Many clinical trials often collect information on multiple longitudinal outcomes. Multilevel item response theory (MLIRT) models have been increasingly used to analyze this type of multivariate longitudinal data. The continuous outcomes in the MLIRT models are often assumed to be normally distributed. However, the normality assumption is often violated due to skewness and/or outliers and thus may produce biased results. The skew-normal/independent (SNI) distribution has been increasingly used to handle the skewness and outlier problems to produce robust inference. Moreover, patients’ follow-up may be stopped by some terminal events such as death or dropout and the time to the terminal events may be dependent on the multiple longitudinal outcomes. In this article, we proposed a joint modeling framework based on the MLIRT model to account for three data features: skewness, outliers, and dependent censoring. Extensive simulation studies were conducted to evaluate the performance of various models. Our proposed methods were applied to the motivating DATATOP study for Parkinson’s disease to investigate the effect of deprenyl in slowing down the disease progression.