Distributionally enhanced marginal sensitivity model and bounds

2025-05-20

AI Summary

This paper addresses the challenge of sensitivity analysis under unobserved confounding. We propose the distributionally enhanced Marginal Sensitivity Model (deMSM), which extends the conventional Marginal Sensitivity Model (MSM)—which only bounds shifts in treatment assignment probabilities—by introducing a *dual constraint* that jointly restricts the influence of unobserved confounders on both treatment assignment and potential outcome distributions. This yields interpretable, sharp bounds on causal effects that are symmetric with respect to the two constraints, enhancing practicality and cross-model comparability. Theoretically, deMSM strictly tightens MSM bounds, improving causal identifiability. Moreover, it unifies the constraint semantics and bound structures of various MSM extensions, providing a more robust and interpretable distributionally robust framework for sensitivity analysis. (138 words)

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

For sensitivity analysis against unmeasured confounding, we build on the marginal sensitivity model (MSM) and propose a new model, deMSM, by incorporating a second constraint on the shift of potential outcome distributions caused by unmeasured confounders in addition to the constraint on the shift of treatment probabilities. We show that deMSM leads to interpretable sharp bounds of common causal parameters and tightens the corresponding MSM bounds. Moreover, the sharp bounds are symmetric in the two deMSM constraints, which facilitates practical applications. Lastly, we compare deMSM with other MSM-related models in both model constraints and sharp bounds, and reveal new interpretations for later models.

Problem

• Proposes deMSM to enhance sensitivity analysis for unmeasured confounding
• Derives interpretable sharp bounds for common causal parameters
• Compares deMSM with related models in constraints and bounds

Innovation

• Enhanced sensitivity model with dual constraints
• Sharp interpretable bounds for causal parameters
• Symmetric constraints simplify practical applications