Bayesian shrinkage approach for a joint model of longitudinal and survival outcomes assuming different association structures.

The joint modeling of longitudinal and survival data has recently received much attention. Several extensions of the standard joint model that consists of one longitudinal and one survival outcome have been proposed including the use of different association structures between the longitudinal and the survival outcomes. However, in general, relatively little attention has been given to the selection of the most appropriate functional form to link the two outcomes. In common practice, it is assumed that the underlying value of the longitudinal outcome is associated with the survival outcome. However, it could be that different characteristics of the patients' longitudinal profiles influence the hazard. For example, not only the current value but also the slope or the area under the curve of the longitudinal outcome. The choice of which functional form to use is an important decision that needs to be investigated because it could influence the results. In this paper, we use a Bayesian shrinkage approach in order to determine the most appropriate functional forms. We propose a joint model that includes different association structures of different biomarkers and assume informative priors for the regression coefficients that correspond to the terms of the longitudinal process. Specifically, we assume Bayesian lasso, Bayesian ridge, Bayesian elastic net, and horseshoe. These methods are applied to a dataset consisting of patients with a chronic liver disease, where it is important to investigate which characteristics of the biomarkers have an influence on survival.