Variable selection for joint models of multivariate longitudinal measurements and event time data

Joint modeling of longitudinal and survival data has attracted a great deal of attention. Some research has been undertaken to extend the joint model to incorporate multivariate longitudinal measurements recently. However, there is a lack of variable selection methods in the joint modeling of multivariate longitudinal measurements and survival time. In this article, we develop penalized likelihood methods for the selection of longitudinal features in the survival submodel. A multivariate linear mixed effect model is used to model multiple longitudinal processes where random intercepts and slopes serve as essential features of the trajectories. We introduce L1 penalty functions to select both random effects in the survival submodel and off-diagonal elements in the covariance matrix of random effects. An estimation procedure is developed based on Laplace approximation. Our simulations demonstrate excellent selection properties of the proposed procedure. We apply our methods to explore the relationship between mortality and multiple longitudinal processes for end stage renal disease patients on hemodialysis. We find that lower levels of albumin, higher levels of neutrophil-to-lymphocyte ratio, and higher levels of interdialytic weight gain at the beginning of the follow-up time, as well as decrease in predialysis systolic blood pressure and increase of neutrophil-to-lymphocyte ratio over time are associated with higher mortality hazard rates.