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In the statistical analysis of this paper I have some questions regarding their approach.

https://academic.oup.com/ndt/article/33/6/1001/3978817

“Variables with non-normal distributions were either log2 or rank transformed, whichever was appropriate. WBCs and morphometric variables were standardized in all regression analyses. A rank transformation itself produces a standardized variable, but those that were not transformed or underwent log2 transformation were subsequently standardized for analysis”

Then later, when addressing Cox regressions:

” Hazard ratios (HRs) were expressed for a 1 SD increment in the distribution of each WBC variable.”

I want some clarification and my coffee is running out (and my skills as a lowly undergradute are being exposed). Are the hazard ratios expressed in the table for the variables log transformed then subsequently standardized? My understanding is that the standardizing to mean 0 and sd of 1 had two effects: helped facilitate comparisons AND also normalized the data? But My understanding is that normal variables are not necessary for Cox regression. Would like some insight. Let me know if I can clarify my question.

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