How to calculate the heterogeneity P value for a variable in two Cox regression models

Dr. Frank Harrell,

Complementing this topic, I have one question regarding interpretation of the proportional hazards assumption with cox.zph:

  • The output includes a chisq, df and p-value for every variable and also for the GLOBAL model. How should I interpret a test that gives me a GLOBAL proportional models p-value > 0.5 but one of the variables presented are in fact < 0.05?

The question may be silly, but I understand that multiple tests for non-proportional hazards can have p-values less than 0.05 by random chance (as would normally happen in multiple testing analysis) and the GLOBAL value reflect an overall model fit for non-proportionally (similar to a correction for multiple testing).

Adding on this: in this situation of a divergent GLOBAL and specific variable p-value for cox.xph, how would you report in an article?

Thanks in advance,

Felippe