Statistical Methods for Modeling Exposure Variables Subject to Limit of Detection

Environmental health research aims to assess the impact of environmental exposures, making it crucial to understand their effects due to their broad impacts on the general population. However, a common issue with measuring exposures using bio-samples in laboratory is that values below the limit of detection (LOD) are either left unreported or inaccurately read by machines, which subsequently influences the analysis and assessment of exposure effects on health outcomes. We address the challenge of handling exposure variables subject to LOD when they are treated as either covariates or an outcome. We evaluate the performance of commonly-used methods including complete-case analysis and fill-in method, and advanced techniques such as multiple imputation, missing-indicator model, two-part model, Tobit model, and several others. We compare these methods through simulations and a dataset from NHANES 2013–2014. Our numerical studies show that the missing-indicator model generally yields reasonable estimates when considering exposure variables as covariates under various settings, while other methods tend to be sensitive to the LOD-missing proportions and/or distributional skewness of exposures. When modeling an exposure variable as the outcome, Tobit model performs well under Gaussian distribution and quantile regression generally provides robust estimates across various shapes of the outcome’s distribution. In the presence of missing data due to LOD, different statistical models should be considered for being aligned with scientific questions, model assumptions, requirements of data distributions, as well as their interpretations. Sensitivity analysis to handle LOD-missing exposures can improve the robustness of model conclusions.