Gagnon R C, Peterson J J
SmithKline Beecham Pharmaceuticals, Statistical Sciences Department (UP-4205), Collegeville, Pennsylvania 19426-0989, USA.
J Pharmacokinet Biopharm. 1998 Feb;26(1):87-102. doi: 10.1023/a:1023228925137.
The area under the curve (AUC) of the concentration-time curve for a drug or metabolite, and the variation associated with the AUC, are primary results of most pharmacokinetic (PK) studies. In nonclinical PK studies, it is often the case that experimental units contribute data for only a single time point. In such cases, it is straightforward to apply noncompartmental methods to determine an estimate of the AUC. In this report, we investigate noncompartmental estimation of the AUC using the long-trapezoidal rule during the elimination phase of the concentration-time profile, and we account for the underlying distribution of data at each sampling time. For data that follow a normal distribution, the log-trapezoidal rule is applied to arithmetic means at each time point of the elimination phase of the concentration-time profile. For data that follow a lognormal distribution, as is common with PK data, the log-trapezoidal rule is applied to geometric means at each time point during elimination. Since the log-trapezoidal rule incorporates nonlinear combinations of mean concentrations at each sampling time, obtaining an estimate of the corresponding variation about the AUC is not straightforward. Estimation of this variance is further complicated by the occurrence of lognormal data. First-order approximations to the variance of AUC estimates are derived under the assumptions of normality, and lognormality, of concentrations at each sampling time. AUC estimates and variance approximations are utilized to form confidence intervals. Accuracies of confidence intervals are tested using simulation studies.
药物或代谢物浓度-时间曲线的曲线下面积（AUC）以及与AUC相关的变异，是大多数药代动力学（PK）研究的主要结果。在非临床PK研究中，通常实验单位仅为单个时间点提供数据。在这种情况下，应用非房室方法来确定AUC的估计值很简单。在本报告中，我们研究了在浓度-时间曲线的消除阶段使用长梯形法则对AUC进行非房室估计，并考虑了每个采样时间数据的潜在分布。对于服从正态分布的数据，在浓度-时间曲线消除阶段的每个时间点，将对数梯形法则应用于算术平均值。对于服从对数正态分布的数据（PK数据常见），在消除过程中的每个时间点，将对数梯形法则应用于几何平均值。由于对数梯形法则包含了每个采样时间平均浓度的非线性组合，因此获得AUC相应变异的估计值并不简单。对数正态数据的出现使该方差的估计更加复杂。在每个采样时间浓度服从正态分布和对数正态分布的假设下，推导了AUC估计值方差的一阶近似值。利用AUC估计值和方差近似值来形成置信区间。通过模拟研究检验置信区间的准确性。
