A Cox-type regression model for the ratio between the mortality in a cohort and that in a reference population is introduced. By means of the model it is possible to include in the survival analysis both individual (possibly time-dependent) characteristics for the study cohort and changing trends in the mortality in the reference population. This is particularly relevant in long-term follow-up studies where there may be considerable changes in the mortality in the reference population. Estimation procedures in the model are discussed and large-sample properties of the estimators are outlined. The model is applied to the analysis of two sets of data concerning the survival among insulin-dependent diabetics in Denmark.