Abstract
We developed a statistical model that quantitatively incorporated the stochastic fluctuations of values, which were estimated as Bayesian credible intervals (BCIs), to analyze environmental monitoring data. We used α-hexabromocyclododecane (α-HBCD) diastereomer compositions of water samples that included data points below limit of quantification. To avoid replacing “not detected (ND)” values with irrelevant values in data analysis, we substituted ND with observed values from the measurement system upon examination of the model. In our study, it was assumed that the magnitude of stochastic fluctuations of observed values in environmental samples was identical to that in iterative measurements of a standard solution at the lowest concentration. Using this model, α-HBCD diastereomer compositions could be estimated along with BCIs even for samples collected from sites where concentrations of α-HBCD were ND or near limit of quantification. The brackish areas in our study showed relatively wide ranges in composition for the 95% BCIs compared with samples from fresh water areas. In the brackish areas, concentrations of HBCD were frequently ND or near limit of quantification. Using this model, it was unnecessary to replace ND with zero or limit of quantification in data analysis, and an environmental assessment could be achieved using all of the data. Therefore, this model is considered to be a widely applicable approach in the analysis of environmental monitoring data including ND.
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The authors thank to Dr. Tetsuo Yamano (Osaka City Institute of Public Health and Environmental Sciences) for his helpful suggestions on an earlier draft of the manuscript.
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WinBUGS code that we used in this study was as follows:
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Ichihara, M., Yamamoto, A., Kakutani, N. et al. A Bayesian approach for estimating hexabromocyclododecane (HBCD) diastereomer compositions in water using data below limit of quantification. Environ Sci Pollut Res 24, 2667–2674 (2017). https://doi.org/10.1007/s11356-016-7990-5
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DOI: https://doi.org/10.1007/s11356-016-7990-5