A Bayesian generalized log-normal model to dynamically evaluate the distribution of pesticide residues in soil associated with population health risks

Exploring better models for evaluating the distribution of pesticide residues in soil and sediment is necessary to assess and avoid population health risk. Frequentist philosophy and probability are widely used in many studies to apply a log-normal distribution associated with the maximum likelihood estimation, which assumes fixed parameters and relies on a large sample size for long-run frequency. However, frequentist probability might not be suitable for analyzing pesticide residue distribution, whose parameters are affected by many complex factors and should be treated as unfixed. This study aimed to implement a Bayesian generalized log-normal (GLN) model to better understand the distribution of pesticide residues in soil and quantify population risks. The Bayesian GLN model, including location, scale, and shape parameters, was applied for the first time to dynamically evaluate pesticide residue distribution in soil and sediments. In addition, a comprehensive human health risk assessment of exposure to lindane via soil was conducted using the lifetime cancer risk for carcinogenic effect, margin of exposure for non-carcinogenic effect, and disability-adjusted life year for health damage. The Bayesian posterior analysis results indicated that the distribution of the concentration of some pesticide was better fitted to a log-Laplace (e.g., the mode value of shape parameter for lindane is 1.079) or showed mixtures of distributions within the family of log-normal distributions (e.g., the mode value of shape parameter for p,p'-DDE is 2.395), which can better explain the long-tail phenomenon of pesticide residue distribution and dynamically evaluate distribution models. For lindane, the 95% uncertainty bounds on the 95th percentile computed from 95% highest probability density regions (credible intervals) of three parameters by using the Bayesian p-box method were [2.063, 1558.609] ng/g, which is several orders of magnitude larger than the computed frequentist 95% confidence interval of [4.690, 8.095] ng/g and indicates that the population could have cancer risk concerns. These uncertainty analysis results from the Bayesian GLN approach indicated a larger variation of Lindane soil residues, which might reflect the complex and unpredictable mechanism of pesticide residue distribution including both unfixed models and distribution parameters. In summary, Bayesian GLN model is more flexible for the dynamic evaluation of pesticide soil residue distribution, retains posteriors for future data analysis, and could better quantify the uncertainties in population health risks. Therefore, this study can provide a novel and dynamical perspective of pesticide residue distribution and help better quantify health risks.