Joint Models with Splines in the Longitudinal Submodel

Abstract

Joint models are used to model data that has both time-to-event and longitudinal components. It is not always reasonable to assume a linear trajectory for longitudinal data, especially data from applications in the biological and medical fields. A spline is a good way to introduce flexibility to account for the non-linearity that is present. This thesis assesses the use of quadratic and cubic B-splines within the longitudinal submodel of a joint model and compares them to a joint model with a longitudinal submodel that only has linear terms. These methods were demonstrated on two datasets from the field of medicine. A simulation study was also conducted to compare three models that employ B-splines in the longitudinal submodel to the traditional linear longitudinal submodel in a joint model. The results of the simulation study suggest that the introduction of B-splines into the longitudinal model marginally impacts results. However, one must be careful not to incorporate too high a degree of B-splines to not over-fit the data. Overall, splines can be a valuable way to incorporate flexibility into joint models.