Nonlinear mixed-effects models for HIV viral load trajectories before and after antiretroviral therapy interruption, incorporating left censoring

Longitudinal studies are common in biomedical research, such as an HIV study. In an HIV study, the viral decay during an anti-HIV treatment and the viral rebound after the treatment is interrupted can be viewed as two longitudinal processes, and they may be related to each other. In this thesis, we investigate if key features of HIV viral decay and CD4 trajectories during antiretroviral therapy (ART) are associated with characteristics of HIV viral rebound following ART interruption. Motivated by a real AIDS dataset, two non-linear mixed effects (NLME) models are used to model the viral load trajectories before and following ART interruption, respectively, incorporating left censoring due to lower detection limits of viral load assays. A linear mixed effects (LME) model is used to model CD4 trajectories. The models may be linked through shared random effects, since these random effects reflect individual characteristics of the longitudinal processes. A stochastic approximation EM (SAEM) method is used for parameter estimation and inference. To reduce the computation burden associated with maximizing the joint likelihood, an easy-to-implement three-step (TS) method is proposed by using SAEM algorithm and bootstrap. Data analysis results show that some key features of viral load and CD4 trajectories during ART (e.g., viral decay rate) are significantly associated with important characteristics of viral rebound following ART interruption (e.g., viral set point). Simulation studies are conducted to evaluate the performances of the proposed TS method and the naive method, which still uses SAEM algorithm but substitutes the censored viral load values with half the detection limit and without bootstrap. It is concluded that the proposed TS method outperforms the naive method.Science, Faculty ofStatistics, Department ofGraduat