A joint model for nonlinear mixed-effects models with censoring and covariates measured with error, with application to AIDS studies

In recent years AIDS researchers have shown great interest in the study of HIV viral dynamics. Nonlinear mixed-effects models (NLMEs) have been proposed for modeling intrapatient and interpatient variations in viral load measurements. The interpatient variation often receives great attention and may be partially explained by time-varying covariates, such as CD4 cell counts. Statistical analyses in these studies are complicated by the following problems: (a) the viral load measurements may be subject to left censoring due to a detection limit, (b) covariates are often measured with substantial errors, and (c) covariates frequently contain missing data. In this article we address these three problems simultaneously by jointly modeling the covariate and the response processes. We adapt a Monte Carlo EM algorithm and a linearization procedure to estimate the model parameters. Our approach is preferable to naive methods and the two-step method in the sense that it produces less-biased estimates with more-reliable standard errors. We analyze a real AIDS dataset and show that the fitted model may provide good prediction for unobserved viral loads.