Integrating Latent Classes in the Bayesian Shared Parameter Joint Model of Longitudinal and Survival Outcomes

Abstract

Cystic fibrosis is a chronic lung disease which requires frequent patient monitoring to maintain lung function over time and minimize onset of acute respiratory events known as pulmonary exacerbations. From the clinical point of view it is important to characterize the association between key biomarkers such as $FEV_1$ and time-to first exacerbation. Progression of the disease is heterogeneous, yielding different sub-groups in the population exhibiting distinct longitudinal profiles. It is desirable to categorize these unobserved sub-groups (latent classes) according to their distinctive trajectories. Accounting for these latent classes, in other words heterogeneity, will lead to improved estimates of association arising from the joint longitudinal-survival model. The joint model of longitudinal and survival data constitutes a popular framework to analyze such data arising from heterogeneous cohorts. In particular, two paradigms within this framework are the shared parameter joint models and the joint latent class models. The former paradigm allows one to quantify the strength of the association between the longitudinal and survival outcomes but does not allow for latent sub-populations. The latter paradigm explicitly postulates the existence of sub-populations but does not directly quantify the strength of the association. We propose to integrate latent classes in the shared parameter joint model in a fully Bayesian approach, which allows us to investigate the association between $FEV_1$ and time-to first exacerbation within each latent class. We, furthermore, focus on the selection of the optimal number of latent classes.