Diabetic Retinopathy (DR) is a prevalent complication among diabetic patients and early detection of DR is crucial in order to prevent vision loss. It is important to predict patients' survival time to the event of DR based on longitudinal observations of certain biomarkers. Such long-term predictions can be used to assess the risk of developing DR in the future. Utilizing electronic health records (EHR) gathered during patients' routine clinical visits, we are able to develop survival models using longitudinal lab measurements. Though the joint modeling of failure time data and longitudinal data have been extensively studied in the literature, existing approaches rarely concern about the unaligned nature of EHR observations. The alignment of longitudinal observations in time is crucial to specify a correct model and hence can significantly impact the ultimate estimation and inference. The mishandling of alignment will cause severe bias and often incorrect results. It is more challenging when the majority of patients are censored, i.e. without a terminal event. To address the challenges that arise from EHR or other type of observational studies, we propose a joint model based on shared random processes with time-reversed longitudinal processes. There are few capable existing literature on the estimation of each individual's curve in the joint modeling, which can be essential for personalized predictions. Regarding this issue, we consider nonparametric Gaussian processes (GP) for those individual curves. This dissertation proposes a Bayesian joint model with nonparametric GP priors for curves and posterior distributions are used for statistical inference. For Bayesian computations, we derive the Gibbs sampling for posterior inference as well as a Riemann manifold Hamiltonian Monte Carlo (RMHMC) technique for sampling non-Gaussian random curves in the posterior. With the fitted model, we further propose a marginal likelihood approach for predicting a patient's time to the terminal event given their longitudinal history. Simulation studies show that our approach can provide reasonable parameter estimation and is superior than other alignment approaches. Finally, we apply our model to a real EHR dataset for estimating and predicting DR survival times.