In previous works concerning colon cancer data coming from French registries we have shown that the proportional hazard hypothesis does not hold for most prognostic factors.

However, some of these non-proportional effects in particular for age and gender may reflect the inability of the method to separate cancer-related mortality from all-causes mortality. This problem can be solved using the relative survival analyses, which provide an estimate of the patient survival corrected for the effect of hazard independent causes of death using the natural mortality in the general population. However, the existing methodology in relative survival analyses does not allow for the incorporation of non-proportional hazards. We propose here to adapt methods yet developed for modelling non-proportional hazards in the Cox model to the specific context of relative survival modelling.