It is common to collect data on multiple biomarkers during study follow-up and the research interest is often to evaluate their predictiveness on important clinical events. The biomakers are intermittently measured, possibly missing at event times, and may be subject to high biological variations. They could also be highly correlated if they are in the same biological pathway, so including them as covariates into a prediction model may cause the collinearity problem and unstable model fit. To tackle these issues, we propose a joint model framework that extracts the latent, continuous trajectory shared by the multiple biomarkers via a longitudinal principal component approach and evaluates the predictiveness of the latent process on event times using the Cox's model. We propose a penalized EM algorithm for simultaneous variable selection and parameter estimation and derive its large sample properties including an oracle property. We illustrate our method on a data set from a lung transplant study to predict chronic lung allograft dysfunction (CLAD) using chemokines measured in bronchoalveolar lavage fluid of the patients.