Mathematician, retired.
Health Phys. 2019 May;116(5):637-646. doi: 10.1097/HP.0000000000000993.
The dose values used in dose-response analyses are often the result of a computer model. Epistemic uncertainties of the model application make it necessary to perform an uncertainty analysis. Such uncertainties are model parameters, model formulations, and input data subject to either classical or Berkson additive or multiplicative measurement error. Epistemic uncertainties are often shared among the computed dose values of all individuals in a cohort or among groups thereof. The effect of these uncertainties on the estimate of the dose-response parameter in least-squares linear regression is difficult to judge. Additive classical error is known to bias the estimate towards lower values (attenuation). The method suggested in this paper is applicable in situations where any combination of uncertainties mentioned above is involved. All it requires is a random sample of dose vectors taken from their joint subjective probability distribution. Such a sample is the output of a Monte Carlo uncertainty analysis of the model application. The covariance matrix of the vectors is used in the computation of correction factors that are possibly true, given the dose vector used in the estimation of the dose-response parameter. The efficiency of the method is demonstrated with five cases. They differ by the combination of uncertainties involved in the uncertainty analysis of a small illustrative dose reconstruction model.
在剂量反应分析中使用的剂量值通常是计算机模型的结果。模型应用的认知不确定性使得有必要进行不确定性分析。这种不确定性是模型参数、模型公式和输入数据，可能存在经典的或 Berkson 加性或乘法测量误差。认知不确定性通常在队列中所有个体的计算剂量值之间或其分组之间共享。这些不确定性对最小二乘线性回归中剂量反应参数估计的影响很难判断。已知经典加性误差会使估计值偏向低值（衰减）。本文提出的方法适用于涉及上述任何组合不确定性的情况。它只需要从它们的联合主观概率分布中抽取剂量向量的随机样本。这样的样本是模型应用不确定性的蒙特卡罗分析的输出。在计算校正因子时，将使用向量的协方差矩阵，这些校正因子可能是基于用于估计剂量反应参数的剂量向量的真实值。该方法的效率通过五个案例进行了演示。它们的区别在于用于小说明剂量重建模型的不确定性分析中涉及的不确定性的组合不同。
