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Simultaneous modeling of detection rate and exposure concentration using semi-continuous models to identify exposure determinants when left-censored data may be a true zero

Journal of Exposure Science & Environmental Epidemiology volume 31, pages 1047–1056 (2021)Cite this article

Abstract

Background

Most methods for treating left-censored data assume the analyte is present but not quantified. Biased estimates may result if the analyte is absent such that the unobserved data represents a mixed exposure distribution with an unknown proportion clustered at zero.

Objective

We used semi-continuous models to identify time and industry trends in 52,457 OSHA inspection lead sample results.

Method

The first component of the semi-continuous model predicted the probability of detecting concentrations ≥ 0.007 mg/m3 (highest estimated detection limit, 62% of measurements). The second component predicted the median concentration of measurements ≥ 0.007 mg/m3. Both components included a random-effect for industry and fixed-effects for year, industry group, analytical method, and other variables. We used the two components together to predict median industry- and time-specific lead concentrations.

Results

The probabilities of detectable concentrations and the median detected concentrations decreased with year; both were also lower for measurements analyzed for multiple (vs. one) metals and for those analyzed by inductively-coupled plasma (vs. atomic absorption spectroscopy). The covariance was 0.30 (standard error = 0.06), confirming the two components were correlated.

Significance

We identified determinants of exposure in data with over 60% left-censored, while accounting for correlated relationships and without assuming a distribution for the censored data.

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Fig. 1: Distribution of predicted probability of a measurement being ≥0.007 mg/m3 for 575 industries.
Fig. 2: Distribution of predicted GMs for all 575 industries.
Fig. 3: Predicted probability of a measurement being ≥0.007 mg/m3 vs. predicted median detected concentration.

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Acknowledgements

We thank Janet Tooze for providing the SAS macro to conduct the mixed distribution modeling and for providing permission to include that code in our supplemental materials. This work was funded by the Intramural Research Program of the Division of Cancer Epidemiology and Genetics, NCI.

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Authors and Affiliations

  1. National Cancer Institute, Division of Cancer Epidemiology & Genetics, Occupational and Environmental Epidemiology Branch, Rockville, MD, USA

    Melissa C. Friesen & Pamela Dopart

  2. National Cancer Institute, Division of Cancer Epidemiology & Genetics, Biostatistics Branch, Rockville, MD, USA

    Hyoyoung Choo-Wosoba, Paul S. Albert & Bin Zhu

  3. Institut de recherche Robert-Sauvé en santé et en sécurité du travail, Chemical and Biological Hazards Prevention, Montréal, QC, Canada

    Philippe Sarazin

  4. Department of Occupational and Environmental Health, Université de Montréal, Montréal, QC, Canada

    Philippe Sarazin & Jérôme Lavoué

  5. Department of Occupational and Environmental Health, University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA

    Jooyeon Hwang

  6. Office of Intramural Research, Center for Information Technology, National Institutes of Health, Bethesda, MD, USA

    Daniel E. Russ

  7. Yale School of Public Health, Yale University, New Haven, CT, USA

    Nicole C. Deziel

Authors
  1. Melissa C. Friesen
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Correspondence to Melissa C. Friesen.

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Friesen, M.C., Choo-Wosoba, H., Sarazin, P. et al. Simultaneous modeling of detection rate and exposure concentration using semi-continuous models to identify exposure determinants when left-censored data may be a true zero. J Expo Sci Environ Epidemiol 31, 1047–1056 (2021). https://doi.org/10.1038/s41370-021-00331-7

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