In the analysis of time-to-event data, accelerated failure time (AFT) models are
attractive alternatives to the commonly used proportional hazard models. In some applications,
important time-dependent covariates may be measured with errors and censored due to detection
limits, such as in AIDS studies. In this case, a common approach is to model the time-dependent
covariates empirically based on observed data to address measurement errors and censoring,
assuming the covariate model continues to hold for censored, mis-measured, or unobserved
covariate values. However, such an empirical covariate model based on observed data may be
problematic since the censored or unobserved true covariate values may behave quite differently
than the observed data. In some applications such as AIDS studies, mechanistic nonlinear
models are available for the covariate process, derived from the underlying data-generation
mechanisms and disease progression. Such a mechanistic nonlinear model provides more reliable
predicted values for the censored or unobserved true covariate values. In this talk, we
consider a nonlinear mixed effects (NLME) covariate model for AFT models,
implemented using a Monte Carlo EM algorithm, under the framework of a joint NLME and AFT
model for simultaneous inference.