I'd like to test for and estimate group differences in NIHSS (National Institute of Health Stroke Scale) change between hospital discharge and three months after hospital discharge.
Because the score is bounded between 0 and 42, the signed difference between the two measurements seems to me inappropriate, as people with a higher score at the first measurement cannot possibly improve as much as people with a worse score at that time, and vice versa. How can I account for this?
I considered a logistic regression model with the change in scores as dependent variable (as the score can be interpreted as a proportion, ie. x/42), but it I don't think I can control in this model for the baseline score, as it is already contained in the change in scores.
It is also of importance that the NIHSS is somewhere between interval and ordinal, being a compound of several different subscores. It is not linear.
I have found some more or less related threads here (such as Should the difference between control and treatment be modelled explicitly or implicitly? or Is it valid to include a baseline measure as control variable when testing the effect of an independent variable on change scores?), and am aware of the 1990 paper by Paul Allison ( http://www.statisticalhorizons.com/wp-content/uploads/Allison.SM90.pdf ).
Edit: What I have looked into