# Measure score change over time while accounting for baseline differences

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

• Good question, although it looks like your links to the other threads on this site are missing! – Andy W Mar 23 '12 at 12:07
• What do you mean by "not linear"? Linearity is a property of the differences between mean outcomes in different groups, it's not a property of any individual's score. Also, this reference could be helpful; whether you adjust for baseline depends on what question you are trying to address. – guest Mar 23 '12 at 20:39
• You're correct, "linear" is not the right word there. What I meant or what is a good part of the deal is that I'm not sure how to even best describe the change in a bounded integer. Somehow neither handling it as an integer nor as a proportion appears to be suited to the nature of the score. Thanks for the reference. – miura Mar 24 '12 at 8:27
• Thanks for sharing this: "Most importantly, Kenny (1975) and Kenny and Cohen (1979) argued that regression toward the mean is not a problem when the objective is to compare two or more stable groups. In such circumstances, the change score method can give results with less bias than the regressor variable method." (Allison, 1990, p.95) Concerning the design, do you have any a priori reasons to believe that regression to the mean is unavoidable? – noumenal Apr 21 '12 at 13:33
• I don't really see regression to the mean as my primary problem. I am more concerned that a change score could be inappropriate because the NIHSS is bounded. Also I don't know which, if any, regression model with three-month NIHSS as dependent and baseline NIHSS as independent variable would be most suitable here. – miura Apr 22 '12 at 10:25