Dear Lena,
I had a similar problem and standardized the variables using their interquartile range for a Cox model. I had problems when I rescaled the variables with the JAMA statistical reviewer but it got accepted when I used this approach. Nevertheless they made us show the results for both the standardized and unstandardized which demonstrated the utility of using interquartile range . Here are the references that I used.
32. Milligan GW, Cooper MC. A study of
standardization of variables in cluster analysis.
J Classif. 1988;5(2):181-204. doi:10.1007/BF01897163
33. Harrell FE Jr. Regression Modeling Strategies:
With Applications to Linear Models, Logistic and
Ordinal Regression, and Survival Analysis. Springer;
2015. doi:10.1007/978-3-319-19425-7
3
Hope that helps. With kind regards, Brydon.