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Statistical Methods for Modeling Exposure Variables Subject to Limit of Detection

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Abstract

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.

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Funding

This research was partially supported by NIH R01ES032808, NIH R01ES032826, and NIH UH3OD023305, and CDC/NIOSH grant U01OH012637.

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Authors and Affiliations

  1. Department of Population Health, New York University Grossman School of Medicine, New York, NY, 10016, USA

    Eunsil Seok, Akhgar Ghassabian, Yuyan Wang & Mengling Liu

  2. Department of Pediatrics, New York University Grossman School of Medicine, New York, NY, 10016, USA

    Akhgar Ghassabian

Authors
  1. Eunsil Seok
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  2. Akhgar Ghassabian
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  4. Mengling Liu
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Correspondence to Mengling Liu.

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Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 3528 KB)

Appendix A: Figure A1. Data flow diagram for deriving final dataset for analysis. Figure A2. Histogram of original and log-transformed and standardized exposures in NHANES dataset. Table A1. Coefficient estimates (and standard error) of exposure variables in a single exposure model. Table A2. Coefficient estimate (and standard error) of exposure variables in a multiple exposures model. Table A3. Coefficient estimates (and standard error) of AGE and IPR variables in an exposure-outcome model. Figure A3 - A14 Estimated effects of GENDER, RACE, EDU, MWD, and CREATININE variables with \(95\%\) confidence intervals when a chemical exposure is an outcome in a model. Table A4. LOD values for two exposure variables and corresponding missing rates. Table A5. Results from five methods in single exposure model under Scenario 2. Figure A15. Histogram of generated skewed exposure variable with different missing rates due to LOD.

Appendix B: Details on ML approach for single exposure model.

Supplementary file 2 (html 2718 KB)

Appendix C: R markdown document implementing all descriptive and analytical processes of the NHANES data application in this article.

Supplementary file 3 (pdf 30 KB)

Appendix D: R code for preprocessing and merging four datasets from NHANES 2013-2014 cycle.

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Seok, E., Ghassabian, A., Wang, Y. et al. Statistical Methods for Modeling Exposure Variables Subject to Limit of Detection. Stat Biosci (2023). https://doi.org/10.1007/s12561-023-09408-3

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