# Partial Identification of Dose Responses with Hidden Confounders

arXiv: https://arxiv.org/abs/2204.11206 · HTML: https://mlsanity.com/paper/2204.11206/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 64 references that are in the map.
- First posted on arXiv 24 Apr 2022.

## Builds on (most cited first, 27 of 27)

- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [Double/Debiased Machine Learning for Treatment and Causal Parameters](https://mlsanity.com/paper/1608.00060/) (2016)
- [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021)
- [Bounds on the conditional and average treatment effect with unobserved confounding factors](https://mlsanity.com/paper/1808.09521/) (2018)
- [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)
- [Moral Framing and Ideological Bias of News](https://mlsanity.com/paper/2009.12979/) (2020)
- [A Class of Algorithms for General Instrumental Variable Models](https://mlsanity.com/paper/2006.06366/) (2020)
- [Sense and Sensitivity Analysis: Simple Post-Hoc Analysis of Bias Due to Unobserved Confounding](https://mlsanity.com/paper/2003.01747/) (2020)
- [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)
- [Scalable Sensitivity and Uncertainty Analysis for Causal-Effect Estimates of Continuous-Valued Interventions](https://mlsanity.com/paper/2204.10022/) (2022)
- [Entropy Balancing for Continuous Treatments](https://mlsanity.com/paper/2001.06281/) (2020)
- [Treatment Effect Risk: Bounds and Inference](https://mlsanity.com/paper/2201.05893/) (2022)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [Nonparametric Estimation of Population Average Dose-Response Curves using Entropy Balancing Weights for Continuous Exposures](https://mlsanity.com/paper/2003.02938/) (2020)
- [Kernel Optimal Orthogonality Weighting: A Balancing Approach to Estimating Effects of Continuous Treatments](https://mlsanity.com/paper/1910.11972/) (2019)
- [Multiply Robust Causal Mediation Analysis with Continuous Treatments](https://mlsanity.com/paper/2105.09254/) (2021)
- [Finding Regions of Heterogeneity in Decision-Making via Expected Conditional Covariance](https://mlsanity.com/paper/2110.14508/) (2021)
- [Correcting Confounding via Random Selection of Background Variables](https://mlsanity.com/paper/2202.02150/) (2022)

## Built on by (most cited first, 7 of 7)

- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Causal Fairness under Unobserved Confounding: A Neural Sensitivity Framework](https://mlsanity.com/paper/2311.18460/) (2023)
- [Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confounding](https://mlsanity.com/paper/2306.09520/) (2023)
- [Amortizing Causal Sensitivity Analysis via Prior Data-Fitted Networks](https://mlsanity.com/paper/2605.10590/) (2026)
- [Your Assumed DAG is Wrong and Here's How To Deal With It](https://mlsanity.com/paper/2502.17030/) (2025)

## Abstract (arXiv)

Inferring causal effects of continuous-valued treatments from observational data is a crucial task promising to better inform policy- and decision-makers. A critical assumption needed to identify these effects is that all confounding variables -- causal parents of both the treatment and the outcome -- are included as covariates. Unfortunately, given observational data alone, we cannot know with certainty that this criterion is satisfied. Sensitivity analyses provide principled ways to give bounds on causal estimates when confounding variables are hidden. While much attention is focused on sensitivity analyses for discrete-valued treatments, much less is paid to continuous-valued treatments. We present novel methodology to bound both average and conditional average continuous-valued treatment-effect estimates when they cannot be point identified due to hidden confounding. A semi-synthetic benchmark on multiple datasets shows our method giving tighter coverage of the true dose-response curve than a recently proposed continuous sensitivity model and baselines. Finally, we apply our method to a real-world observational case study to demonstrate the value of identifying dose-dependent causal effects.