ABSTRACT
In Chapter 6 different models have been presented that can all be considered as extensions of the simple Cox model. The models agree on how to combine covariates through linear predictors, but they differ in the way they model the violation of the proportional hazards model. All these models are considered and compared in Perperoglou et al. (2007), using long term survival data of a large cohort of breast cancer patients. The interesting phenomenon observed in that paper is that there appears to be a large discrepancy between the models when looking at the estimated hazard functions for different covariate patterns, while the differences between the estimated survival functions are much smaller. To get a better understanding of this phenomenon it is helpful to have a closer look at the time-varying coefficient model of Section 6.1,
h(t|x) = h0(t)exp(x>β (t)) . The survival function S(t|x) is directly related to the cumulative hazard H(t|x) = − ln(S(t|x)). The following approximation is crucial for our understanding of the model.
