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Imputation of Below Detection Limit Missing Data in Chemical Mixture Analysis with Bayesian Group Index Regression

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Listed:
  • Matthew Carli

    (Department of Biostatistics, School of Medicine, Virginia Commonwealth University, One Capitol Square, 830 East Main Street, Richmond, VA 23298, USA)

  • Mary H. Ward

    (Occupational and Environmental Epidemiology Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Rockville, MD 20850, USA)

  • Catherine Metayer

    (School of Public Health, University of California Berkeley, Berkeley, CA 94704, USA)

  • David C. Wheeler

    (Department of Biostatistics, School of Medicine, Virginia Commonwealth University, One Capitol Square, 830 East Main Street, Richmond, VA 23298, USA)

Abstract

There is growing scientific interest in identifying the multitude of chemical exposures related to human diseases through mixture analysis. In this paper, we address the issue of below detection limit (BDL) missing data in mixture analysis using Bayesian group index regression by treating both regression effects and missing BDL observations as parameters in a model estimated through a Markov chain Monte Carlo algorithm that we refer to as pseudo-Gibbs imputation. We compare this with other Bayesian imputation methods found in the literature (Multiple Imputation by Chained Equations and Sequential Full Bayes imputation) as well as with a non-Bayesian single-imputation method. To evaluate our proposed method, we conduct simulation studies with varying percentages of BDL missingness and strengths of association. We apply our method to the California Childhood Leukemia Study (CCLS) to estimate concentrations of chemicals in house dust in a mixture analysis of potential environmental risk factors for childhood leukemia. Our results indicate that pseudo-Gibbs imputation has superior power for exposure effects and sensitivity for identifying individual chemicals at high percentages of BDL missing data. In the CCLS, we found a significant positive association between concentrations of polycyclic aromatic hydrocarbons (PAHs) in homes and childhood leukemia as well as significant positive associations for polychlorinated biphenyls (PCBs) and herbicides among children from the highest quartile of household income. In conclusion, pseudo-Gibbs imputation addresses a commonly encountered problem in environmental epidemiology, providing practitioners the ability to jointly estimate the effects of multiple chemical exposures with high levels of BDL missingness.

Suggested Citation

  • Matthew Carli & Mary H. Ward & Catherine Metayer & David C. Wheeler, 2022. "Imputation of Below Detection Limit Missing Data in Chemical Mixture Analysis with Bayesian Group Index Regression," IJERPH, MDPI, vol. 19(3), pages 1-17, January.
    • Handle: RePEc:gam:jijerp:v:19:y:2022:i:3:p:1369-:d:734788
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    References listed on IDEAS

    as
    1. van Buuren, Stef & Groothuis-Oudshoorn, Karin, 2011. "mice: Multivariate Imputation by Chained Equations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 45(i03).
    2. David C. Wheeler & Salem Rustom & Matthew Carli & Todd P. Whitehead & Mary H. Ward & Catherine Metayer, 2021. "Assessment of Grouped Weighted Quantile Sum Regression for Modeling Chemical Mixtures and Cancer Risk," IJERPH, MDPI, vol. 18(2), pages 1-20, January.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    4. Gelman A., 2004. "Parameterization and Bayesian Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 537-545, January.
    5. David C. Wheeler & Salem Rustom & Matthew Carli & Todd P. Whitehead & Mary H. Ward & Catherine Metayer, 2021. "Bayesian Group Index Regression for Modeling Chemical Mixtures and Cancer Risk," IJERPH, MDPI, vol. 18(7), pages 1-19, March.
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    Cited by:

    1. David C. Wheeler & Joseph Boyle & Matt Carli & Mary H. Ward & Catherine Metayer, 2023. "Neighborhood Deprivation, Indoor Chemical Concentrations, and Spatial Risk for Childhood Leukemia," IJERPH, MDPI, vol. 20(4), pages 1-15, February.

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