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Performed a drug survival analysis (Cox proportional hazard model) on patients with disease X, comparing male subjects with females while adding to the model country.

When checking the assumption of proportional hazard, I found that the test was statistically significant (therefore null hypothesis that it is proportional rejected). See the code I used + my output in R.

cox.model <- coxph(survObject ~ gender + country, data =  dat)
cox.zph(cox.model) 
ggcoxzph(cox.zph(cox.model))

             chisq df      p
    gender   48.7  1  3e-12
    country 745.6 14 <2e-16
    GLOBAL  793.2 15 <2e-16

However when I look at the following plot:

I notice that the residuals start to deviate near the end but eyeballing not so much for country.

This makes me think - isn't the difference statistically significant, simply because I have a large dataset? Current analysis performed on 15k patients.

I remember checking average age for female = 45.3 and male = 45.6 and this difference too was statiscally signifcant.

I have two questions

  1. Would you consider the assumption of proportional hazard violated? Please explain.
  2. What would your next step be?
Karolis Koncevičius
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Pashtun
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    Does this answer your question? [Test Cox proportional hazard assumption (Bad Schoenfeld residuals)](https://stats.stackexchange.com/questions/61131/test-cox-proportional-hazard-assumption-bad-schoenfeld-residuals) This happens with large data sets. Only you and your colleagues can decide whether the deviation from PH is large enough to matter for your purposes. – EdM Sep 20 '21 at 19:51

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