Appraising relative and excess mortality in population-based studies of chronic diseases such as end-stage renal disease

Caroline Elie¹, Y De Rycke², JP Jais¹, P Landais^1
1Université Paris Descartes, Faculté de Médecine, Hôpital Necker-Enfants Malades, Service de Biostatistique et d'Informatique Médicale, Paris, France; ²Institut Curie, Service de Biostatistique, Paris, France

Purpose: Modeling excess and relative mortality represents two ways of considering general population mortality rates (ie, background mortality) in cohort studies. Excess mortality is obtained by subtracting the expected mortality from the observed mortality (additive hazard model). Relative mortality is obtained by dividing the observed mortality by the expected mortality (multiplicative hazard model). Our first objective was to compare the results of these two models in a population-based cohort including 5115 dialyzed patients older than 70 years (mean age 79 years, range 70–97 years). Our second objective was to explore an alternative model combining both excess and relative mortality.
Patients and methods: Effects of covariates on excess mortality and relative mortality were assessed using a generalized linear model and a Cox model, respectively. The model, combining both excess and relative mortality, is derived from the Aalen model.
Results: The effect of age and sex was different according to the additive or multiplicative model used, whereas the effect of the first modality of dialysis or the primary nephropathy was similar. Because there was no evidence of lack of fit, the choice of one of these two models was not obvious. The combined model showed that the two components, additive and multiplicative, had to be kept. In this case, the combined model led to results similar to the pure additive and multiplicative univariate models, except for the method of dialysis, which did not exert an effect on both excess and relative mortality.
Conclusion: We underlined the complementary interest of modeling excess and relative mortality in looking for factors associated with mortality related to end-stage renal disease. The combined model appeared attractive in offering the possibility of reducing the model to the most appropriate one. When both components have to be retained, it better describes the effect of covariates on excess and relative mortality.

Keywords: additive hazard model, multiplicative hazard model, expected mortality, generalized linear model, Cox model