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Net survival is the survival that would be observed if the only possible cause of death was the studied cancer. It gets rid of mortality differences that would be attributable to causes other than cancer. In addition, it enables comparisons between countries and periods. Proposed models for estimating net survival are based on splitting observed mortality into expected mortality and excess mortality. In fact, excess mortality is the mortality due to the studied cancer. And expected mortality in general population is the mortality due to causes other than cancer. Expected mortality derives from life tables. However, some (demographic) covariates are not included in life tables. So, they give inaccurate values of expected mortality and lead bias in the estimates of the effects on excess mortality. To overcome this problem, a multivariate regression model for estimating excess mortality when the expected mortality in the studied population differs from that in the general population has been proposed. The main limit of this model lies in the assumption of proportionality between hazards of the different categories of the additional covariate. We propose to relax this assumption of proportionality. We use a proportional hazards model with a piecewise constant baseline for excess mortality. Parameters of the proposed model are estimated by maximum likelihood. To illustrate the interest of the method, we use simulation studies.