I am working on fitting a Cox model to predict. But several predictors violated the proportional hazards assumption. I am gonna to do stratified Cox model to adjust them. But the results of stratified Cox model would not include any information or influence of those stratified predictors. As I really want to see the influence of one important predictor, I assume it's very important for the outcome of my data. Is there another way to do this?
You could include an interaction with time in your model. You definitely want to read Singer/Willett (2003) Applied longitudinal data analysis: modeling change and event occurrence, chapter 15, in particular section 15.3 Nonproportional Hazard Models via Interactions with Time. Google books has a preview.