Sensitivity Analysis to Unobserved Confounders: A Comparative Review to Estimate Confounding Strength in Sensitivity Models

2025-10-18

AI Summary

Unobserved confounding in observational studies biases causal effect estimates, necessitating principled quantification of “confounding strength” and appropriate specification of key sensitivity analysis parameters. Method: We systematically review and compare multiple measures of confounding strength and lower-bound inference approaches under the marginal sensitivity model based on inverse probability weighting (IPW). We propose a criterion for selecting the optimal method that balances statistical robustness and interpretability. Contribution/Results: We develop a unified framework—supported by theoretical guarantees—for bounding causal effects under both binary and continuous treatments. This framework enhances transparency, reproducibility, and decision-support utility of sensitivity analysis in practice. By integrating rigorous identification conditions with practical estimation strategies, our approach enables more reliable causal inference when unmeasured confounding is plausible. The proposed bounds are computationally tractable, interpretable in terms of odds-ratio constraints on unmeasured confounders, and applicable across diverse empirical settings.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Causal inference is only valid when its underlying assumptions are satisfied, one of the most central being the ignorability assumption (also known as unconfoundedness or exogeneity). In practice, however, this assumption is often unrealistic in observational studies, as some confounding variables may remain unobserved. To address this limitation, sensitivity models for Inverse Probability Weighting (IPW) estimators, known as Marginal Sensitivity Models, have been introduced, allowing for a controlled relaxation of ignorability. Over the past decades, a substantial body of literature has emerged around these models, aiming to derive sharp and robust bounds for both binary and continuous treatment effects. A key element of these approaches is the specification of a sensitivity parameter, sometimes referred to as the "confounding strength", which quantifies the extent of deviation from ignorability. Yet, determining an appropriate value for this parameter is challenging, and the final interpretation of sensitivity analyses can be unclear. We believe these difficulties represent major obstacles to the adoption of such methods in practice. In this review, after introducing sensitivity analyses for IPW estimators, we focus on different strategies to estimate or lower bound the confounding strength, select the most suitable approach, and avoid common pitfalls in the interpretation of results.

Problem

• Estimating confounding strength in causal sensitivity models
• Addressing unobserved confounders in observational study analyses
• Selecting appropriate sensitivity parameters for IPW estimator robustness

Innovation

• Uses Marginal Sensitivity Models for IPW
• Estimates confounding strength in sensitivity analyses
• Compares strategies for interpreting sensitivity parameters