When negative control exposures fail to detect bias

Researchers increasingly utilize negative control exposures (NCEs), variables known to have no effect on the outcome, to detect residual confounding. However, an NCE analysis may provide little evidence of confounding despite substantial bias in the estimated exposure effect. We study, analytically and via simulations, how the magnitude and source of exposure-NCE association affect the large-sample NCE coefficient and statistical power of regression-based bias-detection. We show that the power does not always increase with bias, and that stronger confounder-exposure associations can increase bias while reducing the NCE coefficient and power. Furthermore, the correlation between the exposure of interest and the NCE is insufficient to characterize how well the NCE will detect confounding. Additional exposure-NCE common causes that affect the outcome only through the exposure can attenuate the NCE coefficient toward zero or reverse its sign, even when confounding bias remains unchanged. These changes can occur even when the overall exposure-NCE correlation is fixed. Adjusting for such common causes alleviated sign reversal in our simulations but did not uniformly improve power. Negative controls can be a powerful tool to detect unmeasured confounding. Researchers should consider the sources of exposure-NCE association and interpret null or counterintuitive NCE findings with caution.