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CRYSTAL BALL ARTICLES
Simulation Techniques for Risk-Based Financing Estimates in
Behavioral Health Managed Care
By Henry Yennie, BCSW
November 11, 1999
Background
As managed care initiatives sweep through public sector behavioral health and social services,
an increasing number of providers are faced with estimating costs, prices and/or rates for a
risk-based financing project. These estimates are fraught with danger and tremendous risk for
these organizations, many of which have difficulty with basic cost-finding analyses. This paper
outlines a model for rate setting that introduces the concept of simulation modeling to the
traditional rate estimation process. The purpose is to assist organizations in understanding the
nature of the risk in these types of arrangements and to assist in the formulation of realistic rate
estimates.
The Basics of Capitation Rate Setting
The tools for rate setting vary from organization to organization with the most common being a
spreadsheet-based model. In this paper we will focus on capitation rate setting and use a typical
HMO carve-out model as the example.
The most common calculation method for determining a capitation rate is the fee-for-service
method, which projects the cost of services delivered based on the contracted or calculated costs
per unit of service. The projected utilization of different types of services is combined with the
projected costs per unit of service to yield a total cost translated into a per member per month
rate.
In general, a capitation rate will have the following three components:
1. The estimated cost of direct clinical services, expressed as a "per member per month"
number.
This component of the capitation rate expresses the organization’s projection of the
cost of delivering direct clinical services to the covered group and results from the
following formula:
Cost of Service = Number of services x cost per unit of
service
The number of services to be delivered is a function of the following variables:
ITEM
DEFINITION
Population
Penetration
The number of covered members who will actually use
services
Utilization
per 1,000
Number of services used by the covered members
expressed in per 1,000 member units. This number is
derived by calculating:
The total episodes of care
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The average length of each episode
The total number of units of service
The formula for services per 1,000 members may be used to calculate the statistic for any
time period chosen, such as for the day, for the month, year to date, and so forth. When
calculating units per 1000, use the assumption of a 365-day year as opposed to a
12-month year to prevent variations that are due solely to the length of the month. The
formula is as follows:
[A / (B / 365)] / (C / 1000)
Where A = services per time unit
B = days per time unit
C = plan membership
This calculation can and should be done for hospital days, outpatient visits, and all other
levels of care.
Depending upon the types of covered services, as defined in the benefit plan, the
organization must determine the utilization of services for a variety of levels of care. A
common "continuum of care" for which utilization must be projected is as follows:
Acute 24-hour care and 23-hour observation
Partial hospitalization and day treatment
Intensive outpatient services
Outpatient service
Again, depending upon the benefit plan, these utilization projections should be calculated
for both mental health and chemical dependency services separately. Also, given the
organization’s scope of services or the composition of the network, this continuum may be
expanded or contracted to reflect the range of services available for member treatment.
Combining these variables into an "experience table" for our sample member group of
92,000 covered lives for one year of service might look as follows:
Level of Care
Penetration Admits ALOS
Total Units
Days/Visits/1000
Inpatient MH
0.32%
298
7
2,027
22.0
Partial MH
0.07%
64
6
412
4.5
Alt. Res. MH
0.00%
2
155
286
3.1
Outpatient MH
1.67%
1,533
7
10,422
113.3
Inpatient CD
0.06%
59
6
365
4.0
Partial CD
0.04%
35
7
238
2.6
Alt. Res. CD
0.00%
3
9
23
0.3
Outpatient CD
0.01%
6
4
23
0.3
Combining the utilization projections with the cost of service estimates will yield the first
general estimate of the capitation rate.
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Costs for services can be determined as follows:
If the organization is accepting capitation for its services only, a full cost study
should be completed to determine both the direct and indirect costs for each type of
service to be delivered by the organization under the capitation arrangement. This
can be derived from financial and statistical reports, and it should take into account
all of the overhead expenses required to deliver those services.
If the organization is providing services through a network of practitioners, then the
organization should have contracts with those practitioners that state the rates to be
paid for various services. If these practitioners include hospital units and other
facility-based services, then per diem contracts should be obtained to facilitate cost
projections as well as contain costs for the contract.
The determination of unit costs can be fairly straightforward for institutional services that
are based on per diem payments. If, for example, the psychiatric inpatient service network
consists of two hospitals, one with a $400 per diem and the other with a $500 per diem, a
simple average or weighted average based on the projected volume of services to be
delivered by each can be used. The following is an example:
Facility
Total Days
Per Diem
Total Cost
Unit A
250
$400
$100,000
Unit B
350
$500
$175,000
Totals
600
$275,000
Weighted Average Cost per Day
$458.33
A similar method can be used to determine the average cost per unit of outpatient service
when the organization uses clinicians with varying disciplines and contract rates.
2. The estimated overhead costs required to support the management of the contract
expressed as a "per member per month" number.
Every capitated arrangement will require support services and an administrative
infrastructure to support the services directly provided by the organization and to support
the authorization and payment of services provided by others through a network. These
overhead costs should be carefully detailed and added to the direct costs of clinical
services to arrive at an equitable capitation rate. Failure to incorporate some portion of
overhead costs in a capitated arrangement can lead to negative financial results.
Overhead costs can be estimated by preparing a budget outlining the type, number and
costs of the services required to support management of the contract. The total cost of
these administrative services is then converted into a PMPM rate and added to the direct
clinical cost PMPM to continue building the capitation estimate.
Some of the elements influencing the type and size of supporting administrative
infrastructure are as follows:
Type of clinical management protocol utilized (i.e. aggressive, moderate, etc.)
Number of covered lives and number of benefit plans administered
Use and required size of a practitioner network
Quality and clinical efficiency of the organization and/or the provider network
National Committee on Quality Assurance (NCQA) and Health Plan Employer Data
and Information Set (HEDIS) reporting requirements
Presence and nature of claims payment requirements
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Presence and nature of member service requirements
As with utilization control and risk management, a large group size allows the organization
to more effectively spread the overhead costs. Further, if overhead costs can be allocated
among several different capitation contracts, the organization can allocate more of each
capitation rate to clinical service delivery and profit.
3. The estimated profit for the organization expressed as a "per member per month"
number.
The third major component of a capitation rate is the allocation of an amount for profit and
an allowance for capital costs. This can be either a fixed cost added to the two other
components of clinical service costs and overhead or a percentage of the total costs. The
latter method is the most common. While there is wide variation in the percentage of profit
allocated to a contract, a common range is 6% to 10% of total costs.
In our sample model, we will focus only on the first rate component, the cost of care.
VARIABILITY AND RISK IN THE MODEL
Most organizations tend to construct this model in a spreadsheet, using single-point estimates for
the variables involved to arrive at an estimated rate. What is usually missing from these models is
a calculation of the probability of the estimate occurring along with an estimate of the degree of
risk involved in each of the variables and in the final estimate.
Using our sample data for the HMO carve-out, we can construct a model similar to the following:
Level of Care
Units/1000
Cost per Unit
Cost PMPM
Inpatient MH
22.0
$458.33
$0.841
Partial MH
4.5
$225.00
$0.084
Alt. Res. MH
3.1
$75.00
$0.019
Outpatient MH
113.3
$58.00
$0.548
Inpatient CD
4.0
$458.33
$0.152
Partial CD
2.6
$225.00
$0.048
Alt. Res. CD
0.3
$75.00
$0.002
Outpatient CD
0.3
$85.00
$0.002
TOTALS
$1.696
The "Cost PMPM" was derived using the following formula:
(Forecast Annual Utilization Rate/1000) x FFS Rate
___________________________________
12 Months
As an example, the formula for inpatient mental health is:
(0.022*458.33)/12
Given the data in our sample, this procedure yields an initial rate estimate for the cost of services
of $1.696 per member per month. As the model is in spreadsheet form, we can manipulate the
values of each cell to see the effect on the final cost of care.
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LIMITS OF SPREADSHEET MODELS
In our model for the cost of services, variables can be characterized as either "unknown" (we
have no knowledge about the true value) or "uncertain"(some knowledge about the true value).
The major variables that are unknown or uncertain are:
Penetration rates for the various levels of care
Utilization assumptions for the various levels of care, primarily ALOS
Cost assumptions for the various levels of care
Once we have reached this point in our model construction and recognize the potential variability
in the estimate, we are faced with a common dilemma: What values do we change and what are
the probabilities of those values occurring in real life? In other words, how do we know our
estimate is valid, and what is the nature and extent of the risk involved for our organization?
We typically answer these questions using a variety of single-point variations in the model, i.e. we
change the value of one cell and see the effect on the target value (The "Cost PMPM" in our
model). We can go a step further and construct "worse case", "most likely case", and "best case"
scenarios. But again, this limits us to three likely outcomes, and we are still missing a measure of
the degree of risk involved and the probability of any of those cases occurring.
We are still faced with a substantial obstacle: How many changes and what changes do we make
for the variables? In our model, for example, it would be impractical to substitute a variety of
different possible values for the "outpatient mental health visits per 1000 per month" variable in
order to see the outcome on cost. This type of single-cell input is impractical for all the variables in
the model. Although it might be physically possible to substitute a large number of values for
each variable, it quickly becomes practically impossible to track the effects of each change on the
target cell.
David T. Hulett succinctly states the problem: "Future estimates are not facts but statements of
probability about how things will turn out. Because estimates are probabilistic assessments, costs
may actually be higher or lower than estimated even by seasoned professional estimators."
USING SIMULATION TECHNIQUES
The use of simulation techniques allows us to directly address the probability features of a
capitation estimate by conducting a large number of "what ifs" on each uncertain variable in the
model. In short, it allows us to perform a cost risk analysis. This type of analysis allow us to
answer the following questions:
"What is the most likely cost?" The traditional method assumes that this is the baseline
cost computed by summing the estimates of cost for the various levels of care, but this is
not so.
"How likely is the baseline estimate to be overrun?" Traditional methods do not address
this problem.
"What is the cost risk exposure?" This is also the answer to the question; "How much
contingency do we need on this project?" For capitation projects, the issue would the
correct amount of reserves to set aside for potential cost overruns.
"Where is the risk in this project?" This is the same as: "Which cost elements cause the
most need for the contingency?" Risk analysis principles can be used to answer this
question.
Use of simulation techniques in rate setting is recognition of the variability inherent in the
"uncertain" variables in the model. The quickest and most efficient way to perform these analyses
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is through the use of simulation software. This example will use Crystal BallÓ by Decisioneering,
Inc. to illustrate the advantages of these techniques.
Additional Data Requirements
All cost risk estimate techniques are based on probability distributions. A probability distribution
describes the likelihood of specific values occurring out of a range or set of values. If the range of
values is limited to certain fixed values, the probability distribution is said to be discrete. If the
range of values contains an infinite set of possible values, the distribution is said to be
continuous.
Depending upon the nature of the data, there are a variety of probability distribution types that
can describe the data. The two most popular distribution types that "fit" behavioral healthcare
data include:
The Triangular distribution: The triangular distribution shows the number of successes
when you know the minimum, maximum, and most likely values. For example, you could
describe the number of intakes seen per week when past intake data show the minimum,
maximum, and most likely number of cases seen. It has a continuous probability
distribution.
The parameters for the triangular distribution are Minimum, Maximum, and Likeliest. There
are three conditions underlying triangular distribution:
The minimum number of items is fixed.
The maximum number of items is fixed.
The most likely number of items falls between the minimum and maximum values,
forming a triangular shaped distribution, which shows that values near the minimum
and maximum are less apt to occur than those near the most likely value.
The Lognormal distribution: The lognormal distribution is widely used in situations where
values are positively skewed (where the distribution has a long right tail; negatively skewed
distributions have a long left tail; a normal distribution has no skewness). Examples of data
that "fit" a lognormal distribution include financial security valuations or real estate property
valuations. Financial analysts have observed that the stock prices are usually positively
skewed, rather than normally (symmetrically) distributed. Stock prices exhibit this trend
because the stock price cannot fall below the lower limit of zero but may increase to any
price without limit. Similarly, healthcare costs illustrate positive skewness since unit costs
cannot be negative. For example, there can’t be negative cost for services in a capitation
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contract. This distribution accurately describes most healthcare data.
The parameters for the lognormal distribution are Mean and Standard Deviation.
The three conditions underlying lognormal distribution are:
The unknown variable can increase without bound, but is confined to a finite value
at the lower limit.
The unknown variable exhibits a positively skewed distribution.
The natural logarithm of the unknown variable will yield a normal curve.
Other common distribution types not used in this paper include:
Binomial
Beta
Custom
Exponential
Extreme Value
Gamma
Geometric
Hypergeometric
Logistic
Negative Binomial
Normal
Pareto
Poisson
Uniform
Weibull
In order to describe the distribution types of the "uncertain" variables in our model, we need
additional data about the uncertain variables. There are several sources for this additional data:
Analysis of Historical Data: If an organization has historical data describing an uncertain
variable, a simple analysis will yield the appropriate distribution and parameters, such as
the mean and the standard deviation.
Interviews with Experts: In those cases where historical data is unavailable or unreliable,
additional information may be obtained from interviews with staff or other experts. This is
particularly applicable for descriptions of data that fit a triangular distribution. As Hulett
states, "(Interview) participants can describe and estimate the low, most likely and high
range estimates."
Proxy Estimates: Proxy estimates refer to the use of similar data sets. These can often be
obtained from consulting firms specializing in claims data analysis and risk-based rate
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estimation.
Once an organization is able to describe the likely distributions of the uncertain variables,
simulation techniques can be employed. We will employ the Monte Carlo simulation technique as
used in the Crystal BallÓ software. This technique employs a series of random numbers,
constrained by the distribution parameters chosen, to calculate the cost risk model and the
resulting effect on the target cells – the cost of care. This technique can accommodate models
such as ours that have a large possible number of "what-ifs" that would be impractical to
manipulate on a case-by-case basis.
As an example, the process can conduct up to 10,000 trials – or "what ifs" – on each assumption
cell using the parameters defined in the underlying distribution. As Hulett states, "A Monte Carlo
simulation "solves" the problem many times. Each solution is called an iteration. For each
iteration, the simulation program selects a cost (or utilization parameter) at random from the
probability distribution specified by the analyst for each uncertain cost (or utilization) element."
Another sampling technique available in Crystal Ball is the Latin Hypercube method or
(technique). This differs from the Monte Carlo technique in that it uses a stratified sampling
technique. This is preferable when additional accuracy in distribution "tails" is desired. In other
words, Latin Hypercube simulation stratifies the distribution and ensures that "what-if" values are
chosen from each stratum. On the other hand, Monte Carlo simulation chooses "what if" values
at random from the entire range of the distribution, and consequently may or may not take
sufficient sample values from the tails. The differences in the techniques can be illustrated in the
following simple drawing:
For illustrative purposes, we used a lognormal distribution for the "uncertain" penetration rates in
the model. Using the data in our sample model, we defined the following distributions for the
uncertain utilization variables:
Assumption: Inpatient MH
Lognormal distribution with parameters:
Mean
Standard Dev.
Assumption: Partial MH
Lognormal distribution with parameters:
Mean
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Standard Dev.
Assumption: Outpatient MH
Lognormal distribution with parameters:
Mean
Standard Dev.
Assumption: Inpatient CD
Lognormal distribution with parameters:
Mean
Standard Dev.
Assumption: Partial CD
Lognormal distribution with parameters:
Mean
Standard Dev.
Assumption: Outpatient CD
Lognormal distribution with parameters:
Mean
Standard Dev.
0.02%
1.67%
0.50%
0.06%
0.02%
0.04%
0.01%
0.01%
0.01%
Using the software’s capability to run 10,000 trials, we produced the following means for the
model:
Level of Care
Penetration Admits ALOS
Total
Units
Units/
1000
Unit
Cost
Cost
PMPM
Inpatient MH
0.33%
300
7
2,037
22.1
458.3
0.846
Partial MH
0.07%
64
6
411
4.5
225.0
0.084
Alt. Res. MH
0.00%
2
155
286
3.1
75.0
0.019
Outpatient MH
1.67%
1,532
7
58.0
0.547
Inpatient CD
0.06%
59
6
367
4.0
458.3
0.152
Partial CD
0.04%
35
7
239
2.6
225.0
0.049
Alt. Res. CD
0.00%
3
9
23
0.3
75.0
0.002
Outpatient CD
0.01%
5
4
23
0.3
85.0
0.002
TOTALS
2.17%
2,000
10,419 113.2
1.701
The model produced a mean expected Cost PMPM of $1.701, very near our spreadsheet
estimate. One frequency chart output of the model can be illustrated as follows:
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The following important information can be obtained from this chart:
The range of possible "Costs PMPM" plus or minus three standard deviations from the
mean of $1.701 is $0.750 to $2.750. This represents a wide range of possible outcomes
(99.73%).
The "certainty level" of actual costs coming in at or below the projected mean of $1.701 is
only 54.4%. In other words, given the nature of the underlying data, we have a 45.6%
chance of the actual Cost PMPM being more than the projected mean.
The "negative outcomes" indicate the areas of probability where the costs exceed the
capitation revenue of $1.701 PMPM.
Another view of the output is a cumulative chart:
The blue-shaded area shows the range of possible outcomes below the mean at the 54%
certainty level. Another way to view this output is that the organization would have to provide at
least $1.05 PMPM in reserve to cover possible cost overruns. For most organizations, this is an
unacceptable level of risk. An organization willing to tolerate only a 20% chance of cost overruns
would require a PMPM rate of at least $1.946 as illustrated below ($2.750 – $1.701):
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DETERMINING THE RISK IN THE MODEL
Simulation can be used effectively to determine the nature/source of uncertainty of the risk
inherent in the model through the use of sensitivity analysis. A key output of the software is the
identification of the specific variables that have the greatest effect on the outcomes of the model.
We can rank the variables by their contribution to risk in the model. This analysis allows an
organization to focus analytical resources on those uncertainties in the estimate that matter the
most. For our sample model, the sensitivity analysis is as follows:
Given our data, the two variables of Inpatient Mental Health utilization and Outpatient Mental
Health utilization together contribute to 97% of the variance in the model. This has two important
implications:
1. The analysis points to these two variables as those most likely to contribute to variance
from the mean cost PMPM. Thus, they should be primary targets for clinical improvement
and management and should become "key indicators" for the project. Additional planning
and discussions with clinical leadership can often yield strategies for control of these
important variables.
2. Because of their importance, the organization can devote additional analytical resources to
the data that produced the underlying distributions. Perhaps another data set can be
acquired and the distribution parameters refined. The sensitivity analysis allows an
organization to focus resources on those variables that matter the most in the model and
the ultimate outcome.
Summary
This paper has outlined the relative advantages of using simulation techniques in the
development of risk-based pricing proposals. Traditional spreadsheet models that rely on
single-point cost and utilization estimates do not furnish adequate information on the potential
risk involved. Using simulation software such as Crystal Ball® , we were able to calculate a large
number of "what ifs" on each uncertain variable defined in the model. As Hulett states,
"Traditional methods cannot answer the important questions of: (1) How likely are we to overrun?
(2) What is our exposure? and (3) Where is the risk in the project?" Using Monte Carlo simulation,
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an organization faced with a capitation opportunity can gain critical knowledge about the
reasonableness of rates, and the nature of the risk involved in the model.
The sample used in this paper is a simple reproduction of complex financial models used in actual
rate estimates. An actual model would involve a larger number of variables An organization
should be prepared to devote sufficient resources to data gathering and analysis in order to
ensure these methods produce reliable data.
For more information, contact:
Henry Yennie, BCSW
Senior Associate
1219 Carter Avenue
Baton Rouge, LA 70806
225-923-2343 voice
225-924-3622 fax
[email protected]
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