Dear Alfonso and Jeff

Thank you both for your very helpful answers!
I have a following question regarding centering of covariates that have values for only 1 group:
In this study, I have 2 groups- controls and Parkinson's disease patients. I want to compare the ROI-ROI FC between the groups when accounting for UPDRS-III (motor function scores). The issue is that only the PD patients have UPDRS scores. A level of zero on the UPDRS can be assumed for the controls and therefore I entered zeroes for the controls in the UPDRS covariate.
My question is: do I need to mean-center the UPDRS covariate?
I see that centering has a huge effect on the results and I infer that it is required. However, I thought centering will be problematic since a PD subject with a value of zero (that is, the average UPDRS) will be considered the same as a control with a value of zero.

Many thanks for your answers, it helps a lot!