Joint Models of Two Longitudinal Biomarkers and Clustered Survival Data for Cluster-Informed Dynamic Prediction With Application to Periodontitis.

Joint modeling of longitudinal data and time-to-event data have been extended to accommodate multilevel data structures. In dental studies, data often exhibit a multilevel hierarchy: each patient has multiple teeth, and one or more biomarkers are measured repeatedly over time for each tooth. In addition to biomarker measurements, the time to tooth loss may vary differently between patients as some patients are more susceptible to tooth loss, conditional on other risk factors. In this paper, we account for intra-patient and intra-tooth correlations in the longitudinal measurement of a continuous biomarker, probing pocket depth (PPD), and a binary biomarker, mobility. We also account for the correlation in time to tooth loss between teeth within the same patient. We jointly model the two longitudinal measurements and the risk of tooth loss using Bayesian estimation. We develop a cluster-informed dynamic prediction framework for the survival outcome, in which the prediction for a given unit is informed not only by its own observed history but also by the observed longitudinal trajectories and event outcomes of other units within the same cluster. We evaluate the predictive performance in terms of discrimination and calibration, accounting for censoring and the multilevel data structure. Our simulation study shows that the proposed joint model produced more accurate estimates and better predictive performance compared to the standard bivariate joint model that ignores the multilevel data structure. We applied our model to electronic periodontal data obtained from the Canadian Armed Forces (CAF).