Sand Salomon J, von Rosen Dietrich, Filipsson Agneta Falk
Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden.
Risk Anal. 2003 Oct;23(5):1059-68. doi: 10.1111/1539-6924.00381.
A benchmark dose (BMD) is the dose of a chemical that corresponds to a predetermined increase in the response (the benchmark response, BMR) of a health effect. In this article, a method (the hybrid approach) for benchmark calculations from continuous dose-response information is investigated. In the formulation of the methodology, a cut-off value for an adverse health effect has to be determined. It is shown that the influence of variance on the hybrid model depends on the choice of determination of the cut-off point. If the cut-off value is determined as corresponding to a specified tail proportion of the control distribution, P(0), the BMD becomes biased upward when the variance is biased upward. On the contrary, if the cut-off value is directly determined to some level of the continuous response variable, the BMD becomes biased upward when the variance is biased downward. A simulation study was also performed in which the accuracy and precision of the BMD was compared for the two ways of determining the cut-off value. In general, considering BMRs of 1, 5, and 10% (additional risk) the precision of the BMD became higher when the cut-off value was estimated by specifying P(0), relative to the case with a direct determination. Use of the square-root of the maximum-likelihood estimator of the variance in BMD estimation may provide a bias that is reflected by the cut-off formulation (downward bias if specifying P(0), and upward bias if specifying the cut-off, c, directly). This feature may be reduced if an unbiased estimator of the standard deviation is used in the calculations.
基准剂量（BMD）是指与健康效应的预定反应增加量（基准反应，BMR）相对应的化学物质剂量。在本文中，研究了一种从连续剂量反应信息进行基准计算的方法（混合方法）。在该方法的制定过程中，必须确定不良健康效应的临界值。结果表明，方差对混合模型的影响取决于临界值确定方式的选择。如果将临界值确定为对应于对照分布的指定尾部比例P(0)，则当方差向上偏倚时，BMD会向上偏倚。相反，如果将临界值直接确定为连续反应变量的某个水平，则当方差向下偏倚时，BMD会向上偏倚。还进行了一项模拟研究，比较了两种确定临界值方式下BMD的准确性和精密度。一般来说，考虑1%、5%和10%（额外风险）的BMR，相对于直接确定临界值的情况，当通过指定P(0)来估计临界值时，BMD的精密度会更高。在BMD估计中使用方差的最大似然估计值的平方根可能会产生一种偏差，这种偏差会因临界值公式而体现出来（如果指定P(0)则为向下偏差，如果直接指定临界值c则为向上偏差）。如果在计算中使用标准差的无偏估计量，这种特征可能会减少。
