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#1
04-24-2012, 08:28 PM
 actuary_pilot Member SOA AAA Join Date: Jul 2003 Location: Louisville, KY Posts: 1,009
Mate Outline page #405

The TNHP Savings = N% * [M% + Shift * (P%-M%)]

where

N%=the percent of total claims controlled by non preferred providers
P%= cost differential between tier providers = 1- average preferred cost per unit/average non preferred cost per unit
M% = member liability differential
Shift = the assumed percentage of non preferred users reacting to the increased liability by switching to preferred providers

By Distributing the N% you get

TNHP Savings = N% * M% + N% * Shift * (P% - M%)

which is the percent of claims times the member liability differential + the percent of total claims that shift to preferred providers * the difference between the cost differential btw. providers and the member liability differential

Here is my question:

(N% * Shift) represents the members that switch to the preferred provider
it seems to me to make more sense that the first part of the formula (N% * M%) should actually be N% * (1-shift) * M% in other words that part of the formula would make more sense if it was the savings from the members who didn't shift to the preferred plan, i.e. the savings arising from members who use non preferred providers from the decrease in cost savings.

So to put it another way should the formula be
TNHP Savings = N% * [(1-Shift)*M% + Shift * (P%-M%)]
#2
04-24-2012, 09:18 PM
 Atropellador Member Join Date: May 2008 Posts: 2,696

This is on pages 406-407 in my copy of MATE.

Your proposal makes intuitive sense. Horman did say his formula is just an approximation. To test it, you could further assume:

N0 = number of claims
P0 = average unit cost out-of-network, which would make the average in-network unit cost P0(1 - P%)
M0 = average member cost sharing % in-network, which would make the out-of-network cost sharing M0 + M%

Then, before the shift, the total paid claims in-network equals
N0(1 - N%)(1 - M0)P0(1 - P%)

The out-of-network paid claims total
N0 N%(1 - M0 - M%)P0

After the shift, the claims become
N0(1 - N% + N% * shift)(1 - M0)P0(1 - P%)
in-network, and
N0 N%(1 - shift)(1 - M0 - M%)P0
out-of-network.

Subtract the paid dollars after the shift from those before, then divide the difference by the paid dollars before the shift.

Last edited by Atropellador; 04-24-2012 at 09:48 PM.. Reason: make "shift" multiplicative
#3
04-24-2012, 09:21 PM
 Atropellador Member Join Date: May 2008 Posts: 2,696

The reading starts on page 6.
#4
04-24-2012, 09:42 PM
 actuary_pilot Member SOA AAA Join Date: Jul 2003 Location: Louisville, KY Posts: 1,009

I read the article - but

TNHP Savings = N% * [(1-Shift)*M% + Shift * (P%-M%)]

seems to make more sense than

TNHP Savings = N% * [M% + Shift * (P%-M%)]

N% * Shift is the members who are shifting. M% represents the savings from the cost sharing imposed from non preferred network. But if N% * shift starts using the preferred network, then N%-N%*Shift is left over, which is the same as N%*(1-Shift).
#5
04-24-2012, 09:57 PM
 Atropellador Member Join Date: May 2008 Posts: 2,696

Oh, that's right, "shift" is multiplicative, not additive. I edited the formulas in post #2 accordingly.

I'd posted the link for the benefit of readers who don't have the MATE Study Manual.

And like I'd said initially, your formula makes sense. Take the extreme case, where shift = 1 and everyone goes in-network. Horman's formula produces savings of N% P%. Yours produces N% (P% - M%), which I think is more correct, since it reflects both the cost sharing and the network discounts.
#6
04-25-2012, 12:57 AM
 gosuruss Member SOA Join Date: Feb 2007 Favorite beer: whatever is free Posts: 4,327 Blog Entries: 2

The confusion in this thread is the base level you are starting at.

The reason the formula does make sense is because it is assumed currently that all providers have the same exact cost sharing. So, if 100% were to move from non preferred to preferred, all that would change is that now they are paying the lower paid cost per unit (N% * P%). The M% piece of the equation is the _additional_ cost sharing you are adding to non preferred providers, which results in savings. So you really have two options: Either the non preferred dollars have an increase in cost sharing, or they shift to preferred network where paid cost per unit is lower. So, N%*shift*P + N%*(1-shift)*M% is your total cost savings. I struggled with this formula for a bit but it started to make sense when i figured out where they were coming from.
__________________
No rational argument will have a rational effect on a man who does not want to adopt a rational attitude. -Karl Popper
#7
04-25-2012, 08:03 AM
 actuary_pilot Member SOA AAA Join Date: Jul 2003 Location: Louisville, KY Posts: 1,009

OK I think I'm convinced the formula in the book is right.

Because N%*shift*P% + N%*(1-shift)*M%
= N% * Shift * P% + N% *M% -N% * Shift * M%
= N%*M% + N%*Shift*P% - N%*Shift*M%
=N%*M% + N%*Shift*(P%-M%)
=N%*(M%+Shift*(P%-M%)

What threw me off was the P%-M% - the given formula made it seem as if the savings for those who shifted was P%-M%. But in reality it is P%. After thinking about it I started asking myself why would the savings for those who shifted be P%-M% - especially if the ones who stayed had a savings of M%. There would be no reason to subtract off the M% from the savings. But that isn't what the given formula was saying and that is what I missed.

To me,

N%*shift*P% + N%*(1-shift)*M%

is more intuitive than the equivalent

N%*(M%+Shift*(P%-M%)

since the first formula says:

the savings is the (percent of members that shifts from non preferred to preferred)*(the savings due network differentials)

+ (the savings from the members that don't shift) * (the savings from the decreased benefits in the non preferred network)
#8
04-25-2012, 05:22 PM
 bosactuary SOA AAA Join Date: Mar 2012 Posts: 6

Are there any sample questions on Hosp tiering? I didn't see any. I'd like to see this with real numbers.
#9
04-27-2012, 08:57 AM
 actuary_pilot Member SOA AAA Join Date: Jul 2003 Location: Louisville, KY Posts: 1,009

thank you gosuruss for your input and atropellador. it was very useful.
#10
04-27-2012, 10:00 AM
 gosuruss Member SOA Join Date: Feb 2007 Favorite beer: whatever is free Posts: 4,327 Blog Entries: 2

Quote:
 Originally Posted by actuary_pilot thank you gosuruss for your input and atropellador. it was very useful.
haha I bet it was. That was a nice question to receive on this exam!
__________________
No rational argument will have a rational effect on a man who does not want to adopt a rational attitude. -Karl Popper

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