Developing Risk Scores from Cox Regression model? A simple question on the development of risk prediction models from Cox regressions.
Suppose, as an example, that I want to create a risk score for 1-year mortality in patients with cardiovascular disease.
Performing a Cox regression, I found 3 dichotomous variables (yes/no; lets call them variable1, variable2 and variable3 for simplicity), independently associated with the outcome. Each of these variables has a beta coefficient within the regression model.
In order to develop a scoring system to predict the risk of mortality at 1 year, I need to assign a score to the presence of each variable. Obviously, points within the score can (and should) be "weighted" according to the importance of the predictor on the outcome (e.g., variable 1 may give 1 point, while variable3 may give more points, if present).
Which approach should be used to establish how many point should be assigned to each variable in the Cox-Regression?
One approach (perhaps naive) would be to transform the beta-coefficients into scores, but I would like to know if there is a more "rigorous" method, and especially if there are reference papers to use as guidance.
 A: The question implies that statistical significance testing was used to select variable for the model.  This is a big mistake as discussed at length on this site and in my RMS course notes.  Once you successfully fit and check a pre-specified model, the points are just the regression coefficients.
A: Your "naive" method, combining the predictor values with their regression coefficients, is the way to go.
The individual Cox regression coefficients represent the change in log-hazard associated with each of your predictors. That's about as direct a measure of "the importance of the predictor on the outcome" as you can find, if your model is well-calibrated.
Calculating the linear predictor of the model based on all the predictors (sum of products of predictor values times coefficient values) then provides a combined estimate of log-hazard relative to baseline conditions. In your case with only 3 binary predictors and (apparently) no interactions, you only have 8 distinct "scores" to assign that way, so it's pretty simple.
In more complicated cases you can use a Cox model to produce a nomogram that can give a combined linear-predictor value graphically. Harrell has several examples of nomograms in his class notes, with Cox model nomograms specifically illustrated in Chapters 20 and 21. That document, his textbook, and the references therein provide the documentation that you need.
