Bias Amplification in Epidemiologic Analysis of Exposure to Mixtures

BACKGROUND: The analysis of health effects of exposure to mixtures is a critically important issue in human epidemiology, and increasing effort is being devoted to developing methods for this problem. A key feature of environmental mixtures is that some components can be highly correlated, raising the issues of confounding by coexposure and colinearity. A relatively unexplored topic in epidemiologic analysis of mixtures is the impact of residual confounding bias due to unmeasured or unknown variables. OBJECTIVES: This paper examines the potential amplification of such biases when correlated exposure variables are included in regression models. METHODS: We use directed acyclic graphs (DAGs) to describe different simple scenarios involving residual confounding. We derive expressions for the expected value of the resulting bias using linear models and multiple linear regression. RESULTS: Approaches to the analysis of mixtures that involve regressing the outcome on several exposures simultaneously can in some cases amplify rather than reduce confounding bias. DISCUSSIONS: The problem of bias amplification can worsen with stronger correlation between mixture components or when more mixture components are included in the model. CONCLUSIONS: Investigators must consider steps to minimize possible bias amplification in the design and analysis of epidemiologic studies of multiple correlated exposures. This may be particularly important when biomarkers of exposure are used.