I am using Cox proportional hazards models for survival analysis. The specific reason I am interested in them is because they give a nice way to quantify effect size between groups via the hazard ratio, assuming the PH assumption is not violated.
I use R's
survival package for the modeling. The models I am making have no interaction terms between predictors. I am currently in the following situation for some models:
- the model is a good fit, with concordance over 80% (obtained via
- the PH assumption is violated for one or more predictors (e.g. very small $p$-values for some predictors in
This leads me to a couple of questions:
- What is the main consequence hereof?
- Is there still some value in the hazard ratios for predictors for which the PH assumption is invalidated?
- How can the fit be so good despite a key assumption being violated?