A young age at diagnosis of cancer is often seen as an indicator of the aggressiveness of the tumor. However, empirical studies have shown conflicting results on the association between age at diagnosis and survival. There are two choices of time scale for a Cox regression model: time since diagnosis, and age. The regression analysis of relative survival rates is an alternative to the Cox model. Using breast cancer data from a population-based cancer registry, we illustrate the features of Cox models using the two time scales and compare them with the relative survival approach. Using a Cox model with time since diagnosis as the time scale, a younger age at diagnosis is associated with a lower mortality; using age as the time scale gives the opposite result. The relative survival approach agrees with the Cox model with age as the time scale. We maintain that a careful clarification of research purpose and a careful choice of methods are necessary.