The Role of Measured Covariates in Assessing Sensitivity to Unmeasured Confounding

2026-02-16

AI Summary

This study addresses a critical yet often overlooked issue in observational research: when proxy variables are used to control for unmeasured confounding, covariates highly correlated with the exposure may inadvertently amplify sensitivity to residual confounding—an effect commonly neglected in conventional sensitivity analyses. Within a regression framework, this work formally characterizes this phenomenon and introduces a novel, observable metric based on the ratio of the exposure model coefficient to the residual variance, which quantifies how covariate structure exacerbates sensitivity to unmeasured confounding. By integrating multicollinearity into the interpretive framework of sensitivity analysis, the approach is validated through linear regression, proxy variable modeling, and sensitivity assessment in the context of smoking and lung cancer. Empirical results demonstrate that increasing socioeconomic stratification over time has heightened the sensitivity of recent data to unmeasured confounding.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Evaluation and Analysis

Application Category

• Security and Privacy: Large-scale security measurements
• 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

Abstract

Sensitivity analysis is widely used to assess the robustness of causal conclusions in observational studies, yet its interaction with the structure of measured covariates is often overlooked. When latent confounders cannot be directly adjusted for and are instead controlled using proxy variables, strong associations between exposure and measured proxies can amplify sensitivity to residual confounding. We formalize this phenomenon in linear regression settings by showing that a simple ratio involving the exposure model coefficient and residual exposure variance provides an observable measure of this increased sensitivity. Applying our framework to smoking and lung cancer, we document how growing socioeconomic stratification in smoking behavior over time leads to heightened sensitivity to unmeasured confounding in more recent data. These results highlight the importance of multicollinearity when interpreting sensitivity analyses based on proxy adjustment.

Problem

• unmeasured confounding
• proxy variables
• sensitivity analysis
• multicollinearity
• observational studies

Innovation

• sensitivity analysis
• unmeasured confounding
• proxy variables
• multicollinearity
• linear regression