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In biomedical studies it is common to collect data on multiple biomarkersduring study follow-up for dynamic prediction of a time-to-event clinicaloutcome. The biomarkers are typically intermittently measured, missing at someevent times, and may be subject to high biological variations, which cannot bereadily 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 biologicalpathway. To address these issues, we propose a flexible joint model frameworkthat models the multiple biomarkers with a shared latent reduced ranklongitudinal principal component model and correlates the latent process to theevent time by the Cox model for dynamic prediction of the event time. Theproposed joint model for highly correlated biomarkers is more flexible thansome existing methods since the latent trajectory shared by the multiplebiomarkers does not require specification of a priori parametric time trend andis determined by data. We derive an Expectation-Maximization (EM) algorithm forparameter estimation, study large sample properties of the estimators, andadapt the developed method to make dynamic prediction of the time-to-eventoutcome. Bootstrap is used for standard error estimation and inference. Theproposed method is evaluated using simulations and illustrated on a lungtransplant data to predict chronic lung allograft dysfunction (CLAD) usingchemokines measured in bronchoalveolar lavage fluid of the patients.

A Flexible Joint Model for Multiple Longitudinal Biomarkers and A  Time-to-Event Outcome: With Applications to Dynamic Prediction Using Highly  Correlated Biomarkers