How to choose the best of two highly correlated predictors in cox proportional hazards regression

Question

I have built a good model of time-to-stroke under cox ph assumptions using a predictor of stroke risk (Framingham risk score). It incorporates a score according to Age, Gender, controlled / uncontrolled bp, cardiovascular risk factors and can be seen here : http://www.framinghamheartstudy.org/risk/index.html

I have hypothesised that it will be a predictor of time to event in my population.

However, it incorporates age, in fact it is correlated 85% +/-3% with age. So my question is: How do I effectively assess whether it is a better predictor than age alone. (It's pretty useless clinically if it's not) My intuition has been to include age alone then the framingham score alone in the model with the controlling predictors and then compare the AIC between the two fits, choosing the one which changes the AIC most - compared to the model with only the controlling predictors in it.

Is this a good solution to this in general? Or is it just plain wrong.

Answer 1

In my opinion, this is not a matter of which model fits your data the best (AIC), rather it's a matter of predictive accuracy of your competing models. I would take a look at the extension of ROC curves for survival regression models, for example.

Reference: Heagerty & Zheng - Survival model predictive accuracy and ROC curves - Biometrics. 2005 Mar;61(1):92-105.