I have developed a Cox prognostic model based and internally validated it using bootstrapping. I also evaluated its calibration using Harrell’s $c$ statistic and Somers' $D$.
I have also checked numerous resources, Including Royston P. 2014. Tools for checking calibration of a Cox model in external validation: Approach based on individual event probabilities. Stata Journal 14: 738–755.
Now I want to externally validate my model with another model. I don’t have an individual-level dataset of the model against which I want to validate my model. It is a published Framingham equation in the form:
Predicted risk-at time $t =$
baseline hazard $\times \exp[0.8\ $age $+0.54 $ sex $+0.9\ $ diabetes $+0.5\ $smoking$]$.
I want to use the coefficients in the published Framingham equation (as prognostic index) to validate my model, and subsequently get the $c$ statistics.
According to Tilford JM, Roberson PK, Fiser DH. 1995. Using
lroc to evaluate mortality prediction models. Stata Technical Bulletin 28: 14-18 available here, in logistic regression, I have read that it can be computed by converting this into a matrix:
mat b = (0.8, 0.54, 0.9, 0.5 ) mat colnames b = age sex diabetes smoking
Then the post-estimation command
lroc can be used to produce the ROC curve and $c$ statistics.
I would really appreciate a suggestion from anyone on how can a $c$ statistic be obtained in a similar scenario for a Cox model.