Generalized Linear Mixed Models with Censored Covariates and Measurement Errors, with Applications in HIV/AIDS Studies

Generalized linear mixed models (GLMMs) are widely used for the analysis of longitudinal data. Covariates are usually collected along with the response variable. In practice, some of these covariates may be measured with errors and may also be censored or missing. Ignoring measurement errors and censoring in data analysis may lead to biased results. In this article, motivated by HIV/AIDS studies, we consider two joint nonlinear mixed effects (NLME) models to model the entire covariate process at two different study phases to address measurement errors and censoring, together with a GLMM response model. Since the NLME covariate models are based on the underlying data-generation mechanisms, they may provide better "predictions" of mis-measured and censored covariate values than commonly used empirical models. A computationally efficient stochastic approximation EM algorithm (SAEM) is used for joint likelihood inference. Simulations are conducted to evaluate the proposed joint model. A dataset from an HIV/AIDS study is analyzed in detail. We find that the negative association between CD4 and viral load, the two most important variables in HIV/AIDS studies, both during an anti-HIV treatment and after the treatment interruption, is stronger than previous findings. This new finding has important implications in HIV/AIDS studies.