Learning pharmacokinetic models for in vivo glucocorticoid activation

Research output: Contribution to journalArticle

External organisations

  • Oxford Centre for Diabetes, Endocrinology and Metabolism, University of Oxford, Oxford, UK.
  • Centre for Endocrinology, Diabetes and Metabolism, Birmingham Health Partners & Department of Endocrinology, 3rd Floor Heritage Building, Queen Elizabeth Hospital, Birmingham
  • School of Engineering, University of Warwick, UK
  • Faculty of Mathematics and Natural Sciences, University of Groningen, NL


To understand trends in individual responses to medication, one can take a purely data-driven machine learning approach, or alternatively apply pharmacokinetics combined with mixed-effects statistical modelling. To take advantage of the predictive power of machine learning and the explanatory power of pharmacokinetics, we propose a latent variable mixture model for learning clusters of pharmacokinetic models demonstrated on a clinical data set investigating 11β-hydroxysteroid dehydrogenase enzymes (11β-HSD) activity in healthy adults. The proposed strategy automatically constructs different population models that are not based on prior knowledge or experimental design, but result naturally as mixture component models of the global latent variable mixture model. We study the parameter of the underlying multi-compartment ordinary differential equation model via identifiability analysis on the observable measurements, which reveals the model is structurally locally identifiable. Further approximation with a perturbation technique enables efficient training of the proposed probabilistic latent variable mixture clustering technique using Estimation Maximization. The training on the clinical data results in 4 clusters reflecting the prednisone conversion rate over a period of 4 hours based on venous blood samples taken at 20-minute intervals. The learned clusters differ in prednisone absorption as well as prednisone/prednisolone conversion. In the discussion section we include a detailed investigation of the relationship of the pharmacokinetic parameters of the trained cluster models for possible or plausible physiological explanation and correlations analysis using additional phenotypic participant measurements.


Original languageEnglish
Pages (from-to)222-231
JournalJournal of Theoretical Biology
Early online date23 Jul 2018
Publication statusPublished - 14 Oct 2018


  • Dynamic systems, Pharmacokinetics, Identifiability analysis, Perturbation analysis, 11β-HSD activity, In vivo Glucocorticoid Activation, Probabilistic models, Gaussian mixture model, Expectation maximization, Clustering, Partially observed time series analysis