National Institute for Public Health and the Environment (RIVM), Bilthoven, The Netherlands.
Altern Lab Anim. 2013 Mar;41(1):19-31. doi: 10.1177/026119291304100105.
In environmental risk assessment, Species Sensitivity Distributions (SSDs) can be applied to estimate a PNEC (Predicted No-Effect Concentration) for a chemical substance, when sufficient data on species toxicities are available. The European Chemicals Agency (ECHA) recommendation is 10 biological species. The question addressed in this paper, is whether QSAR-predicted toxicities can be included in SSD based PNEC estimates, and whether any modifications need to be made to account for the uncertainty in the QSAR-model estimates. This problem is addressed from a probabilistic modelling point of view. From classical analysis of variation (ANOVA), we review how the error-in-data SSD problem is similar to separation into between-group and within-group variance. ECHA guidance suggests averaging similar endpoint data for a species, which is consistent with group means, as in ANOVA. This exercise reveals that error-in data reduces the estimation of the between species variation, i.e. the SSD variance, rather than enlarging it. A Bayesian analysis permits the assessment of the uncertainty of the SSD mean and variance parameters for given values of mean species toxicity error. This requires a hierarchical model. Prototyping this model for an artificial five-species data set seems to suggest that the influence of data error is relatively minor. Moreover, when neglecting this data error, a slightly conservative estimate of the SSD results. Hence, we suggest including (model-predicted) data as model point estimates and handling the SSD as usual. The Bayesian simulation of the error-in-data SSD leads to predictive distributions, being an average of posterior spaghetti plot densities or cumulative distributions. We derive new predictive extrapolation constants with several improvements over previous median uncertainty log10HC5 estimates, in that they are easily calculable from spreadsheet Student-t functions and based on a more realistic uniform prior for the SSD standard deviation. Other advantages are that they are single-number extrapolation constants and they are more sensitive to small sample size.
在环境风险评估中，当有足够的物种毒性数据时，可以应用物种敏感性分布 (SSD) 来估计化学物质的预测无效应浓度 (PNEC)。欧洲化学品管理局 (ECHA) 的建议是使用 10 种生物物种。本文探讨的问题是，QSAR 预测的毒性是否可以包含在基于 SSD 的 PNEC 估计中，以及是否需要进行任何修改来考虑 QSAR 模型估计的不确定性。这个问题从概率建模的角度来解决。从经典方差分析 (ANOVA) 来看，我们回顾了数据 SSD 误差问题与分组方差和组内方差的分离有何相似之处。ECHA 指南建议对物种的相似终点数据进行平均，这与 ANOVA 中的组平均值一致。这项研究表明，数据误差会减小物种间变异（即 SSD 变异）的估计，而不是扩大它。贝叶斯分析允许在给定物种平均毒性误差值的情况下，评估 SSD 均值和方差参数的不确定性。这需要一个层次模型。为一个人工的五物种数据集原型化这个模型似乎表明数据误差的影响相对较小。此外，当忽略这个数据误差时，SSD 的结果略为保守。因此，我们建议将（模型预测的）数据作为模型点估计，并按常规处理 SSD。数据误差 SSD 的贝叶斯模拟会导致预测分布，即后验意大利面条图密度或累积分布的平均值。我们提出了新的预测外推常数，与之前的中值不确定性对数 10HC5 估计相比有几个改进，因为它们可以从电子表格学生 t 函数中轻松计算得出，并且基于 SSD 标准差的更现实的均匀先验。其他优点是它们是单数值外推常数，并且对小样本量更敏感。
