title: Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches.
abstract: Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery.
authors.affiliation: University of Warwick, School of Engineering, Coventry, CV4 7AL, UK. m.a.tragardh@warwick.ac.uk.|CVMD iMed DMPK, AstraZeneca R&D, 431 83, Mölndal, Sweden. m.a.tragardh@warwick.ac.uk.
authors.forename: Magnus
authors.identifier: http://orcid.org/0000-0002-0440-6775
authors.initials: M
authors.lastname: Trägårdh
authors.affiliation: University of Warwick, School of Engineering, Coventry, CV4 7AL, UK.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Chappell
authors.affiliation: CVMD iMed Bioscience, AstraZeneca R&D, 431 83, Mölndal, Sweden.
authors.forename: Andrea
authors.initials: A
authors.lastname: Ahnmark
authors.affiliation: CVMD iMed Bioscience, AstraZeneca R&D, 431 83, Mölndal, Sweden.
authors.forename: Daniel
authors.initials: D
authors.lastname: Lindén
authors.affiliation: University of Warwick, School of Engineering, Coventry, CV4 7AL, UK.
authors.forename: Neil D
authors.initials: ND
authors.lastname: Evans
authors.affiliation: CVMD iMed DMPK, AstraZeneca R&D, 431 83, Mölndal, Sweden.
authors.forename: Peter
authors.initials: P
authors.lastname: Gennemark
mesh_terms: D000465:Algorithms; D000818:Animals; D001499:Bayes Theorem; D001682:Biological Availability; D003198:Computer Simulation; D055808:Drug Discovery / Q000379:methods*; D000518:Eflornithine / Q000493:pharmacokinetics*; D008390:Markov Chains; D051379:Mice; D015233:Models, Statistical; D009010:Monte Carlo Method; D051381:Rats; D012044:Regression Analysis; D012984:Software
chemical_list: D000518:Eflornithine
keywords: Deconvolution; Input estimation; Markov Chain Monte Carlo method; Nonlinear dynamic systems; Optimal control