Modelling of drug-effect on time-varying biomarkers

Model-based quantification of drug effect is an efficient tool during pre-clinical and clinical phases of drug trials. Mathematical modelling can lead to improved understanding of the underlying biological mechanisms, help in finding shortcomings of experimental design and suggest improvements, or be an effective tool in simulation-based analyses. This thesis addresses the modelling of time-varying biomarkers both with and without drug-treatment. Pharmacokinetic/pharmacodynamic models were used to describe observed drug concentrations and biomarkers. These are modelled in the framework of compartmental modelling described by ordinary differential equations. This thesis contains two papers in manuscript-form. In the first paper, a metaanalysis was performed of an existing model and previously published data for the stress-hormone cortisol and the drug dexamethasone. Cortisol exhibits a circadian rhythm, resembling oscillations, and is therefore a time-varying target for treatment. The aim was to utilize the model for prediction of the outcome of a medical test used in veterinary treatments on horses. In addition to model parameters, inter-individual variability was modelled and estimated in a Bayesian framework. This allowed simulation of test outcomes for the whole population, which in turn were used to evaluate available test protocols and suggest improvements. In the second paper, an improved model was constructed for the cytokine TNFα after challenge with LPS in addition to intervention treatment. TNFα is not measurable in healthy subjects but release into blood plasma can be provoked by challenge with LPS. The result is a short-lived turnover of TNFα. A test compound targeting intervention of TNFα release was included in the study. Comprehensive experimental data from two studies was available and allowed to model features of TNFα release, that were not addressed in previously published models. The final model was then used to analyse the current experimental design and correlations between LPS challenge and test compound effectiveness. The paper provides suggestions for future experimental designs.

[1]  Fredrik Lindsten,et al.  Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo , 2017, ArXiv.

[2]  É. Moulines,et al.  Convergence of a stochastic approximation version of the EM algorithm , 1999 .

[3]  David H. Anderson.  Compartmental Modeling and Tracer Kinetics , 1983 .

[4]  J. Rosenthal,et al.  Optimal scaling of discrete approximations to Langevin diffusions , 1998 .

[5]  Sophie Donnet,et al.  EM algorithm coupled with particle filter for maximum likelihood parameter estimation of stochastic differential mixed-effects models , 2010 .

[6]  Jiqiang Guo,et al.  Stan: A Probabilistic Programming Language. , 2017, Journal of statistical software.

[7]  M. Jirstrand,et al.  Exact Gradients Improve Parameter Estimation in Nonlinear Mixed Effects Models with Stochastic Dynamics , 2018, The AAPS Journal.

[8]  M. Betancourt,et al.  Hamiltonian Monte Carlo for Hierarchical Models , 2013, 1312.0906.

[9]  Xh Huang,et al.  Pharmacometrics: The Science of Quantitative Pharmacology. , 2007 .

[10]  Anders Vretblad,et al.  Fourier Analysis and Its Applications , 2005 .

[11]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[12]  Robert L. Wolpert,et al.  Statistical Inference , 2019, Encyclopedia of Social Network Analysis and Mining.

[13]  P. Moral.  Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications , 2004 .

[14]  Jon Wakefield,et al.  Bayesian Analysis of Population PK/PD Models: General Concepts and Software , 2002, Journal of Pharmacokinetics and Pharmacodynamics.

[15]  Yaning Wang,et al.  Derivation of various NONMEM estimation methods , 2008, Journal of Pharmacokinetics and Pharmacodynamics.

[16]  W J Jusko,et al.  Characteristics of indirect pharmacodynamic models and applications to clinical drug responses. , 1998, British journal of clinical pharmacology.

[17]  Dirk Husmeier,et al.  ODE parameter inference using adaptive gradient matching with Gaussian processes , 2013, AISTATS.

[18]  David Barber,et al.  Gaussian Processes for Bayesian Estimation in Ordinary Differential Equations , 2014, ICML.

[19]  Andrew Gelman,et al.  The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo , 2011, J. Mach. Learn. Res..

[20]  Radford M. Neal.  MCMC Using Hamiltonian Dynamics , 2011, 1206.1901.

[21]  D. Roden,et al.  The genetic basis of variability in drug responses , 2002, Nature Reviews Drug Discovery.

[22]  G. Wilkinson,et al.  Drug metabolism and variability among patients in drug response. , 2005, The New England journal of medicine.

[23]  Neil D. Lawrence,et al.  Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes , 2008, NIPS.

[24]  M. Jirstrand,et al.  Using sensitivity equations for computing gradients of the FOCE and FOCEI approximations to the population likelihood , 2015, Journal of Pharmacokinetics and Pharmacodynamics.

[25]  M. Hedeland,et al.  A quantitative approach to analysing cortisol response in the horse. , 2016, Journal of veterinary pharmacology and therapeutics.

[26]  L. Skovgaard.  NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA. , 1996 .

[27]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[28]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[29]  Varun Garg,et al.  Comparison of four basic models of indirect pharmacodynamic responses , 1993, Journal of Pharmacokinetics and Biopharmaceutics.

[30]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[31]  T. Sideris.  Ordinary Differential Equations and Dynamical Systems , 2013 .

[32]  Matthew J. Beal.  Variational algorithms for approximate Bayesian inference , 2003 .

[33]  M. Girolami,et al.  Bayesian Solution Uncertainty Quantification for Differential Equations , 2013 .

[34]  Malcolm Rowland,et al.  Physiologically-based pharmacokinetics in drug development and regulatory science. , 2011, Annual review of pharmacology and toxicology.