We have some clinical variables on patients under a disease partially characterized by a key clinical variable. To study how this disease behaves in different levels of the key clinical variable, we divided our patients into groups of different intervals of the value (e.g. 0~100, 100~200, 200~300 of the variable value).
Although these intervals have been used in clinical practice, they are almost arbitrary intervals. Now we wonder if some of the intervals can be collapsed, meaning if the patients do not separate between the intervals in terms of the other clinical variables.
We did this by building a logistic regression model using the other clinical variables to predict patients in one interval apart from those in another interval. Do you think it is an OK way to answer our question?
If not, do you have an idea about how to determine the collapsibility? Further, let's say we want to come up with new intervals in an unbiased fashion (e.g. 0~150, 150~300, etc instead of 0~100, 100~200, 200~300), what would you do?