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I had to transform some of my primary variables of interest (log transform). Others were left untransformed as they were normally distributed in the sample (Pfat, etc.). To allow for comparisons of hazards, I was advised to standardize all the variables. I know the hazard ratio is simply exp(Beta Coeff.) but how do I interpret this appropriately if the variables have been both log-transformed and standardized?

I'm not willing to share my data but can provide answers if needed. All the predictors and covariates are explaining disease free survival.


marked as duplicate by EdM, kjetil b halvorsen, mdewey, Peter Flom regression Jan 27 at 13:25

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  • $\begingroup$ Transformations to give predictors normal distributions aren't necessary; they should be done to satisfy regression's linearity assumptions. Interpretation of a log-transformed predictor is discussed here. There isn't a conceptual difference between linear regression in that discussion and your Cox regressions; for a log2-transformed predictor, the hazard ratio will be the extra hazard associated with a doubling of the value. It's not clear what you mean by "standardized." Please read that page and edit your question if further questions remain. $\endgroup$ – EdM Jan 26 at 21:06
  • $\begingroup$ @EdM Thank you for your comments. By standardizing I meant (x-u/std.dev). Like a z-score. Is this a nonsensical approach? For some data sets, my results only hold when I standardize. I realize may be wrong, but help me understand why. $\endgroup$ – mindhabits Jan 27 at 2:28
  • $\begingroup$ Standardizing predictors without other transformations should only affect the magnitudes of regression coefficients, not statistical significance etc. The apparent significance of interaction terms expressed as treatment contrasts can differ with standardization, but not when analyzed properly with ANOVA. If your specific question on interpreting coefficients of log-transformed predictors is answered, you should submit another question related to how standardization seems to be affecting your results. It would help to have more specifics on your data; consider using aliases for variable names. $\endgroup$ – EdM Jan 27 at 3:10