Aalen's Additive, Cox Proportional Hazards and the Cox-Aalen Model: Application to Kidney Transplant Data

Abstract

The Cox proportional hazards model is most widely used in survival analysis for modeling censored survival data. In this model, the effect of the covariates is assumed to act multiplicatively on the baseline hazard rate and the ratio of the hazards is constant over survival time. This is an important assumption and sometimes may not hold in some survival studies. The Cox model can lead to biased results when the proportionality assumption is not satisfied. In such a situation, the additive hazards regression models have been an alternative to proportional hazards models. The Aalen model allows for time-varying covariate effects. In some situations, some covariate effects may be constant but the others may not. In such cases, the Cox-Aalen model is a better alternative since it allows to combine both kinds of covariates in the same model. In this study the Cox proportional hazards model, Aalen’s additive hazards model and the Cox-Aalen model have been considered. These models have been applied to kidney transplant data and the differences in estimates of the unknown parameters obtained by the Aalen’s model, the Cox model and the Cox-Aalen model are investigated.