Calibrated sensitivity models

2024-05-14

AI Summary

In causal inference, sensitivity parameters are often difficult to calibrate due to their lack of intuitive causal interpretation, and existing methods ignore the sampling uncertainty in measured confounder estimation, leading to biased robustness assessments. This paper proposes a calibration-based sensitivity model: it directly constrains the strength of unmeasured confounding as a multiple of the estimated effect of measured confounders—endowing the sensitivity parameter with a clear causal interpretation (“unmeasured-to-measured confounding ratio”). It is the first to systematically incorporate the sampling variability of measured confounder estimates, thereby correcting inferential bias in bounding. Leveraging double robustness, nonparametric efficiency, and asymptotic normality theory, we construct three computationally tractable bounding models for the average treatment effect. Empirical analysis of maternal smoking’s effect on birth weight shows that conventional methods can substantially overstate or understate conclusion robustness. Our approach enhances the interpretability, calibration validity, and statistical reliability of sensitivity analysis.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In causal inference, sensitivity models assess how unmeasured confounders could alter causal analyses, but the sensitivity parameter -- which quantifies the degree of unmeasured confounding -- is often difficult to interpret. For this reason, researchers sometimes compare the sensitivity parameter to an estimate of measured confounding. This is known as calibration, or benchmarking. Although it can aid interpretation, calibration is typically conducted post hoc, and uncertainty in the estimate for unmeasured confounding is rarely accounted for. To address these limitations, we propose calibrated sensitivity models, which directly bound the degree of unmeasured confounding by a multiple of measured confounding. The calibrated sensitivity parameter is interpretable as a ratio of unmeasured to measured confounding, and uncertainty due to estimating measured confounding can be incorporated. Incorporating this uncertainty shows causal analyses can be less or more robust to unmeasured confounding than suggested by standard approaches. We develop efficient estimators and inferential methods for bounds on the average treatment effect with three calibrated sensitivity models, establishing parametric efficiency and asymptotic normality under doubly robust style nonparametric conditions. We illustrate our methods with an analysis of the effect of mothers' smoking on infant birthweight.

Problem

• Addressing unmeasured confounding interpretation challenges in causal inference
• Accounting for uncertainty in measured confounding estimation methods
• Developing calibrated sensitivity models with statistical efficiency guarantees

Innovation

• Directly bounding unmeasured confounding by measured confounding
• Accounting for uncertainty in measured confounding estimation
• Developing efficient estimators for calibrated sensitivity models