# Hidden yet quantifiable: A lower bound for confounding strength using randomized trials

arXiv: https://arxiv.org/abs/2312.03871 · HTML: https://mlsanity.com/paper/2312.03871/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 67 references that are in the map.
- First posted on arXiv 6 Dec 2023.

## Builds on (most cited first, 23 of 23)

- [Removing Hidden Confounding by Experimental Grounding](https://mlsanity.com/paper/1810.11646/) (2018)
- [Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach](https://mlsanity.com/paper/2111.12161/) (2021)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Causal inference methods for combining randomized trials and observational studies: a review](https://mlsanity.com/paper/2011.08047/) (2020)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [Bounds on the conditional and average treatment effect with unobserved confounding factors](https://mlsanity.com/paper/1808.09521/) (2018)
- [A Review of Generalizability and Transportability](https://mlsanity.com/paper/2102.11904/) (2021)
- [Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap](https://mlsanity.com/paper/1711.11286/) (2017)
- [Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing](https://mlsanity.com/paper/2102.04543/) (2021)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [B-Learner: Quasi-Oracle Bounds on Heterogeneous Causal Effects Under Hidden Confounding](https://mlsanity.com/paper/2304.10577/) (2023)
- [Sense and Sensitivity Analysis: Simple Post-Hoc Analysis of Bias Due to Unobserved Confounding](https://mlsanity.com/paper/2003.01747/) (2020)
- [Elastic Integrative Analysis of Randomized Trial and Real-World Data for Treatment Heterogeneity Estimation](https://mlsanity.com/paper/2005.10579/) (2020)
- [How and Why to Use Experimental Data to Evaluate Methods for Observational Causal Inference](https://mlsanity.com/paper/2010.03051/) (2020)
- [Detecting hidden confounding in observational data using multiple environments](https://mlsanity.com/paper/2205.13935/) (2022)
- [Falsification before Extrapolation in Causal Effect Estimation](https://mlsanity.com/paper/2209.13708/) (2022)
- [Falsification of Internal and External Validity in Observational Studies via Conditional Moment Restrictions](https://mlsanity.com/paper/2301.13133/) (2023)
- [Methods for Integrating Trials and Non-Experimental Data to Examine Treatment Effect Heterogeneity](https://mlsanity.com/paper/2302.13428/) (2023)
- [Covariate Balancing Sensitivity Analysis for Extrapolating Randomized Trials across Locations](https://mlsanity.com/paper/2112.04723/) (2021)
- [Risk ratio, odds ratio, risk difference... Which causal measure is easier to generalize?](https://mlsanity.com/paper/2303.16008/) (2023)
- [RCT Rejection Sampling for Causal Estimation Evaluation](https://mlsanity.com/paper/2307.15176/) (2023)
- [Study designs for extending causal inferences from a randomized trial to a target population](https://mlsanity.com/paper/1905.07764/) (2019)
- [Conditional Cross-Design Synthesis Estimators for Generalizability in Medicaid](https://mlsanity.com/paper/2109.13288/) (2021)

## Built on by (most cited first, 8 of 8)

- [Prediction-powered Generalization of Causal Inferences](https://mlsanity.com/paper/2406.02873/) (2024)
- [Efficient Randomized Experiments Using Foundation Models](https://mlsanity.com/paper/2502.04262/) (2025)
- [Benchmarking Observational Studies with Experimental Data under Right-Censoring](https://mlsanity.com/paper/2402.15137/) (2024)
- [The Hardness of Validating Observational Studies with Experimental Data](https://mlsanity.com/paper/2503.14795/) (2025)
- [Distributionally robust risk evaluation with an isotonic constraint](https://mlsanity.com/paper/2407.06867/) (2024)
- [Falsification of Unconfoundedness by Testing Independence of Causal Mechanisms](https://mlsanity.com/paper/2502.06231/) (2025)
- [Transportability without Graphs: A Bayesian Approach to Identifying s-Admissible Backdoor Sets](https://mlsanity.com/paper/2505.12801/) (2025)
- [Uncovering Bias Mechanisms in Observational Studies](https://mlsanity.com/paper/2506.01191/) (2025)

## Abstract (arXiv)

In the era of fast-paced precision medicine, observational studies play a major role in properly evaluating new treatments in clinical practice. Yet, unobserved confounding can significantly compromise causal conclusions drawn from non-randomized data. We propose a novel strategy that leverages randomized trials to quantify unobserved confounding. First, we design a statistical test to detect unobserved confounding with strength above a given threshold. Then, we use the test to estimate an asymptotically valid lower bound on the unobserved confounding strength. We evaluate the power and validity of our statistical test on several synthetic and semi-synthetic datasets. Further, we show how our lower bound can correctly identify the absence and presence of unobserved confounding in a real-world setting.