Schoenfeld residuals

Question

In a Cox proportional hazards model with many variables, if the Schoenfeld residuals are not flat for one of the variables, does this invalidate the entire model or can just the poorly-performing variable be ignored? That is, interpret the coefficients for the other variables, but do not interpret the resulting coefficients for the poorly-performing variable.

There are several standard ways of dealing with a model where the Schoenfeld residuals aren't flat. Assume for the moment that we can't do them.

Answer 1

Judgement of proportional hazards(PH) should be based on the results from a formal statistical test and the Schoenfeld residuals (SR) plot together.

If the SR plot for a given variable shows deviation from a straight line while it stays flat for the rest of the variables, then it is something you shouldn't ignore. First thing you can do is to look at the results of the global test. The global test might indicate the overall assumption of PH holds true [or not]. If the global test is fine then switching the reference category of the variable for which the assumption didn't held true, you might be able to achieve PH. The hazards may be proportional when compared to one reference category but not the other. Hence, by switching the reference categories, you might be able to find the category which results in PH assumption being true.

If the switching doesn't solve your problem, and assuming you have got the right variables in your model, then this indicates that the hazards is not proportional for this particular variable i.e. different hazards at different time points. Hence, you may want to introduce interaction between variable and time in your model.