An important assumption of the Cox model is the homogeneity of the effect of an explanatory variable over time. In other words, the hazards ratio (HR) is assumed to be constant over time. Several methods can be used to test this assumption.

Graphical approach

The log (-log (S (t))) curves - with S (t) the survival function and t, the time - can be plotted for each value of the qualitative variable. The difference between the curves must be constant over time. If the curves intersect, the effect of the variable of interest can be time-dependent.

The test based on the Schoenfeld' residuals

The p-value corresponds to the probability of error if the assumption of proportionality is rejected.

What you can do when hazards are non-proportional ?

If you observe a non-proportional effect, you can include a time-dependent effect if it concerns the explanatory variable of interest. If the variable is taken into account as a possible confounding factor, you can stratify the baseline hazard of the Cox model on this variable.