Reduced rank hazard regression with fixed and time-varying effects of the covariates

Modelling survival data from long-term follow-up studies presents challenges. The commonly used proportional hazards model should be extended to account for dynamic behaviour of the effects of fixed covariates. This work illustrates the use of reduced rank models in survival data, where some of the covariate effects are allowed to behave dynamically in time and some as fixed. Time-varying effects of the covariates can be fitted by using interactions of the fixed covariates with flexible transformations of time based on b-splines. To avoid overfitting, a reduced rank model will restrict the number of parameters, resulting in a more sensible fit to the data. This work presents the basic theory and the algorithm to fit such models. An application to breast cancer data is used for illustration of the suggested methods.