These Figures (see next 2 slides) show the hazard ratio (HR) estimates obtained with the PH relative survival model of Estève and the non-PH cubic splines model.

AGE: The constant PH model considerably underestimates early risks (The confidence intervals do not overlap) and overestimates later risks. These results are consistent with those shown before for the piecewise PH relative survival model but the smooth spline estimate is more clinically plausible than the disjoint step function Moreover, the model based on restricted cubic spline functions (only 3 parameters for three knots, independent of the number of time-segments) is more parsimonious than the piecewise PH relative survival model (6 parameters for 6 time segments).

STAGE: According to the cubic spline model, the impact of higher stage, reaches maximum at approximately 2 years. This estimated pattern suggests that advanced cancer stages have relatively moderate impact on very early mortality, mostly due to post-surgical complications. This impact increases sharply during the first year after the diagnosis and then gradually decreases over several years, with hazard ratios being elevated even 10 years later.

PERIOD OF DIAGNOSIS: Due to the flexibility of the cubic spline functions, this cubic spline model allowed us to fit the inversion of the HR with time as shown in this figure for period of diagnosis. In contrast to the PH relative survival analysis, the restricted cubic spline model suggests that the protective effect of the more recent period is limited to the first months after diagnosis, which can possibly be attributed to an improvement in post-surgery intensive care.