Many longitudinal studies (e.g. observational studies and randomized clinical trials) have collected multiple rating scales at each visit in the form of patient-reported outcomes (PROs) in the close unit interval [0 ,1]. We propose a joint modeling framework to address the issues from the following data features: (1) multiple correlated PROs; (2) the presence of the boundary values of zeros and ones; (3) extreme outliers and heavy tails; (4) the PRO-dependent terminal events such as death and dropout. Our modeling framework consists of a multivariate augmented mixed-effects sub-model based on Beta rectangular distributions for the multiple longitudinal outcomes and a Cox model for the terminal events. The simulation studies suggest that in the presence of outliers, heavy tails, and dependent terminal event, our proposed models provide more accurate parameter estimates than the joint model based on Beta distributions. The proposed models are applied to the motivating Long-term Study-1 (LS-1 study, n = 1741) of Parkinson's disease patients.
Keywords: Augmented Beta; Beta rectangular distribution; Beta regression; Markov chain Monte Carlo; longitudinal data; proportional data.