The study of long‐term HIV dynamics using semi‐parametric non‐linear mixed‐effects models

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. Copyright © 2002 John Wiley & Sons, Ltd.