Cox models with dynamic ridge penalties on time-varying effects of the covariates

Analysis of long-term follow-up survival studies require more sophisticated approaches than the proportional hazards model. To account for the dynamic behaviour of fixed covariates, penalized Cox models can be employed in models with interactions of the covariates and known time functions. In this work, I discuss some of the suggested methods and emphasize on the use of a ridge penalty in survival models. I review different strategies for choosing an optimal penalty weight and argue for the use of the computationally efficient restricted maximum likelihood (REML)-type method. A ridge penalty term can be subtracted from the likelihood when modelling time-varying effects in order to control the behaviour of the time functions. I suggest using flexible time functions such as B-splines and constrain the behaviour of these by adding proper penalties. I present the basic methods and illustrate different penalty weights in two different datasets.