4G-05 - Assessing U-Comparability of Negative Controls Using Proxy Variables for Unmeasured Confounders: A Simulation Study

Background: Negative controls are commonly used to detect residual confounding in observational studies, but no empirical methods exist for selecting negative controls that accurately capture the underlying bias structure (U-comparability).

Objectives: To propose a novel empirical approach for evaluating the U-comparability of negative control exposures (NCEs) using proxy variables for unmeasured confounders, and to explore through Monte Carlo simulation structural conditions under which these proxies effectively distinguish U-comparable from non-U-comparable NCEs.

Methods: We generated a synthetic dataset of 10,000 independent observations per iteration over 1,000 iterations. For each dataset, we generated the following variables from specified probability distributions: a continuous primary exposure, an outcome, three unmeasured confounders, four NCEs, and thirty proxies for each unmeasured confounder (with differing correlations to both the unmeasured confounders and the NCEs). We then estimated the effects of these proxies on the primary exposure and each NCE via multivariate linear regressions and quantified effect similarity by computing rank correlations (Spearman’s rho) of proxy effect sizes. Analyses were repeated under varying scenarios: the strength of unmeasured confounding ( < 10% to 40% of the true effect), the correlation between proxies and unmeasured confounders (signal), and the correlation between proxies and NCEs unrelated to the confounders (noise). Resulting rank correlations across 1,000 iterations were summarized for each scenario.

Results: Positive rank correlations (median Spearman’s rho range: 0.084–0.811) were observed for U-comparable NCEs, correlations centered around zero for NCEs not associated with the unmeasured confounders, and negative values (–0.067 to –0.572) for NCEs correlated with irrelevant confounders. The similarity in proxy effects increased as the strength of confounding increased. Higher levels of unwanted correlation between proxies and NCEs weakened the performance of the similarity measure for detecting U-comparability. When these unwanted correlations were minimal, Spearman’s rho ranged from 0.472 to 0.811 as the confounding effect size rose from < 10% to 40%. Stronger correlations (rho=0.3 vs. 0.1) between proxies and unmeasured confounders further enhanced the method’s ability to detect U-comparability.

Conclusions: This simulation study demonstrates that proxy variables for unmeasured confounders can help assess the confounding structure of negative controls, highlighting conditions that make such evaluations most informative.