Joint models for time-to-event and bivariate longitudinal data

The joint models analyse the effect of a longitudinal covariate onto the risk of an event. They are composed of two sub-models, the longitudinal and the survival sub-model. In this paper the focus is on the case in which the longitudinal sub-model is bivariate, considering more than one longitudinal covariate. For the longitudinal sub-model a multivariate mixed model can be proposed. Whereas for the survival sub-model, a Cox proportional hazards model is proposed, considering jointly the influence of both the longitudinal covariates onto the risk of the event. The purpose of the paper is to implement an estimation method that is able to deal with the computational problem given by the introduction of other covariates and the increase of the number of parameters that must be estimated in a model that is already highly computationally demanding.