贺娜娜, 孙金芳, 何杰宇, 余小金. 基于贝叶斯模型平均的基准剂量估计及其在白银市人群镉暴露评估中的应用[J]. 环境与职业医学, 2022, 39(9): 1004-1010. DOI: 10.11836/JEOM22055
引用本文: 贺娜娜, 孙金芳, 何杰宇, 余小金. 基于贝叶斯模型平均的基准剂量估计及其在白银市人群镉暴露评估中的应用[J]. 环境与职业医学, 2022, 39(9): 1004-1010. DOI: 10.11836/JEOM22055
HE Nana, SUN Jinfang, HE Jieyu, YU Xiaojin. Benchmark dose estimation based on Bayesian model averaging and its application to evaluation of cadmium exposure of population in Baiyin[J]. Journal of Environmental and Occupational Medicine, 2022, 39(9): 1004-1010. DOI: 10.11836/JEOM22055
Citation: HE Nana, SUN Jinfang, HE Jieyu, YU Xiaojin. Benchmark dose estimation based on Bayesian model averaging and its application to evaluation of cadmium exposure of population in Baiyin[J]. Journal of Environmental and Occupational Medicine, 2022, 39(9): 1004-1010. DOI: 10.11836/JEOM22055

基于贝叶斯模型平均的基准剂量估计及其在白银市人群镉暴露评估中的应用

Benchmark dose estimation based on Bayesian model averaging and its application to evaluation of cadmium exposure of population in Baiyin

  • 摘要: 背景

    最优模型法估计基准剂量(BMD)时未考虑模型选择的不确定性,国内暂无使用贝叶斯模型平均(BMA)估计BMD的研究。

    目的

    将BMA应用于我国镉污染的暴露评估研究,讨论BMA在基于剂量-反应模型的BMD估计中的作用,为有害物质健康风险评估提供方法学支持。

    方法

    模拟研究基于甘肃省白银市某镉污染区数据获得的不同剂量-反应模型(Gamma、Log-logistic、Log-probit、Two-stage和Weibull模型)的参数和中国5个镉污染区的尿镉范围,模拟不同正确模型、不同剂量组数(5、8)、不同样本量(50、100、200)的模拟数据,比较BMA和最优模型法的优劣。实例分析使用甘肃省白银市某镉污染区的镉暴露数据。模拟研究和实例分析均以尿镉为镉暴露指标,β2-微球蛋白异常率为效应指标,基准反应设定为10%,分别使用正确模型(模拟数据时使用的模型)、最优模型法赤池信息准则(AIC)最小的模型和BMA估计BMD及其95%置信区间下限(BMDL);比较不同方法估计的BMD、BMDL及相对偏差。

    结果

    对于模拟研究,随着样本量或剂量组数增加,BMD的第5百分位数和第90百分位数区间大致呈现变窄趋势;当正确模型为单一模型时,BMA估计的BMD相对偏差大于最优模型法;当正确模型为等权重混合模型时,BMA估计的BMD相对偏差小于最优模型法。基于实例数据,最优模型为Log-probit模型(AIC=1814.46),其次为Log-logistic模型(AIC=1814.57);Log-probit模型、Log-logistic模型和BMA估计的BMD(BMDL)分别为3.46(2.68)、3.16(2.33)和2.92(2.07) μg·g−1

    结论

    在正确模型已知时,最优模型法依然是值得推荐的方法;但在有害物质剂量-反应关系高度不确定或来源人群、暴露分组等不同时,BMA与最优模型法相比,理论上更充分地考虑了可能存在的多个备选模型,能提供更为稳定的BMD和BMDL估计。

     

    Abstract: Background

    The optimal model method for estimation of benchmark dose (BMD) does not consider the uncertainty of model selection. There is a lack of studies on using Bayesian model averaging (BMA) to estimate BMD.

    Objective

    To apply BMA to the exposure assessment of cadmium pollution in China, discuss the role of BMA in estimating BMD based on dose-response models, and to provide methodological support for health risk assessment of hazardous substances.

    Methods

    The parameters of five dose-response models (Gamma, Log-logistic, Log-probit, Two-stage, and Weibull models) estimated from the data from a cadmium-contaminated area in Baiyin City of Gansu Province and the urinary cadmium ranges in five cadmium-contaminated areas in China were used to simulate the data of varied correct models with different numbers of dosage groups (5 and 8) and different sample sizes (50, 100, and 200), then the performance of BMA and traditional optimal model were compared. The case analysis used the cadmium exposure data in Baiyin, Gansu Province. All analyses set urinary cadmium as the indicator of cadmium exposure, the abnormal rate of β2-microglobulin as the effect indicator, and the benchmark response to 10%. The correct model (the model used when simulating data), optimal model the model with smallest Akaike information criterion (AIC), and BMA were used to estimate BMD and lower confidence limit of benchmark dose (BMDL); the BMDs, BMDLs, and relative deviations from different methods were compared.

    Results

    In the simulation study, with increasing sample size or the number of dosage groups, the intervals of the 5th percentile and the 90th percentile of BMD tended to be narrower; when the correct model was a single model, the relative deviation of BMD estimation by BMA was greater than that of the traditional optimal model; when the correct model was an equal weight mixed model, the relative deviation of BMD estimation by BMA was less than that by the traditional optimal model. For the data of cadmium-contaminated areas, the optimal model was a Log-probit model (AIC=1814.46), followed by a Log-logistic model (AIC=1814.57); the BMDs (BMDLs) estimated by the Log-probit model, the Log-logistic model, and BMA were 3.46 (2.68), 3.16 (2.33), and 2.92 (2.07) μg·g−1, respectively.

    Conclusion

    The traditional optimal model is still recommended when the correct model is known. However, when the dose-response relationship of a hazardous substance is uncertain or with different sources or exposure grouping, compared with the traditional optimal model, BMA theoretically provides more stable estimation of BMD and BMDL by considering multiple possible alternative models.

     

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