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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?

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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.

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