🚀 go-pugleaf

Hi,

I have a question on the use of ratios verses differences for statistical 
inferences.  The situation is that we have two ordinal measures from patients 
in several hospitals. For each patient we have a match between score on 
admission and a score on discharge.  We want to compare the change in patients 
from admission to discharge across hospitals.  

The scale of the admission score ranges from 0 to 4.  The scale of the 
discharge score ranges from 1 to 4.  The higher the score then the sicker the
patient is on either admission or discharge.  Each scale has been tested for its
reliability.  However, we have no data on the reliability of the scales
when they are combined to describe changes in patient status from admission
to discharge.

Our choices for comparison are to take the ratio of the admission/discharge
score for each individual patient (the ratio has to be formulated this way 
because of the possibility of a 0 admission score)
OR
to take the difference between the two individual patient scores 
(admission - discharge).  

I believe that the difference score should be used
and tested by nonparametric methods.  My colleague resists using
the difference because of uncertainty about the effect on reliability and 
power to  detect differences.  

Any suggestions or pointers to literature on  a comparison between
difference and ratio measures would be greatly appreciated.

Thanks
Jim Murray
jfmurray@umaxc.weeg.uiowa.edu