The Role of Measured Covariates in Assessing Sensitivity to Unmeasured Confounding

TL;DR

This paper explores how the structure of measured covariates, especially proxies, influences the sensitivity of causal inferences to unmeasured confounding in observational studies, emphasizing the role of multicollinearity.

Contribution

It formalizes the impact of proxy variables on sensitivity analysis in linear regression and introduces an observable measure for this effect.

Findings

Proxy variables can amplify sensitivity to unmeasured confounding.

Growing socioeconomic stratification increases sensitivity in recent data.

Multicollinearity affects interpretation of sensitivity analyses.

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.