Semmar Nabil, Bruguerolle Bernard, Boullu-Ciocca Sandrine, Simon Nicolas
Laboratory of Medical Pharmacology, Medical School of Marseilles, UPRES EA 3784, 27 Bd Jean Moulin, 13385, Marseilles cedex 5, France.
J Pharmacokinet Pharmacodyn. 2005 Aug;32(3-4):333-58. doi: 10.1007/s10928-005-0040-4.
To be analyzed, the heterogeneity characterizing biological data calls for using appropriate models involving numerous variables. A high variable number could become problematic when one needs to determine a priori the most significant variable combination in order to reduce the inter-individual variability (IIV). Alternatively to multiple introductions of single variables, we propose a single introduction of a multivariate variable. We present cluster analysis as a stratification strategy that combines the initial single covariates to build a multivariate categorical covariate. It is an exploratory multivariate analysis that outlines homogeneous categories of individuals (clusters) according to similarities from the set of covariates. It includes many clustering techniques combining a distance measure and a linkage algorithm, and leading to various stratification patterns. The cluster analysis approach is illustrated by a case study on cortisol kinetics in 82 patients after intravenous bolus administration of synacthen (synthetic corticotropin). Using NONMEM, a basic infusion model was initially achieved for cortisol, and then a classical covariate selection was applied to improve IIV. The best fit was between the elimination rate constant k and the body mass index (BMI), which improved IIV of k. An alternative method is presented consisting in the population into homogeneous and non-overlapping groups by applying a cluster analysis. Such categorization (or clustering) was carried out using Euclidean distance and complete-linkage algorithm. This algorithm gave five dissimilar clusters that differed by increasing BMI, obesity duration, and waist-hip ratio. The dispersion of k according to the five clusters showed three distinctvariation ranges a priori, which corresponded a posteriori(after NONMEM modeling) to three sub-populations of k. After grouping the clusters that had similar variation ranges of k, we obtained three final clusters representing non-obese, intermediate, and extreme obese sub-populations. The pharmacokinetic model based on three clusters was better than the basic model, similar to the classical covariate model, but had a stronger interpretability: It showed that the stimulation and elimination of cortisol were higher in the extreme obese followed by intermediate then non-obese subjects.
为了进行分析，生物数据的异质性特征需要使用涉及众多变量的适当模型。当需要先验地确定最显著的变量组合以减少个体间变异性（IIV）时，变量数量过多可能会成为问题。作为单个变量多次引入的替代方法，我们建议引入一个多变量。我们将聚类分析作为一种分层策略，它结合初始的单个协变量来构建一个多变量分类协变量。这是一种探索性多变量分析，根据协变量集的相似性勾勒出个体的同质类别（聚类）。它包括许多结合距离度量和连锁算法的聚类技术，并导致各种分层模式。通过对82例患者静脉推注合成促肾上腺皮质激素（synthetic corticotropin）后皮质醇动力学的案例研究来说明聚类分析方法。使用NONMEM，最初为皮质醇建立了一个基本输注模型，然后应用经典的协变量选择来改善IIV。最佳拟合是在消除速率常数k和体重指数（BMI）之间，这改善了k的IIV。提出了另一种方法，即通过应用聚类分析将总体分为同质且不重叠的组。这种分类（或聚类）使用欧几里得距离和完全连锁算法进行。该算法给出了五个不同的聚类，它们在BMI、肥胖持续时间和腰臀比增加方面存在差异。根据这五个聚类，k的离散度先验地显示出三个不同的变化范围，后验地（在NONMEM建模之后）对应于k的三个亚组。在对k变化范围相似的聚类进行分组后，我们得到了代表非肥胖、中度和极度肥胖亚组的三个最终聚类。基于三个聚类的药代动力学模型比基本模型更好，与经典协变量模型相似，但具有更强的可解释性：它表明极度肥胖受试者中皮质醇的刺激和消除高于中度肥胖受试者，然后是非肥胖受试者。
