I would like to better understand your point. I don't know much about the technicalities you are alluding to.
If each facility is analyzed in isolation, and assuming that the total amount of data collected from that is the same as the way they did it, won't you get the same results?
Typing that, it comes to me that your suggestion could allow for more possible conclusions (and options for improvements, if truly needed). One possible conclusion might be that there are differences between urban / suburban, for example. Perhaps blacks in a suburban hospital get the same meds as whites. Perhaps whites in an urban hospital get less.
Is this what you are driving at?
I need to go back and reread how they handled Asians and Hispanics.
For example, let us assume there are two hospitals, call them A and B. Hospital A administers opiate analgesics to 80% of all incoming patients, black or white, who present with symptoms of appendicitis. Clearly, no racism is present.
Hospital B administers opiate analgesics to 20% of all incoming patients, black or white, who present with symptoms of appendicitis. Clearly, no racism there, either.
Now, Hospital A is in a majority white community, where 90% of the patients are white; Hospital B is in a majority black community, with 90% of the patients being black.
Therefore, from Hospital A we have 72 white patents and 8 black patients (of 100) being administered opiates. From Hospital B, we have 2 white patients and 18 black patients being administered opiates.
However, when we combine the data, 74 white patients were administered opiates, but only 26 black patients. From two sets of data which clearly show no racism, we get a combined set which shows tremendous racism.
The difference is due to the hospitals, not due to racism.
Since the data from the study does not separate out the hospitals, there is no way to tell for sure if the difference is actually due to racism, or just due to the fact that different hospitals may have different policies on administering opiates.