Categorical variable as predictor of change - which analysis?


I wold really appreciate some insight/advice regarding issue below.

We are trying to analyse if diagnostic categories (4 seperate categories) of categories based on other variables (also 4 categories) better predict treatment response (defined as change in symptom scores (I measurement - II measurement)). If it would only be on one level (one category predicting the change I would run two-way repeated measures ANOVA), but the get stuck with the question which would be the best way to compare the results and which could let us make conclusions about which categories are better at predicting the score change.

I hope my question is formulated clearly. Thank you in advance!