Excel Play: Raising the Value of PAMA Median for Sole Source Tests by Selective Appeals

 Under PAMA, CMS sets 3 year prices (or 1 year prices for ADLT tests) based on the median of reported private payer prices by CPT code.    It's a weighted median.   It turns out this is difficult to calculate analytically in Excel (they could make such a function, but don't), but it's fairly easy to model in Excel by making dummy columns for calculations.  However, it requires some functions that an entry level Excel user probably won't know.  (I certainly didn't).

Let's say a lab is a sole source lab (SNEAKYLAB) with very few test payments - 13 payments at each dollar amount from $1 to $12.   The median is the 7th value, with 6 values above and below it.   The median payment for this PAMA test is $6.   

Now let's say during the six month data period, in the sixth month, SNEAKYLAB appeals the four lowest payments ($0.50, $1, $2, $3).  Now the median value of the reporting paid tests is $8.  Starting from $6, that's +$2 or 33% higher.   If the lab's margin was $2, it's now $4, or twice as high.

But the real math would be more complicated.  Let's say the lab has 85 test payments, with a Guassian distribution centered around $7.  For example, it got 13 payments at $47, and only 5 payments at $11.   Here's the data.  The 85 payments will have a median at 42.5, so the median lies above the 35th payment but before the 48th payment, and the weighted median is $7.

Let's try the same appeal process again.  The lab appeals the $4 and lower claims.  Now it has 68 claims to report, so the median is the 34th claim, which lies between 24 and 35, so the median payment is $8.  That's only a $1 increase, but again, if the lab's profit margin was $2, it's now $3 or 50% higher.

The question arises, can you analytically calculate this for a complex distribution (and thousands of claims?)   Real PAMA data, like for BRCA 81211 in CY2017, have a lot of claims (over 90,000) and a wide range of prices (from $1 to a few over $10,000).    It's notorious that Excel lacks a simple way to calculate weighted median directly (see here or here).  But it's not hard to create a weighted median roadmap by modeling.  You get this:

It's easy to see by inspection what happens with different appeals strategies truncating the table from the bottom up.   If we appeal everything $4 and less, we have 68 claims, the median is 34, and that falls between Excel A5 and A6 (inspecting around C5, C6, and then looking leftward for the price.)   If we appeal everything $6 and less, we have 48 claims, the median is the 24th claim (D7), and we'll find the 24th claim around row 5 (C5), and looking leftward, the median payment is now $9.

Here's what I was able to figure out today.  You can actually add a couple more columns to do this directly in Excel.   

To get the row of data that holds a particular median value, we use the function MATCH:

Column E =MATCH(Dn, C$2:C$13, 1)

We then use data in Column E to read to the left to pull a price from Column A.

Column F= INDIRECT("A"&En)

IN THE TABLE YOU SEE BELOW:  

If my math is right, if you appeal 2% or 6% of the 85 claims, the median doesn't change.  If you appeal 20% of the claims, the median jumps from $7 to $8.   After that, you have to jump to appealing 59% of the claims to get the median to jump again (to $9).    So you might find the sweet spot is appealing 20% of claims.   (Note: I have to add +2 to "MATCH" to make this work, so it may be imperfect, but the system is directionally correct.)

I tried this with 94,975 real BRCA claims from the PAMA dataset of 2017, ranging from $1 to $44,206 (at which top price 22 claims were reporting in PAMA).   

The median that I got in Excel with this approach was $2400. If you appealed 25% of claims, the median rose to $2640 or +10%.    If you appealed 40% of claims, the median rose to $2805, or +17%.   If you appealed 50% of claims, the median rose to $2922, or 22%.   

BRCA data for 2017 was extremely lumpy (huge numbers of cases clustered with lots of payments at a few price points close to the real median), so for that code's distribution, it proved difficult to move the median a lot with smaller volumes of appeals.  Movement would be greater with a more Gaussian distribution of BRCA prices.   Still, if you look at profit margin, marginal increases of 10% in payment would double a 10% profit margin to a 20% profit margin.

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I reran with 82175 PAMA data (KRAS).  There were 5409 claims and a median of $193, for me.  If you appealed the lowest 10%, the median rose to $197.    If you appealed the lowest 20%, or 30% the same.   If you appealed the lowest 40%, the median rose to $204, only +3% of the base.  If you appealed the lowest 50%, the median rose to $236.   This is +23% of the base median.