Proportional hazards and additive regression analysis of survival for severe breast cancer

The primary objective of this work was to investigate and compare the use of the Cox proportional hazards model and Aalen’s additive model in analysing survival data. Survival data from a study of 52 patients with advanced breast cancer was investigated using the Cox proportional hazards model. The model was optimized by examining different aspects by use of appropriate residual plots. Covariates judged not to improve the model significantly were removed. The model was stratified with regard to tumour size to account for different baseline hazards. After optimizing the Cox model, the same data was used to fit an additive model according to Aalen. Plots of the martingale residual process and Arja’s plot was used to check model fit and optimize model options. The information gained from fitting of the two models is similar in some respects but also quite different in others. Both procedures resulted in the same covariates selected to remain in the model. The Cox model yield easily interpreted estimates of the covariates effects, but the assumption of proportional hazard is necessary to make these estimates valid. The additive model and the plots of the cumulative regressions functions give an appealing understanding of how the hazard profile is distributed. Most often however, these cumulative regression functions do not easily transform into a single numerical estimate of the covariate effect. ∗Postal address: Swedish Institute for Infectious Disease Control, SE-171 82 Solna, Sweden. E-mail: [email protected]. Supervisor: Mikael Andersson. Chapter