Cox PH Model postestimation

[Josh Wang]

Dear all,
I finished a Cox PH regression, the results are satisfied. But the test of proportional-hazards assumption is not passed. The overall prob>chi2 is 0.0000, in details the value of prob>chi2 the categorical variable is also 0.0000.
BUT the graphical tests seem to be all passed. I attached them. I have add the strata to test again, the results are same.
Can I still use Cox model or I need to change to any others survival models?
Thank you.

Best
Josh

[Carlo Lazzaro]

Josh:
I'd trust the visual inspection.
Statistical tests can easily reject the null if you have a remarkable sample size.

[Josh Wang]

Josh:
I'd trust the visual inspection.
Statistical tests can easily reject the null if you have a remarkable sample size.

Thank you Carlo for your reply.
I have a sample with 140,000 observations, I'm not sure if it is a remarkable sample size.
The null of the proportional-hazard assumption test is that it is held, but my statistical result is null rejected.

Best.
Josh

[Carlo Lazzaro]

Josh:
1) 140,000 observations are a remarkable sample sizes;
2) sorry, but I cannot follow your second point.

[Josh Wang]

Josh:
1) 140,000 observations are a remarkable sample sizes;
2) sorry, but I cannot follow your second point.

Sorry Carlo, Let me clarify clearly.
The null of the test of proportional-hazards assumption is the proportional hazard holds and no violation of the assumption, so after Cox regression, I did the PH test, but the global p value is 0.0000 which is less than 0.05, we reject the null. So the assumption was violated and the proportional hazard doesn't hold. It seems I couldn't use Cox model.

But the p values of categorical variables (X3 & X4) are bigger than 0.05, and the graphical tests are also passed. So My question here is can I still use Cox?

Thank you for your help!

Best
Josh

[Clyde Schechter]

The test is "accepting" (actually, just "not rejecting") the null hypothesis that PH holds for all of the individual covariates except and (barely) C3. It is rejecting it for the model as a whole. But with N = 140,000, these tests are far too non-specific. They will reject extremely minor, unimportant deviations from PH that are of no real consequence in terms of the proper specification of the model and getting useful results. I agree with Carlo's advice in #2: forget about the tests (I wouldn't have done them in the first place with such a large N) and go with the graphic findings.

[Josh Wang]

The test is "accepting" (actually, just "not rejecting") the null hypothesis that PH holds for all of the individual covariates except and (barely) C3. It is rejecting it for the model as a whole. But with N = 140,000, these tests are far too non-specific. They will reject extremely minor, unimportant deviations from PH that are of no real consequence in terms of the proper specification of the model and getting useful results. I agree with Carlo's advice in #2: forget about the tests (I wouldn't have done them in the first place with such a large N) and go with the graphic findings.

Thank you Clyde for your information, that's really helpful to me.
I also used the Loglogistic model as robustness and the results are the same as that of Cox.

Best
Josh