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

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.