Bayesian semiparametric mixed-effects joint models for analysis of longitudinal-competing risks data with skew distribution

The joint analysis of longitudinal competing risks data has received much attention recently. However, most joint models for this type of data assume parametric functions for both longitudinal and competing risks processes which has its limitation for practical use. Motivated by studying the relationship between two biomarkers modified by time in an AIDS study, we develop the semiparametric mixed effects joint models for longitudinal-competing risks data analysis. The proposed models differ from existing models in that: i) the commonly used parametric models in the joint models are extended to semiparametric settings to account for irregular data observed in real studies; ii) we employ skew distributions for random errors to account for skewness in data. We propose a Bayesian approach to jointly model two processes which are connected through the share of random effects. An example from a recent AIDS clinical study illustrates the methodology by jointly modeling the viral load and time to death due to AIDS or other reasons to compare potential models with various scenarios and different distribution specifications. The analysis results show a strongly negative relationship between virologic and immunologic biomarkers and CD4 counts reduce risks from both AIDS and other causes. In addition, nonlinear time effects are observed on the viral load at the population level while individual variation is large. These findings may help us to design a better treatment strategy for AIDS patients.