Cluster analysis: An alternative method for covariate selection in population pharmacokinetic modeling

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.