A relative survival regression model using B-spline functions to model non-proportional hazards

Relative survival, a method for assessing prognostic factors for disease-specific mortality in unselected populations, is frequently used in population-based studies. However, most relative survival models assume that the effects of covariates on disease-specific mortality conform with the proportional hazards hypothesis, which may not hold in some long-term studies. To accommodate variation over time of a predictor's effect on disease-specific mortality, we developed a new relative survival regression model using B-splines to model the hazard ratio as a flexible function of time, without having to specify a particular functional form. Our method also allows for testing the hypotheses of hazards proportionality and no association on disease-specific hazard. Accuracy of estimation and inference were evaluated in simulations. The method is illustrated by an analysis of a population-based study of colon cancer.