;In many clinic trials, it become very common to collect survival time and time-dependent covariates simultaneously. In this situation, we are interested not only in the event time but also in the longitudinal covariates. Joint modeling approach has been successfully handle this kind of data. In many the literature, the Cox model is mostly widely used survival model. However, it must follow the proportional hazards assumption, which fails in many medical studies or clinic trials. In particular, when the data contains several longitudinal biomarkers, it is usually the case that proportionality doesn′t hold for part of the biomarkers. To overcome this case, we propose a joint modeling approach for the accelerated failure time model with multivariate longitudinal covariates. The estimation is based on a joint likelihood function using Monte Carlo EM algorithm. The unspeified baseline hazard function is approximated by a kernel smooth function so that Newton-Raphson method can be applied to derive the estimates without closed form in the EM steps. Simulation studies are conducted to evaluate the performance of the proposed joint model approach. A case study on Taiwanese AIDS cohort study is used to demonstrate the usefulness of the estimating procedures.
