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.

翻译：敏感性分析被广泛用于评估观察性研究中因果结论的稳健性，但其与测量协变量结构的交互作用常被忽视。当潜在混杂因素无法直接校正而需通过代理变量进行控制时，暴露与测量代理变量之间的强关联可能放大对残余混杂的敏感性。我们在线性回归框架中形式化了这一现象，证明通过暴露模型系数与残差暴露方差的简单比值可量化这种敏感性增强效应。将该框架应用于吸烟与肺癌的研究，我们发现随时间推移吸烟行为中社会经济分层现象的加剧，导致近期数据对未测量混杂因素的敏感性显著升高。这些结果凸显了在基于代理变量调整的敏感性分析中，多重共线性问题对结果解读的重要性。