I am running an analysis on a Cox model where I used PCA features extracted from medical images to predict survival. However, when I examine the coefficients on these features they are very small. (Implemented with Lifelines package in python)
coef exp(coef) z p -log2(p)
0 0.01 1.01 3.41 <0.005 10.59
1 0.02 1.02 7.09 <0.005 39.42
Grade_II -0.39 0.68 -2.97 <0.005 8.4
Grade_III -0.27 0.77 -2.1 0.04 4.82
These 2 PCA features have large z-scores so I expect they should have large coefficients. I think it may have something to do with the fact that the features are standardized before running PCA, so 1.01 is actually a large change. I want to be able to just look at the coefficients and be able to tell how these PCA features compare to the categorical variables Grade_II and Grade_III. Looking at the coefficients it seems like the PCA features have very little effect compared to grade but in fact they actually have a large effect. I want to be able to show a large coefficient for readability purposes, but I am not sure what the correct thing to do is. Do I "unstandardize" the PCA features right before running the Cox regression? Do I divide them all by the standard deviation? I don't think I can just divide by an abritary number because then it would be hard to compare the coefficients.