Application of the four-parameter logistic model to bioassay: comparison with slope ratio and parallel line models.
Application of the four-parameter logistic model to bioassay: comparison with slope ratio and parallel line models.
复制标题
四参数 Logistic 模型在生物测定中的应用：与斜率和平行线模型的比较。
作者：
A. Vølund
具有S型对数剂量关系的定量反应的生物测定可以通过将非线性剂量-反应模型直接与数据进行拟合来进行分析。证明了以前应用于免疫分析的四参数Logistic模型(Healy 1972)适用于胰岛素的自由脂肪细胞生物测定(Moody，Stan，Stan和Gliemann 1974)。结果表明，生物测定的标准斜率模型和平行线模型在极端剂量区可近似于Logistic模型，而平行线模型可用于中等剂量区。描述了应用于一般试验设计的四参数Logistic模型的全部统计分析。为了便于计算，开发了APL计算机程序，包括非线性曲线拟合、拟合度和平行度检验以及相对效力的点和区间估计。给出了根据这些方法分析的胰岛素的游离脂肪细胞生物测定的例子。对效力的有效估计要求将剂量集中在剂量-反应曲线斜率最大的区域。关于测试的平行性和允许化验之间的可变性和不可预测的可能性，可能更可取的是使用剂量分布在大范围内的化验设计，并应用剂量-反应模型，该模型与四参数Logistic模型一样，能够适用于整个可行的剂量范围。
Bioassays with a quantitative response showing a sigmoid log-dose relationship can be analysed by fitting a non-linear dose-response model directly to the data. It is demonstrated that the four-parameter logistic model, previously applied to immunoassay (Healy 1972), is applicable to the free fat cell bioassay of insulin (Moody, Stan, Stan and Gliemann 1974). It is shown that the standard slope ratio and parallel line models for bioassay can be considered as approximations to the logistic in the extreme dose regions, while the parallel line model can be expected to fit in the middle region. The full statistical analysis of the four-parameter logistic model applied to a general assay design is described. An APL computer program has been developed to facilitate the calculations, which include non-linear curve-fitting, tests of goodness of fit and parallelity, as well as point and interval estimates of the relative potency. Examples of free fat cell bioassays of insulin that have been analysed according to these methods are given. Efficient estimation of the potency calls for concentrating the doses in the region with the steepest slope of the dose-response curve. With respect to testing the parallelity and to allow for assay-to-assay variability and unpredictable potencies, it may be preferable to use an assay design with doses distributed over a wide range and to apply a dose-response model which, like the four-parameter logistic, is capable of fitting over the whole feasible dose range.