Longitudinal and survival process are often associated together in many clinical trials and other medical and reliability studies. Longitudinal and survival data frequently arise in some ways in practice and also survival data often arise in longitudinal trajectory as well. In regression models, if the covariates are measured with errors but treated as accurately measured, the statistical inference will be misleading, since, a significant covariate may be found to be non- significant. Hence, the measurement errors in covariates must be taken into account for valid inference. The joint analyses of two models often assumed to be linked to shared parameters or shared unobserved variables. Our primary interest is in the survival model with measurement errors in time-dependent covariates, the unobserved “true values” of the time-dependent covariate in the survival model are the responses of the longitudinal model, so the longitudinal model and the survival model share the same unobserved variable. In literature, there are two commonly used approaches for joint modeling such as Naive two-stage methods and the likelihood methods. In this approach, a well-defined parametric model is a crucial component. Another problem with parametric likelihood inference is the risk of model misspecification. We investigate the use of a nonparametric empirical likelihood based two-stage joint modeling of longitudinal and survival data.
