsanity.com/paper/2605.07993/) (2026)
- [On efficiency gains via augmenting a tiny sample with a massive auxiliary sample](https://mlsanity.com/paper/2608.26610/) (2026)

## Abstract (arXiv)

A fundamental challenge in observational causal inference is that assumptions about unconfoundedness are not testable from data. Assessing sensitivity to such assumptions is therefore important in practice. Unfortunately, some existing sensitivity analysis approaches inadvertently impose restrictions that are at odds with modern causal inference methods, which emphasize flexible models for observed data. To address this issue, we propose a framework that allows (1) flexible models for the observed data and (2) clean separation of the identified and unidentified parts of the sensitivity model. Our framework extends an approach from the missing data literature, known as Tukey's factorization, to the causal inference setting. Under this factorization, we can represent the distributions of unobserved potential outcomes in terms of unidentified selection functions that posit an unidentified relationship between the treatment assignment indicator and the observed potential outcomes. The sensitivity parameters in this framework are easily interpreted, and we provide heuristics for calibrating these parameters against observable quantities. We demonstrate the flexibility of this approach in two examples, where we estimate both average treatment effects and quantile treatment effects using Bayesian nonparametric models for the observed data.