title: The study of long-term HIV dynamics using semi-parametric non-linear mixed-effects models.
abstract: Modelling HIV dynamics has played an important role in understanding the pathogenesis of HIV infection in the past several years. Non-linear parametric models, derived from the mechanisms of HIV infection and drug action, have been used to fit short-term clinical data from AIDS clinical trials. However, it is found that the parametric models may not be adequate to fit long-term HIV dynamic data. To preserve the meaningful interpretation of the short-term HIV dynamic models as well as to characterize the long-term dynamics, we introduce a class of semi-parametric non-linear mixed-effects (NLME) models. The models are non-linear in population characteristics (fixed effects) and individual variations (random effects), both of which are modelled semi-parametrically. A basis-based approach is proposed to fit the models, which transforms a general semi-parametric NLME model into a set of standard parametric NLME models, indexed by the bases used. The bases that we employ are natural cubic splines for easy implementation. The resulting standard NLME models are low-dimensional and easy to solve. Statistical inferences that include testing parametric against semi-parametric mixed-effects are investigated. Innovative bootstrap procedures are developed for simulating the empirical distributions of the test statistics. Small-scale simulation and bootstrap studies show that our bootstrap procedures work well. The proposed approach and procedures are applied to long-term HIV dynamic data from an AIDS clinical study.
authors.affiliation: Frontier Science & Technology Research Foundation, 1244 Boylston Street, Suite 303, Chestnut Hill, MA 02467, USA. wu@sdac.haravard.edu
authors.forename: Hulin
authors.initials: H
authors.lastname: Wu
authors.forename: Jin-Ting
authors.initials: JT
authors.lastname: Zhang
mesh_terms: D000163:Acquired Immunodeficiency Syndrome / Q000188:drug therapy / Q000821:virology*; D023241:Antiretroviral Therapy, Highly Active; D002986:Clinical Trials as Topic; D003198:Computer Simulation; D006678:HIV / Q000254:growth & development*; D006801:Humans; D008137:Longitudinal Studies; D008954:Models, Biological; D017711:Nonlinear Dynamics; D019562:Viral Load