A Joint Model for Nonlinear Mixed-Effects Models with Censoring and Covariates Measured with Error

In recent years AIDS researchers have shown great interest in the study of HIV viral dynamics. Nonlinear mixed-effect models (NLME) have been proposed for modeling the intraand inter-patients variations. The inter-patients 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: i) the viral load measurements may subject to left censoring due to a detection limit; ii) covariates are often measured with substantial errors; and iii) 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 twostep method in the sense that it produces less biased estimates with more reliable standard errors.