title: A Bayesian approach to parameter estimation in HIV dynamical models.
abstract: In the context of a mathematical model describing HIV infection, we discuss a Bayesian modelling approach to a non-linear random effects estimation problem. The model and the data exhibit a number of features that make the use of an ordinary non-linear mixed effects model intractable: (i) the data are from two compartments fitted simultaneously against the implicit numerical solution of a system of ordinary differential equations; (ii) data from one compartment are subject to censoring; (iii) random effects for one variable are assumed to be from a beta distribution. We show how the Bayesian framework can be exploited by incorporating prior knowledge on some of the parameters, and by combining the posterior distributions of the parameters to obtain estimates of quantities of interest that follow from the postulated model.
authors.affiliation: Department of Medical Statistics, Leiden University Medical Center, University of Leiden, P.O. Box 9604, 2300 RC Leiden, The Netherlands. h.putter@lumc.nl
authors.forename: H
authors.initials: H
authors.lastname: Putter
authors.forename: S H
authors.initials: SH
authors.lastname: Heisterkamp
authors.forename: J M A
authors.initials: JM
authors.lastname: Lange
authors.forename: F
authors.initials: F
authors.lastname: de Wolf
mesh_terms: D001499:Bayes Theorem; D015496:CD4-Positive T-Lymphocytes / Q000276:immunology; D003198:Computer Simulation; D015658:HIV Infections / Q000276:immunology / Q000821:virology*; D015497:HIV-1 / Q000254:growth & development*; D006801:Humans; D008390:Markov Chains; D008954:Models, Biological; D009010:Monte Carlo Method; D012367:RNA, Viral / Q000097:blood
chemical_list: D012367:RNA, Viral