# Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap

arXiv: https://arxiv.org/abs/1711.11286 · HTML: https://mlsanity.com/paper/1711.11286/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2017.

## Built on by (most cited first, 30 of 33)

- [Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2202.12891/) (2022)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [Scalable Sensitivity and Uncertainty Analysis for Causal-Effect Estimates of Continuous-Valued Interventions](https://mlsanity.com/paper/2204.10022/) (2022)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Generalizing Off-Policy Learning under Sample Selection Bias](https://mlsanity.com/paper/2112.01387/) (2021)
- [Robust Fitted-Q-Evaluation and Iteration under Sequentially Exogenous Unobserved Confounders](https://mlsanity.com/paper/2302.00662/) (2023)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [The s-value: evaluating stability with respect to distributional shifts](https://mlsanity.com/paper/2105.03067/) (2021)
- [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)
- [Hidden yet quantifiable: A lower bound for confounding strength using randomized trials](https://mlsanity.com/paper/2312.03871/) (2023)
- [Partial Identification of Dose Responses with Hidden Confounders](https://mlsanity.com/paper/2204.11206/) (2022)
- [Efficient and Sharp Off-Policy Learning under Unobserved Confounding](https://mlsanity.com/paper/2502.13022/) (2025)
- [Confounding-Robust Policy Improvement with Human-AI Teams](https://mlsanity.com/paper/2310.08824/) (2023)
- [New-Onset Diabetes Assessment Using Artificial Intelligence-Enhanced Electrocardiography](https://mlsanity.com/paper/2205.02900/) (2022)
- [Off-Policy Evaluation with Out-of-Sample Guarantees](https://mlsanity.com/paper/2301.08649/) (2023)
- [A Fast Bootstrap Algorithm for Causal Inference with Large Data](https://mlsanity.com/paper/2302.02859/) (2023)
- [Distributionally robust risk evaluation with an isotonic constraint](https://mlsanity.com/paper/2407.06867/) (2024)
- [Amortizing Causal Sensitivity Analysis via Prior Data-Fitted Networks](https://mlsanity.com/paper/2605.10590/) (2026)
- [Distributionally Robust Causal Inference with Observational Data](https://mlsanity.com/paper/2210.08326/) (2022)
- [Kernel Conditional Moment Constraints for Confounding Robust Inference](https://mlsanity.com/paper/2302.13348/) (2023)
- [Towards Robust Off-policy Learning for Runtime Uncertainty](https://mlsanity.com/paper/2202.13337/) (2022)
- [Deep Sensitivity Analysis for Objective-Oriented Combinatorial Optimization](https://mlsanity.com/paper/2403.00016/) (2024)
- [Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring](https://mlsanity.com/paper/2510.13397/) (2025)
- [High-Dimensional Gaussian Mean Estimation under Realizable Contamination](https://mlsanity.com/paper/2603.16798/) (2026)
- [A Convex Framework for Confounding Robust Inference](https://mlsanity.com/paper/2309.12450/) (2023)
- [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)
- [Fast Uncertainty Quantification for Kernel-Based Estimators in Large-Scale Causal Inference](https://mlsanity.com/paper/2603.13662/) (2026)

## Abstract (arXiv)

To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the "missing at random" and "no unmeasured confounder" assumptions. However, these assumptions are unverifiable using empirical data and pose serious threats to the validity of the qualitative conclusions of the statistical inference. A sensitivity analysis asks how the conclusions may change if the unverifiable assumptions are violated to a certain degree. In this paper we consider a marginal sensitivity model which is a natural extension of Rosenbaum's sensitivity model that is widely used for matched observational studies. We aim to construct confidence intervals based on inverse probability weighting estimators, such that asymptotically the intervals have at least nominal coverage of the estimand whenever the data generating distribution is in the collection of marginal sensitivity models. We use a percentile bootstrap and a generalized minimax/maximin inequality to transform this intractable problem to a linear fractional programming problem, which can be solved very efficiently. We illustrate our method using a real dataset to estimate the causal effect of fish consumption on blood mercury level.