A flexible joint model for multiple longitudinal biomarkers and a time‐to‐event outcome: With applications to dynamic prediction using highly correlated biomarkers

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.