Cystic fibrosis (CF) is a lethal autosomal disease hallmarked by respiratory failure. Maintaining lung function and minimizing frequency of acute respiratory events known as pulmonary exacerbations are essential to survival. Jointly modeling longitudinal lung function and exacerbation occurrences may provide better inference. We propose a shared-parameter joint hierarchical Gaussian process model with flexible link function to investigate the impacts of both demographic and time-varying clinical risk factors on lung function decline and to examine the associations between lung function and occurrence of pulmonary exacerbation. A two-level Gaussian process is used to capture the nonlinear longitudinal trajectory, and a flexible link function is introduced to the joint model in order to analyze binary process. Bayesian model assessment criteria are provided in examining the overall performance in joint models and marginal fitting in each submodel. We conduct simulation studies and apply the proposed model in a local CF center cohort. In the CF application, a nonlinear structure is supported in modeling both the longitudinal continuous and binary processes. A negative association is detected between lung function and pulmonary exacerbation by the joint model. The importance of risk factors, including gender, diagnostic status, insurance status, and BMI, is examined in joint models.
Keywords: Bayesian joint model; Bayesian model assessment; Gaussian process; binary process; cystic fibrosis; flexible link function; longitudinal data analysis; medical monitoring.