Actuarial Outpost Performing a Case-Mix Adjustment
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#11
11-17-2017, 09:41 PM
 AMedActuary Member SOA Join Date: May 2007 College: UCLA Alumni Posts: 392

Some more questions:

(1) Why is birth weight given at all then? If that's related, ignoring it will not produce the best adjusted data.
(2) Is severity uniformly distributed for the people in the program? Perhaps you can say this for the benchmark data but is this true for the program members?
(3) Does each condition have its own severity score or does each member just have their own severity score in total (including the severity of all conditions)?
#12
11-17-2017, 10:14 PM
 mistersunnyd Member SOA Join Date: Aug 2016 Studying for how to find a job Posts: 161

(1) It was included for one of the earlier questions, but the case mix adjustment specifically asked for just sing the conditions.
(2,3) Due to the large amount of benchmark data, I assumed that it followed a normal distribution. Then, I separated the conditions into 4 groups by finding the 0-25% LOS range, 25-50% range, and so on. Now I have conditions with a severity number assigned, and each member only has one condition listed and thus only one severity number. After all that, I used my method from my previous comment. I also performed a chi-squared goodness of fit test on the clinic data vs the benchmark, and the result was that the clinic data did follow the benchmark data. I'm not sure if that answers your uniformly distributed question though.
#13
11-17-2017, 10:18 PM
 mistersunnyd Member SOA Join Date: Aug 2016 Studying for how to find a job Posts: 161

Perhaps I should do a Kolmogorov-Smirnov test to check uniformity?
#14
11-20-2017, 04:07 PM
 WhosOnFirst Member Non-Actuary Join Date: Mar 2015 Posts: 153

Quote:
 Originally Posted by mistersunnyd Anyways, the problem specifies that I only use conditions to adjust LOS, so I guess I can leave birth weight out of it. My final method is as follows: since I have four classes of severity (1,2,3,4), the average of that is 2.5, and I will multiply or divide the LOS of each observation by x such that the observation's severity multiplied or divided by x is 2.5. What do you think?
I don't think this methodology will work.

Let's assume that the ALOS for your severity group 1 is 1 day in the benchmark data. If you run your clinic through and the ALOS for severity group 1 is also 1 day then using the method described above results in an adjusted ALOS of 0.4. This doesn't make any sense as a result because the morbidity of the two populations is the same. The reason this method doesn't work is because you are adjusting the indicator variable based upon itself.

What you should do is look at the ALOS in each of the severity levels of the benchmark population. You will have four ALOS like Severity 1 = 1 day, Severity 2 = 3 days, Severity 3 = 5 days, Severity 4 = 10 days. The average for your population overall will be 4.75 days (only because of the way you assigned severity). The next step is to look at the distribution of both the benchmark population and the clinic population. The benchmark is easy as each severity is 25% because of how you assigned the severity levels. Your clinic population may look like Severity 1 = 10%, Severity 2 = 25%, Severity 3 = 30%, and Severity 4 = 35%. If the ALOS for the clinic data is Severity 1 = 1 day, Severity 2 = 2 days, Severity 3 = 4 days, and Severity 4 = 9 Days then the average for the whole clinic is 4.95 (in excel this is the sumproduct of the percentages times the average).

You can now compare on an apples to apples basis in two ways. You can use the averages from the benchmark and the percentages from the clinic and compare the ALOS to the clinic value (sumproduct of the clinic percentages times the ALOS by severity for the benchmark) to get 5.85 as an expected ALOS based upon the clinic distribution versus a 4.95 ALOS from the observed data. This suggests that the clinic program decreased the ALOS by 0.90 days. What this method does is compares an expected result with the actual result by determining what the ALOS for the benchmark population would have been if the severity distribution was the same as the distribution for the clinic population.

However, you were specifically asked to case adjust the clinic population so you need to use a slightly different calculation. You will use distribution of the benchmark population and the severity ALOS from the clinic population (sumproduct of the benchmark percentages times the ALOS by severity for the clinic). The result will be 4.00 days. This is compared to the benchmark ALOS of 4.75. What this method does is determines what the ALOS for the clinic population would have been if the distribution of the severity of the population had been the same as the benchmark's distribution.

Notice that in both cases the direction of the change is the same (ALOS is lower for the clinic population) but the magnitude of the change is different. This is due to the higher or lower weight given to the various severity levels.
What you are adjusting for is the distribution mix of the populations so that you can compare the two populations on an apple to apple basis. If the population distribution is identical then the adjustment results in no change to the ALOS as should be expected.
#15
11-20-2017, 04:16 PM
 WhosOnFirst Member Non-Actuary Join Date: Mar 2015 Posts: 153

One thing I forgot to mention. This assumes that you've categorized the two populations in the same way. In other words, you identified the conditions in the benchmark population that had the longest LOS and classified all incidents of that condition as the same severity. For example, if diabetes is one of your conditions and it was a Severity 4 then it is a Severity 4 regardless of the LOS for the actual claim. What I'm hoping you did was look at the ALOS for each condition that you have and lumped the longest 25% into one category, the next 25% into a second, etc. That is as fine a way as any to do this grouping and then make your case adjustment. If you are using the LOS to assign severity then your analysis will be flawed as you will be trying to adjust the ALOS based upon what the ALOS is.
#16
11-20-2017, 07:53 PM
 mistersunnyd Member SOA Join Date: Aug 2016 Studying for how to find a job Posts: 161

So I still went with the 2.5 ALOS method because if my data had special cases where the patient had a very low LOS(moved to another clinic or passed away) or very high(who knows why), my average would be affected by these extreme values, and I didn't want that to happen. After this, I also checked each condition's percentage in the clinic data and compared it to the condition's percentage in the benchmark data. I multiplied the clinic's condition's LOS if the benchmark had a greater percentage of the condition and divided the LOS otherwise. The deadline has already passed, so I can't do much now. What do you think about my overall method?
#17
11-21-2017, 03:14 PM
 WhosOnFirst Member Non-Actuary Join Date: Mar 2015 Posts: 153

Quote:
 Originally Posted by mistersunnyd So I still went with the 2.5 ALOS method because if my data had special cases where the patient had a very low LOS(moved to another clinic or passed away) or very high(who knows why), my average would be affected by these extreme values, and I didn't want that to happen. After this, I also checked each condition's percentage in the clinic data and compared it to the condition's percentage in the benchmark data. I multiplied the clinic's condition's LOS if the benchmark had a greater percentage of the condition and divided the LOS otherwise. The deadline has already passed, so I can't do much now. What do you think about my overall method?
Um, well, I, uh... <awkward pause> You see, the thing is... What you need to understand is that...

I'll lay it out straight, you gave them a meaningless number. You did do some calculations and used some fancy formulas but there is no meaning behind the adjustments you made. What you did was adjust the LOS for each record which is not what case adjusting is. I think what you were attempting to adjust the LOS because you thought that cause the average for the clinic population to move closer to the mean of the benchmark population. What you need to do was adjust for the mix of conditions, which doesn't change the LOS at all and you don't need to worry about outliers (unless the population size is very small).

Here is a simple example, pretend you want to know the average age of two populations and if they are similar. One group has 50 children and 50 adults. The average age of the children is 12 and the average age of the adults is 42. Therefore the average age of group one is 27. The second group has 30 children and 70 adults with the same average ages as group one. However, the average age for group two is 33. We want to know if the ages of the groups are materially different. The quick answer is yes, the second group is older then the first. Since we can recognize that a group with more adults is going to naturally be older, we may want to adjust the numbers to compare the average age without the impact of the mix of adult versus child. What we really want to do is find a way to tell if the average age is different because of the population mix or something else. In this simple example, we know that the difference is due only to the population mix since the average age for the children and the adults are the same in the two populations. If we case adjust either group one or group two the average ages will come up identical.

If I try to replicate that with your method this is what happens. We'll break group one into four parts, each with 25 people. The average for part 1 is 8, part 2 is 16, part 3 is 38 and part 4 is 46. The average for the children is still 12 and the adults is 42 with the overall average of 27. We'll break the second group in a similar fashion. Same average ages for each part as group one but part 1 and part 2 have 15 children with part 3 and 4 having 35 adults. The average age for group two is still 33. We know that the two groups are in fact identical in age and the only difference is due to the mix of children and adults. If we apply your method (multiplying or dividing by the part number and then multiplying or dividing by 2.5) we end up with an adjusted age of 23.5. That would suggest that group two is younger then group one which we know to be untrue.

I hate to be the bearer of bad news but your methodology is broken. If I was you, I'd properly case adjust the study and see what the result is. If the results are materially different then what your method produced, I'd get in front of that before someone makes a decision based upon your bad numbers.
#18
11-21-2017, 07:05 PM
 mistersunnyd Member SOA Join Date: Aug 2016 Studying for how to find a job Posts: 161

Hmm sorry I'm still having a bit of trouble understanding. This isn't for a company so don't worry haha. Actually, let me clarify the problem a bit since the deadline's passed anyways. Basically, I have benchmark data, data from clinic X, and data from clinic Y. I'm trying to figure out whether clinic X's new program is efficient by looking at ALOS whereas clinic Y is the same as clinic X except clinic Y is not implementing the new program.

If I split the conditions in the benchmark data into four quantiles based on LOS and then used the quantiles on clinic X and Y, would that be OK? Because I am putting conditions with higher LOS in the benchmark in the highest severity group and vice versa. Then, I'm using these conditions to analyze clinic X and Y.
#19
11-22-2017, 11:27 AM
 WhosOnFirst Member Non-Actuary Join Date: Mar 2015 Posts: 153

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.