I have a question on Cox regression using PSI (Percent Spliced In) values as covariates. In all publications I read the authors used PSI values between 0 and 1. However, I am not sure whether a multiplication by 100 would not make more sense regarding the interpretation of the Harzard ratios.
Here are some example results for a univariate cox regression using R. My formula is Surv(times, vital_status)~PSI, where PSI is a continuous variable. I used my normal PSI values (between 0 and 1) and once multiplied them by 100. Here are the results:
PSI between 0 and 1:
coef exp(coef) se(coef) z Pr(>|z|) PSI -1.2900 0.2753 0.6131 -2.104 0.0354 *
PSI between 0 and 100
coef exp(coef) se(coef) z Pr(>|z|) PSI -0.012900 0.987183 0.006131 -2.104 0.0354 *
The coef and se(coef) differ by a factor of 100, while z and the P-value are identical. exp(coef), so the Hazard ratio (HR) obviously differs and I am not sure, which one makes more sense in the interpretation.
As far as I understand it, the HR means that with each 1 unit change, the hazard/risk drops by 1-0.2753= 72.47% (range 0 to 1) and 1-0.987183=1.2817% (range 0 to 100), respectively. A one unit change for the 0 to 1 range means a change of 100% (e.g. going from no inclusion to full inclusion), while for the 0 to 100 range it is 1%. So for me it would make sense to use PSI values between 0 and 100 as the interpretation of the Hazard ratio makes much more sense.
However, all publications I found use a range of 0 to 1, which is why their HRs are very high or very close to 0.
What do you guys think?
Thanks in advance.