I am trying to evaluate the success of a medication adherence intervention. I am trying to assess the success of the program before and after the intervention in terms of number of days a patient took the medication relative to how long they were observed (i.e. # of days medication was taken / # of days observed). The challenge I have is that periods of observations (before and after the program)is different for every patient in the data set.
I would like to control for the number of days to make the assessment to see the actual impact.
One way I thought of doing this is to normalize the data (using min/max) for each patient before and after the program. For instance for the observations before the intervention, I would take the max and min number of days observed before intervention among all the patients and normalize the days medication taken and days observed for each patient (to get it between 1 and 0). Similarly I would do the same for post intervention observations (with min/max of days observed of post intervention).
I am wondering if this is logically correct? One reason I could be wrong is that I am taking the range of "days observed" and using that to normalize "days medication taken". Any suggestions or thoughts?
