A relative survival regression model using B-spline functions to model non-proportional hazards
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Updated: Sep 20, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
Roch Giorgi1, Michal Abrahamowicz, Catherine Quantin
1LERTIM, Faculté de Médecine, Université de la Méditerranée, 27 Bd Jean Moulin 13385 Marseille Cedex, France.
Abstract:
Relative survival, a method for assessing prognostic factors for disease-specific mortality in unselected populations, is frequently used in population-based studies. However, most relative survival models assume that the effects of covariates on disease-specific mortality conform with the proportional hazards hypothesis, which may not hold in some long-term studies. To accommodate variation over time of a predictor's effect on disease-specific mortality, we developed a new relative survival regression model using B-splines to model the hazard ratio as a flexible function of time, without having to specify a particular functional form. Our method also allows for testing the hypotheses of hazards proportionality and no association on disease-specific hazard. Accuracy of estimation and inference were evaluated in simulations. The method is illustrated by an analysis of a population-based study of colon cancer.
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