I have been reading various responses on this topic but I do not yet understand how the p-value is interpreted to determine if the proportional hazards assumption holds or not.
I have a global p-value of 0.0506 with all features having p-values >0.1. My understanding of the null hypothesis is that the proportional hazards assumption holds if the p-value is <0.05 but if the p-value is larger than 0.05 then it should mean that there is not enough evidence to reject the null hypothesis and this does not mean that the PH Assumption Holds or we should accept the Null. But in most responses, it seems to suggest that if the p-value is not significant then the proportional hazards hold? Using the inference test via Schoenfeld residuals shows all the variables being not flat around the 0 line.
Best Answer
If the global p-value is significant then the PH assumption does not hold for the model. Schoenfeld is like a Shapiro-Wilk test of normality, if $p<0.05$ then the feature is not normally distributed. If Schoenfeld $p<0.05$, then the model or feature does not meet the PH assumption. You would need the global p-value to not be less than 0.05 before you start dipping into the individual feature p-values.
Also for Cox PH regression and the PH assumption, it's better to have categorical features for which you can plot the survivorship function and the follow-up days (months) on the log scale to see if the lines cross. (although the PH assumption is based on the hazard functions crossing, you can still see the crossings within the survivorship functions). The attached plots show these S(t). vs days (log scale) for a 3-level categorical factor and a 4-level factor. The PH assumption holds for the 3-level factor, but not for the 4-level factor, since one of the lines cross. The global p-value for the model was about 0.4, and the p-value for the 4-level factor was <0.05.