Statistical Sampling and Extrapolation WEDNESDAY, MARCH 15, 2017 - - PowerPoint PPT Presentation

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Medicaid Audit Overpayments: Challenging Statistical Sampling and Extrapolation

Today’s faculty features:

2pm Eastern | 1pm Central | 12pm Mountain | 11am Pacific WEDNESDAY, MARCH 15, 2017

​ David R. Ross, Shareholder, O’Connell and Aronowitz, Albany, N.Y .

• Dr. Patricia L. Maykuth, Ph.D, President, Research Design Associates, Decatur, Ga.

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MEDICAID OVERPAYMENTS:

Challenging State Audit Allegations of Overpayment and the Use of Statistical Sampling and Extrapolation

Presented by : Pat Maykuth, Ph .D., President, Research De sign A s sociates, I n c. David R. Ross, Es q., Sh areholder, O’Connell & A ronowitz , P.C. March 15, 2017 2: 00 p . m. to 3: 30 p . m.

Introduction and A Primer on the Legal Issues In Statistical Sampling and Extrapolation

PART 1 OF THE PRESENTATION

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What is Sampling?

Sampling is taking a subset of the claims in a Medicaid provider’s universe of claims for the purpose of auditing them. How is the sample of claims chosen? Usually via computer software. The sample must be randomly selected to be valid.

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What is Extrapolation?

Extrapolation takes the results of an audited sample of claims and projects the dollar amount of the overpayment from the sample

• ver the universe of paid claims.

The audited sample has a known amount of dollars in error so that amount is projected to the universe for a global repayment amount.

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Legal Basis for Statistical Sampling for Overpayment Estimation

US HHS “may introduce the results of a statistical sampling study as evidence of the number of violations . . . or the factors considered in determining the amount of [a] civil money penalty. Such statistical sampling study, if based upon an appropriate sampling and computed by valid statistical methods, constitutes prima facie evidence. [T]he burden . . . shifts to the [Provider] to produce evidence reasonably calculated to rebut the findings of the statistical sampling study.”

Excerpt from 45 C.F.R. § 160.536(a)-(b) (emphasis added).

State Medicaid programs generally use a similar approach.

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Individual States and Statistical Sampling

Unlike Medicare, Medicaid has no universal guidance outlining the rules of the process to be used. Your state may have simple or detailed rules, or no rules at all.

• Texas follows the MPIM and uses RAT-STATS.
• California and Florida use “generally accepted statistical standards.”
• New York has no rules at all.

The burden of proof is on the Provider to challenge the statistical sampling and extrapolation.

• The State’s methodology is presumed valid unless and until the

Provider proves otherwise.

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What Are the Legal and Scientific Issues Pertaining to Sampling and Extrapolation?

Understanding what those complex issues are is not easy Do I need an expert? (Hint: you absolutely do)

• Lawyers are not enough (and that’s coming from a lawyer)

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The Role of the Expert: Why You Should Always Have One

A statistical consultant is essential to understanding how the audit was conducted and whether the results are statistically valid.

• Laypersons generally cannot understand these concepts absent

training.

The expert will review both the process actually used and the results in your case. An expert is the only person who will be able to properly answer important questions pertaining to the audit.

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The Role of the Expert: Asking the Important Questions

 Is the process used by the auditors properly designed?  Is this process suitable for use in this audit of my client?  Is the process, as applied to my client in this audit, proper?  Is it different from the norm? If so, how and why?  How was the sample size chosen? Was that selection proper?  Is it adequate (large enough) for the confidence interval?  Did the auditors properly document the audit?

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The Role of the Expert: Asking More of the Important Questions

 Is the software program used for random number generation certified or widely accepted for this purpose?  Was adequate documentation for replication provided?  Was the software program used working as it was designed?

• When in doubt have an expert look at the source code
• Can’t get the source code? Argue violation of due process

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The Role of the Expert: Asking Even More of the Important Questions

 How were the random numbers selected? Were they generated by a valid method?

• Did the auditors perform appropriate tests for randomness on these

numbers?

 Can the results be replicated by the provider?

• If not, there is a serious problem.
• Retaining the seed is a very important factor.
• Is the frame sorted as it was at the time the random numbers were

used to pick the sample?

 What about the extrapolation calculations themselves?

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Right Idea, Wrong Answer

16

Dewey Wins the Election!!

Pollsters surveyed via telephone

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There Are Three Kinds of Lies: Lies, Damned Lies, and Statistics

So which is it? The outcome of any statistical study is determined by that characteristic that is sampled Why were so many polls in the past presidential election saying contradictory things?

• bias
• corrupted frame
• probability of selection unknown
• polling done for advocacy not to answer the question
• sampling error
• response bias

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Ultimately, It Comes Down to Two Basic Questions

• 1. What is the ‘it’ that is being measured by the study?
• 2. Is the ‘it’ being measured correctly?

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Human Baby Due Date

Average human gestation period is 280 days (9.33 months or 40 weeks) A 90% confidence level predicts the due date will be between 273 days and 280 days.

• Assumptions : sample size 20, average 280 days, lower confidence level 273 days, upper

confidence level 287 days

• No calculable confidence level for 1 person

Complication error:

• Only 40% of women give birth on this due day
• Accuracy error of 60%
• Do not know the distribution
• not normal
• Do not know the conception date
• Measurement error

How believable is it to use this estimate for the birth date of one person? How useful is it to a person who wants to know what day the baby is going to be born?

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Right Idea, Wrong Answer

Dewey wins election (not!) – they surveyed only people with telephones Human baby due date example In 1939, the US government predicted we would be out of domestic oil in 13 years It was also predicted that the US space program would have 9-10% catastrophic failure rate Why do these statistical studies fail us? ANSWER: they are not correctly designed for the question being asked Your client’s Medicaid audit may also be incorrectly designed

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A Primer on Sampling and Extrapolation

PART 2 OF THE PRESENTATION

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What is Statistics?

Statistics is a branch of mathematics dealing with:

• the collection,
• analysis,
• interpretation, and
• presentation of masses of quantitative data.

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Terms

Universe – dollar amount of claims paid to a Provider in a specific timeframe Sampling Frame – subset of the universe defined as variables of interest from which the sample will be randomly selected and over which the sample will be extrapolated Sample – a randomly selected subset of a sampling frame to be audited for

• verpayments

Unit of Analysis (Sampling Unit) – what is measured in the audit: claim line, claim, beneficiary, provider (must be invariant throughout the audit) (Please see the List of Terms provided with presentation)

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Universe

(Provider and all claims)

Frame

(All claims for a particular time frame and code)

Sample

(50 claims per sample) 01/01/2010 Code: 12743

Sampling Unit

(Individual claim: must be within frame)

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Corrupted Frame = Bad Sample

Fra

Sampling Frame Universe

Outside Definition

SAMPLE

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Characteristics of a Valid Medicaid Overpayment Study

27

universe frame Inferential Statistics Method: following rules required Sample definition Simple Select seed & random number table Applied to file that is unbiased Calculate sample size Select probability sample Independent

• bservations

Randomly selected Normally distributed Representative Stratified Audit claims in the field Prior history

• f
• verpayment

error Define the who, what, time and how

• verpayment

is measured

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What is a Statistically Valid Random Sample?

For the purpose of today’s discussion, a Statistically Valid Random Sample (SVRS) from a universe of paid Medicaid claims guards against

cherry picking or any bias by the auditor and has to:

• meet the requirements the methodology – especially assumptions about

distribution;

• meet chosen sampling error;
• be of sufficient size to accurately measure the variable;
• be random; and
• be representative (without bias).

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Medicare and Statistical Sampling

Medicare Program Integrity Manual (MPIM) Chapter 81, provides nineteen pages of guidance “to provide instructions for [auditors] for the use of statistical sampling in their reviews to calculate and project (i.e., extrapolate) overpayment amounts to be recovered.”

1 https://www.cms.gov/Regulations-and-Guidance/Guidance/Manuals/Downloads/pim83c08.pdf

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Valid Outcomes Require Proper Execution

 Defined universe and produce  Defined frame and produce  Defined sampling units in a meaningful way for the analysis (the “it”)  Use proper randomization for independence  Accurately measure overpayments

• meet the method assumptions
• use the correct formulas for estimation
• correctly calculate the math
• test key assumptions for randomness, independence, normality &

representativeness  Accurately report actual findings – tell the truth

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Auditor’s Responsibilities

 Know a prior error rate (probe, history, industry norm)  Supervise selection of appropriate sampling unit and choose methodology that is appropriate for audit data - no one size fits all approach  Choose a sample size that is adequate and representative to meet results  Exercise knowledgeable statistical oversight and quality control throughout  Document the process so that it can be replicated  Evaluate non-sampling errors and their impact  Calculate the results correctly  Report findings accurately and ethically

32

Audit Design Must Meet Common Sense Test

The believably (acceptability, trustworthiness or merit) of the result has to be made by judgement. The mechanics of calculation of a probability statistic will be valid, but only meaningful if properly executed.

 If the auditor lacks in-depth understanding of the medical or billing data distribution; or  If a sample is not random, representative or large enough; or  If the criteria of the probability distribution are not met,  Then you should question the validity of the statistical calculations.

Probability math does not change. In order to avoid silly mistakes, the study design has to make sense and then the methodology has to be properly executed.

33

The Data Must Be…

The most common yardstick distribution is the normal (bell shaped) distribution. It includes point estimates and confidence levels commonly used in Medicaid and Medicare audits and voluntary repayments. These parametric statistics require that the data are:

 Independent observations;  Normally distributed;  Random; and  Representative.

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Statistically Valid Random Sample

35

The Concept of ‘Random’

Comes into play twice in the execution of an audit:  Random and representative sample

Tests show the chosen sample is both

 Compare mean of the sample to the frame to estimate overpayment.

If the sample mean is different from what would be expected by chance alone then that difference is not random, and the result is the calculated overpayment

• utcome

36

Random Sample

Must be able to replicate and test the sample. Need:

 The seed used  The identical computer program  The identical input

• Frame size
• Sample size
• Spares

 Test to assure both randomness and appearance of randomness  Test for representativeness

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38

Sample Size Determination Based on Chosen Precision and Confidence

39

RAT-STATS Results

80% 90% 95% 99% 1% 75 77 78 79 2% 63 68 71 75 5% 29* 39 46 56 10% 10* 15* 20* 29* 15% 5* 8* 10* 16* Confidence Level Precision Level

* Sample sizes less than 30

40

Representative Samples

A small yet complete and accurate picture of the data in the frame. A subset of a statistical universe that accurately reflects the numerical membership of the entire universe and its distribution. A representative sample is an unbiased indication of what the frame is like. Representativeness is tested mathematically. When a sample is not representative, the result is known as a sampling error.

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Representative Sample

Frame Sample

42

Distributions:

the Measurement Yardstick

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Probability Yardstick

The single sample chosen for the audit is only one sample (of the chosen size) out of a very large number of samples of that size which could have been chosen from the frame. The sampling distribution of all possible means provides a mathematical model of what is likely to occur if all of the possible samples in the frame were analyzed. If a large number of samples were drawn from the frame

• A mean can be calculated for each sample.
• Each sample mean would not be exactly the same value as most of the others. Rather

sample means would differ from one to another and from the true mean of the frame.

• The means would be different from one another however they would cluster around the

central value (or mean) of the frame.

• There will be more scores in the middle of the distribution than at the ends.
• The differences in the means of different samples are the basis of the error that occurs

inferring from a sample to the frame rather than measuring all of the claims in the frame.

• If repeated random samples (moving toward infinity) were made, their means would be

expected to fall into a normal distribution.

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Sobering How Poor an Estimator a Sample Can Be

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Amount Paid is a Proxy for Overpayment

• Sample selected from amount paid to provider.
• Sample analyzed using overpayment data.
• Never know up front what the overpayment amount is going to be unless
• there is a known history of overpayment dollar amount; OR
• conduct a probe audit.
• Overpayment amounts must meet criteria for using parametric statistics or the

confidence levels are destroyed.

• If overpayments are not correlated with amount paid the analysis cannot

proceed.

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What’s the Big Deal About the Normal Distribution?

In probability theory, the normal (or bell-shaped) distribution is a continuous probability distribution (a function that tells the probability

• f a number in some context falling between any two real numbers).

The normal distribution is symmetric around the mean. The mean, median and mode are the same number. The normal distribution is immensely useful because of the Central Limit Theorem which states that the mean of many random variables independently drawn from the same frame is distributed approximately normally, irrespective of the form of the original distribution. That is, the overpayment means will be randomly distributed if the sample is large ... moving toward infinity.

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Normal Distribution

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Normal Distribution Yardstick

It is the common yardstick of the continuous distribution (dollars) If the mean of the sample is random then expected confidence levels can be established by probability math. The audited sample must be tested and demonstrated to be random and representative The sample mean overpayment is compared to the theoretical distribution yardstick based on how the data would array if they were random If the overpayment mean is different from what would be expected by chance alone, then that difference is not random; rather it is an

• verpayment effect.

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Lower Confidence Level Upper Confidence Level Point Estimate

51

52

Mode Mean

Median

12,072.62 566.09 1,274.35

Where is the Confidence Level? One-sided or Two Illustration, not based on actual data

53

Frame Distribution

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55

Sample Frequency in Dollars

N 15 Mean 430.93 Median 112.00 Mode 120

• Std. Deviation

525.519 Variance 76,170.210 Skewness 0.816 Kurtosis 0.580 Minimum 10 Maximum 1,300 Sum 6,464

56

Non Normal Sample Mean and Standard Deviation

Sample mean +/- 1 standard deviation Mean = $430.92 + 525.510 = 956.43 430.92 - 525.510 = -94.18

57

Sample Overpayment Frequency in Dollars

N 15 Mean 339.333 Median 100.00 Mode 0.0

• Std. Deviation

511.62 Variance 261,763.810 Skewness 1.197 Kurtosis

• 0.524

Minimum 10 Maximum 1,300 Sum 6,464

58

RAT-STATS Overpayment Estimation

Formulae: Confidence Level:

59

RAT-STATS Point Estimate & Confidence Interval

POINT ESTIMATE $27,147 90% CONFIDENCE LEVEL LOWER LIMIT $10,368* demand amount UPPER LIMIT $43,925 PRECISION AMOUNT 16,778 PRECISION PERCENT 61.81% t -VALUE USED 1.761310135775 Lower 27,147 + 16,778 = $43,925 Upper 27,147 - 16,778 = $ 10,368 Confidence Interval = 16,778 + 16,778 = 33,556

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Confidence Levels Non Normal Data

Point Estimate +/- ½ Confidence Interval Confidence Interval: 16,778 + 16,778 = 33,556 Lower 27,147 + 16,778 = $ 43,925 Upper 27,147 - 16,778 = $ 10,368

Lower confidence Level ??? Unknowable

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Poor Questions Lead to Poor Answers

Even well designed probability statistics cannot answer the questions consumers seek.  Can’t predict who is going to be president  Can’t tell what day your baby will be born  Cant tell the overpayment dollar amount for a provider They can tell you how likely the mean of the sample is to represent the true mean of the frame from which it was chosen. No more no less. A badly executed sample can not even tell that. They are simply an exercise in arithmetic, not a probability sample.

62

Poor Audit Design & Execution Produce Only Invalid Results

Statistics in the hands of an inept auditor are like a lamppost to a drunk: they are used more for support than illumination.

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Questions?

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Faculty

David R. Ross, Esq. Shareholder E-mail: dross@oalaw.com (518) 462 5601 O’Connell and Aronowitz, P.C. 54 State Street Albany, NY 12207 Website: www.oalaw.com Pat Maykuth, Ph.D. President

E-mail: pm@researchdesignassociates.com

(404) 373 4637 Research Design Associates, Inc. 721 E Ponce de Leon Decatur, GA 30030 www.researchdesignassociates.com

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