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Statistical Sampling Overview and Principles

- Alvin Binns
- 205-220-4522
- Abinns_at_csallc.com

Scenario

- Provider X is identified for billing excessive

ambulance services. A decision was made to pull

all his/her ambulance services for a specified

two years period. - Results
- - 3,000 claims, 7,000 lines and 1.8M in

payments.

Reasons for Sampling

- Time
- Cost
- Available resources
- Available staff

What is Sampling?

- Sampling - is the selection of observations to

acquire some knowledge of a statistical universe

(population). - From the characteristics of samples, we can infer

the characteristics of universes, if the sample

is representative of the universe.

How Do I Get a Representative Sample?

- In order for statistics to be good estimates of

parameters, they must, on average, return the

value of the universe parameter - When the expected value of a statistic equals a

universe parameter, we call the statistic an

unbiased estimator of that universe parameter

How Do I Get a Representative Sample?

- How do you ensure that your statistic is an

unbiased estimator?

RANDOMIZATION!!!

Randomization

- A sample that is randomly selected from a

universe yields sample statistics that are

unbiased estimates of the universe parameters - Many software packages, such as SAS and RAT-STATS

have a valid random number generator

Probability Sampling

- Another idea behind random sampling is that each

sampling unit has a known probability of being

selected

Sampling Terms

- Universe An event or things of interest that

the researcher wishes to investigate. - Eg. All Medicare beneficiaries that received a

left heart catheterization from Dr. John Doe

between January 1, 2007 and June 30, 2008 paid up

to September 30, 2008.

Sampling Terms

- Samples are usually drawn by taking a subset of

sampling units from the total universe - Sampling units are non-overlapping collection

of elements from the universe that cover the

entire universe (eg claims, beneficiaries)

Estimation

- We can infer the values of the universe from the

sample by the use of estimation - Ideally, we would like gather information from

the sample and then estimate that value for the

entire universe - These estimates calculated from the sample data

are called statistics

Statistics

ENTITY

Sample

Census

Estimates

CHARACTERISTIC

Statistic

Parameter

Estimates

Estimation

- In an simple random sample where we had sampled

100 units out of 1000, suppose we had a 5,000

total overpayment from the sample - The Mean Total Overpayment would then be

Why Should I Care?

- HCFA Ruling 86-1 allows the use of statistical

sampling for the purpose of estimating a

providers overpayment to the Medicare trust fund - Thus, we can use sampling to estimate

overpayments to providers and avoid having to

review the entire universe!

CMS Sampling Guidelines

- CMS guidelines for Statistical Sampling for

Overpayment Estimation - Program Integrity Manual Section 3.10
- Some of the issues addressed are
- Methodologies
- Sample Size
- Estimation techniques

Sampling Guidelines

- This replaces and clarifies (for older cases) the

old HCFA Sampling Guidelines Appendix (CR 1363) - This program memorandum (PM) provides clarified

guidance and direction for Medicare carriers to

use when conducting statistical sampling for

overpayment estimation. The attached replaces

the prior Sampling Guidelines Appendix for

reviews conducted after issuance of this PM. For

reviews conducted prior to this issuance, the

attached are a clarification to aid

interpretation of the earlier instructions,

particularly where specific numbers are suggested

Sampling Methodologies

- Simple Random Sampling
- Cluster Sampling
- Stratified Sampling
- Other Methodologies

Simple Random Sampling

- This is the most straightforward method of

sampling - X number of sampling units are randomly selected

from Y total sampling units in the Universe - Each sampling unit has an equal probability of

being selected

Cluster Sampling

- A cluster sample is a probability sample in which

each sampling unit is a collection, or cluster,

of elements - A good example is the random selection of

beneficiaries, then selecting all relevant claims

from each beneficiary

Stratified Random Sampling

- A stratified random sample is one obtained by

separating the universe elements into

non-overlapping groups, called strata, and then

selecting a simple random sample from each

stratum - An example of this would be samples involving

multiple procedure codes, selecting simple random

samples from each code - Stratified random sampling generally has less

sampling variability that other sampling designs

Stratified Random Sampling Proportional

Allocation Example

Universe 1000 Units

99211

99212

99215

99214

99213

50

150

50

300

450

Sample 100 Units

99211

99212

99213

99214

99215

5

15

30

45

5

PIM 3.10 Sample Sizes

- PIM 3.10 states about sample sizes
- It is neither possible nor desirable to specify

a minimum sample size that applies to all

situations - real-world economic constraints must be taken

into account. As stated earlier, sampling is

used when it is not administratively feasible to

review every sampling unit in the target

universe. In practice, sample sizes may be

determined by available resources. That does not

mean, however, that the resulting estimate of

overpayment is not valid as long as proper

procedures for the execution of probability

sampling have been followed. A challenge to the

validity of the sample that is sometimes made is

that the particular sample size is too small to

yield meaningful results. Such a challenge is

without merit as it fails to take into account

all of the other factors that are involved in the

sample design

PIM 3.10 Sample Sizes

- CSA procedure
- If we can, we like to pull at least 10 of the

universe, however, this is not a rule that is set

in stone - We must, at a minimum, pull at least 30 sampling

units to satisfy distribution requirements

through the central limit theorem

PIM 3.10 Overpayment

- PIM 3.10 also states
- In most situations the lower limit of a

one-sided 90 percent confidence interval should

be used as the amount of overpayment to be

demanded for recovery from the physician or

supplier. The details of the calculation of this

lower limit involve subtracting some multiple of

the estimated standard error from the point

estimate, thus yielding a lower figure.

PIM 3.10 Overpayment

- It further states that
- This procedure, which, through confidence

interval estimation, incorporates the uncertainty

inherent in the sample design, is a conservative

method that works to the financial advantage of

the physician or supplier. That is, it yields a

demand amount for recovery that is very likely

less than the true amount of overpayment, and it

allows a reasonable recovery without requiring

the tight precision that might be needed to

support a demand for the point estimate.

However, you are not precluded from demanding the

point estimate where high precision has been

achieved.

PIM 3.10 Overpayment

- What we really do then is calculate the Mean

Total Overpayment and subtract a multiple of the

standard error from it to achieve the lower level

of the confidence interval

PIM 3.10 Overpayment

- Below is the formula for the total variance for

cluster sampling

PIM 3.10 Overpayment

- Look at how the overpayments work

OP w/ Small Variance (Large n)

OP w/ Large Variance (Small n)

90 Upper Limit

90 Upper Limit

Overpayment

Mean Total Overpayment

Mean Total Overpayment

90 Lower Limit

90 Lower Limit

Sample Size Comparison

Estimation Of Total Amount Of Refund It's Lower

1-sided 90 C.I.

Difference if sample Size 5-10 beneficiary

184,569.45 Difference in sample Size 10-20

beneficiary 207,578.67

Bottom Line

- Large Sample Sizes
- Use when the expected overpayment is large
- Use in high profile cases
- Resource intensive
- Increase precision even more using stratified

sampling plans

- Small Sample Sizes
- Use when the expected overpayment is small
- Use in routine, low cases
- Not as resource intensive
- Does not work as well for stratified sampling

Sub-samples

- It is often beneficial to evaluate a sub-sample

before moving to a full statistical sample.

(sample size of about 30) - Get a good idea of the point estimate (Mean Total

Overpayment). - Sampling for Consent Settlements.

Summary for Sampling

- Define the Universe
- Determine the sampling methodology
- Create the sampling Frame
- Determine sample size
- Create your sample
- After Sampling review is completed
- Perform overpayment Projection

Questions?

- Thank You!

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