Independent-model diagnostics for a priori identification and interpretation of outliers from a full pharmacokinetic database: correspondence analysis, Mahalanobis distance and Andrews curves

Abstract

Population pharmacokinetic (PK) (or pharmacodynamic (PD)) modelling aims to analyse the variability of drug kinetics (or dynamics) between numerous subjects belonging to a population. Such variability includes inter- and intra-individual sources leading to important differences between the variation ranges, the relative concentrations and the global shapes of PK profiles. These various sources of variability suggest that the distance metrics between the subjects can be examined under different aspects. Some subjects are so distant from the majority that they tend to be atypical or outliers. This paper presents three multivariate statistical methods to diagnose the outliers within a full population PK dataset, prior to any modelling step. Each method combined all the concentration-time variables to analyse the differences between patients by referring to a distance criterion: (a) Correspondence analysis (CA) used the chi-square distance to highlight the most atypical profiles in terms of relative concentrations; (b) Mahalanobis distance was calculated to extract PK profiles showing atypical shapes due to atypical variations in concentration; (c) Andrews method combined all the concentration variables into a Fourier transformation to give sine-cosine curves showing the clustering behaviours of subjects under the Euclidean distance criterion. After identification of outlier subjects, these methods can also be used to extract the concentration values which cause the atypical states of the patients. Therefore, the outliers will incorporate different variability sources of the PK dataset according to each method and independently of any PK modelling. Finally, a significant positive trend was found between the number of times outlier concentrations were detected (by one, two or three diagnostics) and the NPDE metrics of these concentrations (after a PK modelling): NPDE were highest when the corresponding concentration was detected by more diagnostics a priori. The application of a priori outlier diagnostics is illustrated here on two PK datasets: stimulated cortisol by synacthen and capecitabine administrated orally.