Shao Kan, Gift Jeffrey S
ORISE Postdoctoral Fellow, National Center for Environmental Assessment, U.S. Environmental Protection Agency.
National Center for Environmental Assessment, U.S. Environmental Protection Agency, Triangle Park, NC, USA.
Risk Anal. 2014 Jan;34(1):101-20. doi: 10.1111/risa.12078. Epub 2013 Jun 11.
The benchmark dose (BMD) approach has gained acceptance as a valuable risk assessment tool, but risk assessors still face significant challenges associated with selecting an appropriate BMD/BMDL estimate from the results of a set of acceptable dose-response models. Current approaches do not explicitly address model uncertainty, and there is an existing need to more fully inform health risk assessors in this regard. In this study, a Bayesian model averaging (BMA) BMD estimation method taking model uncertainty into account is proposed as an alternative to current BMD estimation approaches for continuous data. Using the "hybrid" method proposed by Crump, two strategies of BMA, including both "maximum likelihood estimation based" and "Markov Chain Monte Carlo based" methods, are first applied as a demonstration to calculate model averaged BMD estimates from real continuous dose-response data. The outcomes from the example data sets examined suggest that the BMA BMD estimates have higher reliability than the estimates from the individual models with highest posterior weight in terms of higher BMDL and smaller 90th percentile intervals. In addition, a simulation study is performed to evaluate the accuracy of the BMA BMD estimator. The results from the simulation study recommend that the BMA BMD estimates have smaller bias than the BMDs selected using other criteria. To further validate the BMA method, some technical issues, including the selection of models and the use of bootstrap methods for BMDL derivation, need further investigation over a more extensive, representative set of dose-response data.
基准剂量（BMD）方法已被认可为一种有价值的风险评估工具，但风险评估者在从一组可接受的剂量反应模型结果中选择合适的BMD/BMDL估计值时，仍面临重大挑战。当前方法未明确处理模型不确定性，因此目前需要在这方面为健康风险评估者提供更全面的信息。在本研究中，提出了一种考虑模型不确定性的贝叶斯模型平均（BMA）BMD估计方法，作为连续数据当前BMD估计方法的替代方法。使用Crump提出的“混合”方法，首先应用两种BMA策略，包括“基于最大似然估计”和“基于马尔可夫链蒙特卡罗”方法，作为示范从实际连续剂量反应数据计算模型平均BMD估计值。所检验的示例数据集结果表明，就更高的BMDL和更小的第90百分位数区间而言，BMA BMD估计值比具有最高后验权重的单个模型的估计值具有更高的可靠性。此外，进行了一项模拟研究以评估BMA BMD估计器的准确性。模拟研究结果表明，BMA BMD估计值比使用其他标准选择的BMD具有更小的偏差。为了进一步验证BMA方法，一些技术问题，包括模型选择和用于推导BMDL的自助法的使用，需要在更广泛、更具代表性的剂量反应数据集上进行进一步研究。
