In this thesis, we consider models for survival data with a high-dimensional covariate space. Most models used for such datasets are based on the Cox regression model, of which a critical assumption is that the hazard functions are proportional between individuals. The purpose of this thesis is to develop a way of analysing these datasets that does not require that the proportional hazards assumption is valid. In search of such a method, we study the concept of landmarking and try to develop a way of fitting what van Houwelingen and Putter  refers to as sliding landmark models that works when we have a high number of covariates. An essential part of our strategy is the ‘bet on sparsity principle’ [Hastie et al., 2001], where one assumes that only some of the variables in the dataset have an effect on the outcome. We seek out to implement this using regularisation techniques, such as penalised regression and boosting. In particular, we develop a boosting algorithm for sliding landmark models, based on the likelihood boosting algorithm for Cox regression [Binder and Schumacher, 2008]. The thesis is concluded by a simulation study, where the different models and methods of estimation we consider are used to analyse different simulated datasets, and are compared via a dynamic Brier score [van Houwelingen and Putter, 2011].