Graduate School of Computer Science and Advanced TechnologiesFrance
The joint models for longitudinal data and time-to-event data have recently received numerous attention in clinical and epidemiologic studies. Our interest is in modeling the relationship between event time outcomes and internal time-dependent covariates. In practice, the longitudinal responses often show non-linear and fluctuated curves. Therefore, the main aim of this chapter is to use penalized splines with a truncated polynomial basis to parameterize the non-linear longitudinal process. Then, the linear mixed effects model is applied to subject-specific curves and to control the smoothing. The association between the dropout process and longitudinal outcomes is modeled through a proportional hazard model. Two types of baseline risk functions are considered, namely a Gompertz distribution and a piecewise constant model. The resulting models are referred to as penalized spline joint models; an extension of the standard linear joint models.
Part of the book: Topics in Splines and Applications