When you are adjusting data to account for differences in the population mix, you need to determine your adjusted number by changing the distribution of the population and not the metric your are studying. For your ALOS study, you will use the ALOS from your clinic X for each severity group. You then weight each severity ALOS in clinic X by the distribution for clinic Y. Because of the way you defined the severity groups, this distribution happens to be 25% for each.
What you are doing is answering the question, "What would the ALOS look like for clinic X if the severity mix was the same as for clinic Y?" You can also compare the ALOS for each severity group independently. If your assignment of the severity levels actually represents a grouping of conditions then a comparison of the ALOS between x and y is on an apples to apples basis already. You can then draw the conclusion for each severity group if clinic x's program reduced the ALOS. Case mix adjusts take care of the issue that a disproportionate number of, for example, high severity cases went to clinic x which would naturally drive up the ALOS for the overall ALOS of clinic x. If the program was effective, the ALOS for severity 4 (and hopefully the other severity groups too) would be lower for clinic x then clinic y even though the average for the whole clinic x population is higher then clinic y.
It's about adjusting for distribution, not adjusting the LOS.
