Bayesian Expectile Joint Model With Varying Coefficient for Longitudinal and Semi‐Competing Risks Data

ABSTRACT In the realm of clinical medical research, semi‐competing risks data are usually observed in practice, yet there are few studies on the joint models of longitudinal and semi‐competing risks data. In this paper, a joint model for longitudinal and semi‐competing risks data is proposed. Based on the expectile regression, a linear mixed‐effects longitudinal sub‐model is formulated, and a Cox proportional hazards survival sub‐model is considered under the framework of semi‐competing risks. The two sub‐models are linked by a shared longitudinal trajectory function. To accommodate the time‐varying relationship between the longitudinal response variable and covariates, as well as to introduce flexibility to the structural linkage between longitudinal and survival processes, we incorporate the time‐varying coefficients into the joint model in the form of nonparametric functions. The simultaneous Bayesian inference method is utilized to estimate the model parameters, which not only overcomes the convergence problem, but also improves the accuracy of the parameter estimation while effectively reducing the computational burden. The simulation studies are conducted to assess the performance of the proposed joint model and methodology. Finally, we analyze a dataset from the Multicenter AIDS Cohort Study to illustrate the real application of the proposed model and method. In both simulation studies and empirical analyses, joint modeling methods demonstrate performance that meets expected effects.