Bailey J M, Gregg K M
Department of Anesthesiology, Emory University School of Medicine, Atlanta, Georgia 30322, USA.
Anesthesiology. 1997 Apr;86(4):825-35. doi: 10.1097/00000542-199704000-00013.
Pharmacodynamic data frequently consist of the binary assessment (a "yes" or "no" answer) of the response to a defined stimulus (verbal stimulus, intubation, skin incision, and so on) for multiple patients. The concentration-effect relation is usually reported in terms of C50, the drug concentration associated with a 50% probability of drug effect, and a parameter the authors denote gamma, which determines the shape of the concentration-probability of effect curve. Accurate estimation of gamma, a parameter describing the entire curve, is as important as the estimation of C50, a single point on this curve. Pharmacodynamic data usually are analyzed without accounting for interpatient variability. The authors postulated that accounting for interpatient variability would improve the accuracy of estimation of gamma and allow the estimation of C50 variability.
A probit-based model for the individual concentration-response relation was assumed, characterized by two parameters, C50 and gamma. This assumption was validated by comparing probit regression with the more commonly used logistic regression of data from individual patients found in the anesthesiology literature. The model was then extended to analysis of population data by assuming that C50 has a log-normal distribution. Population data were analyzed in terms of three parameters, (C50), the mean value of C50 in the population; omega, the standard deviation of the distribution of the logarithm of C50; and gamma. The statistical characteristics of the technique were assessed using simulated data. The data were generated for a range of gamma and omega values, assuming that C50 and gamma had a log-normal distribution.
The probit-based model describes data from individual patients and logistic regression does. Population analysis using the extended probit model accurately estimated (C50), gamma, and omega for a range of values, despite the fact that the technique accounts for C50 variability but not gamma variability.
A probit-based method of pharmacodynamic analysis of pooled population data facilitates accurate estimation of the concentration-response curve.
药效学数据通常由多名患者对特定刺激（言语刺激、插管、皮肤切开等）的反应的二元评估（“是”或“否”回答）组成。浓度-效应关系通常用C50来表示，即与药物效应发生概率为50%相关的药物浓度，以及作者表示为γ的一个参数，该参数决定效应浓度-概率曲线的形状。准确估计γ这个描述整条曲线的参数，与估计C50这个曲线上的单个点同样重要。药效学数据的分析通常未考虑患者间的变异性。作者推测，考虑患者间变异性将提高γ估计的准确性，并能估计C50的变异性。
假定个体浓度-反应关系的基于概率单位的模型，其特征由两个参数C50和γ表示。通过将概率单位回归与麻醉学文献中个体患者数据更常用的逻辑回归进行比较，验证了这一假定。然后通过假定C50呈对数正态分布，将该模型扩展到群体数据分析。群体数据根据三个参数进行分析，即（C50），群体中C50的均值；ω，C^50对数分布的标准差；以及γ。使用模拟数据评估该技术的统计学特征。假定C50和γ呈对数正态分布，针对一系列γ和ω值生成数据。
基于概率单位的模型能够描述个体患者的数据，逻辑回归也能。使用扩展概率单位模型进行的群体分析，针对一系列值准确估计了（C50）、γ和ω，尽管该技术考虑了C50的变异性，但未考虑γ的变异性。
基于概率单位的合并群体数据药效学分析方法有助于准确估计浓度-反应曲线。
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