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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.

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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.

3-level

4-level

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  • $\begingroup$ thanks, i do not have categorical variables and all are numeric. so i am using the inference test where all the variables had p values >0.1 while the global p value is at 0.506. i understand that if the pvalue is siginificant then we reject the null hypothesis that the assumption holds so my question was, if the p-value is >0.05, doesn't it mean that we do not have enough evidence to reject the null? or does it mean that we can now assume that proportionality holds? $\endgroup$ – Py_Mel Oct 31 '19 at 15:53
  • $\begingroup$ Proportionality holds if a feature is not significant. It's not recommended to use P>?, since it's not done. Significance or not is always wired to the statement e.g. P<0.05 for significance (reject), or not significant (accept the null) or say "the P-value was not less than 0.05." Mathematically, the inequality notation is acceptable, that is < or >, but it's good practice to instruct students (not saying you are a student) to not get into the habit of using "P>..." $\endgroup$ – user32398 Oct 31 '19 at 18:38
  • $\begingroup$ thank you for the advice. okay, it is confusing sometimes with how the p-value is interpreted in different settings as usually when the p-value is not significant, it means that there is not enough evidence to reject the null which is not the same with accepting the null. $\endgroup$ – Py_Mel Nov 1 '19 at 8:49

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