Comparison of Aalen’s Additive and Cox Proportional Hazards Models for Breast Cancer Survival: Analysis of Population-Based Data from British Columbia, Canada

Background: Regression models for survival data have traditionally been based on the Cox regression model. However, its validity relies heavily on assumption of proportional hazards. Another restriction of the Cox model is insufficiency in dealing with time-varying covariate effects, since the regression coefficients are assumed constant. These weaknesses have generated interest in alternative approaches and with Aalen’s additive model, the effect of the covariates acts on an absolute rather than a relative scale. We here fit the Cox and Aalen’s additive models to breast cancer data for comparison through practical application.
Methods: The data related to 14,826 women diagnosed with breast cancer in BC during 1990-1999 and followed to 2010. Plots of the Martingale Residual Process and Arja’s Plot was used to assess the fit of the additive model. The Cox-Snell residuals, Martingale residuals and scaled Schoenfeld residuals were used to check the Cox model.
Results: In the category of patients younger than 65 years the proportional hazard assumption was satisfied. In this category, by the Cox model, the variables “stage”, “surgery”, “radiotherapy”, “chemotherapy”, “hormone therapy” and interaction between “stage” and “surgery” proved significant. In the same category, by the Aalen’s additive model, similar significant variables are selected except for “hormone therapy”. The sign of estimated coefficients from survival functions based on the both Cox and Aalen’s additive models were alike although estimated coefficients in the two models differed from the viewpoint of magnitude. In the category of patients older than 65 years, the proportional hazard assumption was not satisfied, and the Stratified Cox model and Aalen’s additive model gave similar results.
Conclusions: Based on our findings, if the proportional hazard assumption is not satisfied, the Aalen’s additive model is an appropriate alternative for the Cox model. If the proportional hazard assumption is satisfied, both models are appropriate. Generally, the two models give different pieces of information.