Introducing restricted cubic spline functions for modelling time by covariate interactions in the relative survival model, this new model allows us to formally test the PH hypothesis and to separate the test of lack of any type of time-dependence with the test of linearity of the time-dependence. The results provide strong evidence against the PH hypothesis, which is rejected for all prognostic factors, confirming the need to incorporate modelling of non-proportional hazards in the relative survival analyses. Moreover, it is apparent that in this example the cubic spline model performs better than the linear model, for all prognostic factors.