  In biomedical studies it is common to collect data on multiple biomarkers
during study follow-up for dynamic prediction of a time-to-event clinical
outcome. The biomarkers are typically intermittently measured, missing at some
event times, and may be subject to high biological variations, which cannot be
readily used as time-dependent covariates in a standard time-to-event model.
Moreover, they can be highly correlated if they are from in the same biological
pathway. To address these issues, we propose a flexible joint model framework
that models the multiple biomarkers with a shared latent reduced rank
longitudinal principal component model and correlates the latent process to the
event time by the Cox model for dynamic prediction of the event time. The
proposed joint model for highly correlated biomarkers is more flexible than
some existing methods since the latent trajectory shared by the multiple
biomarkers does not require specification of a priori parametric time trend and
is determined by data. We derive an Expectation-Maximization (EM) algorithm for
parameter estimation, study large sample properties of the estimators, and
adapt the developed method to make dynamic prediction of the time-to-event
outcome. Bootstrap is used for standard error estimation and inference. The
proposed method is evaluated using simulations and illustrated on a lung
transplant data to predict chronic lung allograft dysfunction (CLAD) using
chemokines measured in bronchoalveolar lavage fluid of the patients.
