Considering expected mortality provides an attractive approach to analyse mortality of population-based cohorts of patients presenting with a chronic disease. Two classes of methods are available: either modelling the excess mortality using an additive hazard model or modelling the relative mortality using a multiplicative hazard model. Because these two models are informative to look for factors associated with mortality related to a chronic disease, we developed an alternative model modelling both the excess and the relative mortality. We generalised Andersen and Vaeth's model to fit covariates and obtain directly an estimation of the Excess Mortality Ratio and Relative Mortality Ratio for each covariate. We assessed the performances of the combined model by using simulations, and it appeared satisfactorily. We illustrate the combined model by data collected in patients presenting with end-stage renal disease and treated by dialysis. The combined model offers the possibility of performing pure additive and multiplicative models and thus to compare their log-likelihoods. The combined model appears useful to select one of these pure models or to conclude to the need of modelling both excess and relative mortality. In this latter case, our model enabled better describing the effect of covariates on the excess and relative mortality. Copyright © 2013 John Wiley & Sons, Ltd.