Pharmacodynamic Models: Parameterizing the Hill Equation, Michaelis-Menten, the Logistic Curve, and Relationships Among These Models
Pharmacodynamic Models: Parameterizing the Hill Equation, Michaelis-Menten, the Logistic Curve, and Relationships Among These Models
复制标题
DOI：
10.1080/10543406.2012.756496
复制
发表时间：
2013-05-01
影响因子：
1.1
通讯作者：
Turner, J. Rick
中科院分区：
文献类型：
--
作者：
Reeve, Russell;Turner, J. Rick
希尔方程经常用于剂量反应或暴露反应建模。 Hill 模型的别名包括 Emax 模型和 Michaelis-Menten 模型。对于适当的参数化、如何解释参数、文献中找到的各种参数化的含义是什么以及哪种参数化最接近将希尔方程拟合到数据时产生的统计推论，存在一些困惑。在本文中，我们提出了希尔模型的几个等效版本；表明它们在给定剂量产生相同预测方面是等效的，并且在相同意义上等效于四参数逻辑模型；并推断哪种参数化在具有最小统计曲率和更好的多重共线性的意义上是最佳的。
The Hill equation is often used in dose-response or exposure-response modeling. Aliases for the Hill model include the Emax model, and the Michaelis-Menten model. There is confusion about the appropriate parameterization, how to interpret the parameters, what the meaning is of the various parameterizations found in the literature, and which parameterization best approximates the statistical inferences produced when fitting the Hill equation to data. In this paper, we present several equivalent versions of the Hill model; show that they are equivalent in terms of yielding the same prediction for a given dose, and are equivalent to the four-parameter logistic model in this same sense; and deduce which parameterization is optimal in the sense of having the least statistical curvature and preferable multicollinearity.