Multilevel joint model of longitudinal continuous and binary outcomes for hierarchically structured data.

Joint modeling has been a useful strategy for incorporating latent associations between different types of outcomes simultaneously, often focusing on a longitudinal continuous outcome characterized by an LME submodel and a terminal event subject to a Cox proportional hazard or parametric survival submodel. Applications to hierarchical longitudinal studies have been less frequent, particularly with respect to a binary process, which is commonly specified by a GLMM. Furthermore, many of the joint model developments have not allowed for investigations of nested effects, such as those arising from multicenter studies. To fill this gap, we propose a multilevel joint model that encompasses the LME submodel and GLMM through a Bayesian approach. Motivated by the need for timely detection of pulmonary exacerbation and characterization of irregularly observed lung function measurements in people living with cystic fibrosis (CF) receiving care across multiple centers, we apply the model to the data arising from US CF Foundation Patient Registry. In parallel, we examine the extent of bias induced by a non-hierarchical model. Our simulation study and application results show that incorporating the center effect along with individual stochastic variation over time within the LME submodel improves model estimation and prediction. Given that the center effect is evident in lung function observed in the CF population, accounting for center-specific power parameters by incorporating the symmetric power exponential power (spep) link function in the GLMM can facilitate more accurate conclusions in clinical studies.