Keywords: Bayesian joint model; Cystic fibrosis; flexible link function; Gaussian process; Model assessment
In many clinical trials and follow-up studies, multiple response, either continuous or discrete, are collected simultaneously. The joint modelling of different types of biomarkers is often used recently for the purpose of analyzing the associations between biomarkers and providing more accurate inference. Cystic fibrosis (CF) is a genetic disorder that causes severe damage to the lungs. People with CF often experience progressive loss of lung function and pulmonary exacerbations throughout their clinical course. It has crucial clinical meanings to detect the changing of patient's lung function and early predict the occurrence of respiratory failure to help clinicians intervene in advance to prevent worse loss of lung function for CF patients. We proposed a non-linear shared-parameter joint model to provide more accrue inference of lung functions and examine the associations between lung function and occurrence of respiratory failure. 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 better analyze binary measurements. Bayesian model assessment is used to evaluate each component of the joint model in the simulation and application to the CF data. A nonlinear structure is suggested in both the longitudinal continuous and binary measurement; and the negative association is detected between lung function and pulmonary exacerbation by the joint model.