Statistical sampling

As special agent supervisor with a U.S. state agency, I (Paul Kolb, CFE) was assigned a case involving allegations of fraudulent practices perpetrated by a home-health agency that billed Medicaid and other government-funded health care programs. Tobey Culler, a fraud analyst with the same state agency, and I used the U.S. Department of Health & Human Services (HHS) Office of Inspector General's (OIG) free RAT-STATS program to avoid pouring limited resources into a full-scale audit and file review.

The program gave us a random list of patient files to review based on a tested and proven statistical model. Our investigation led to the successful criminal conviction of the agency's owner while using a fraction of the resources of a typical, full-scale fraud examination.

Many cases, limited resources

With large caseloads and limited resources, fraud examiners need to be able to effectively and efficiently complete fraud examinations. A case is easier, of course, when we've isolated the fraudsters, discovered what they're doing and how they're committing the crimes. But even then, proving and quantifying fraud can be challenging. For example, when you receive an allegation that someone is committing fraud, is it appropriate to obtain and review every single file and transaction with which the suspect came in contact? Sometimes, but often your efforts might not yield good returns on your investment of resources.

Our state's health care fraud section received allegations involving Home Care Inc. At the time of the investigation, Home Care was billing the state Medicaid program about $100,000 a month — totaling more than $10 million since its start of business.

We've seen investigators spend hefty resources on examining big home-health agency case frauds, so we decided to take a different approach — statistical sampling.

Let's try a sample

You can use statistical sampling to investigate a fraction of a huge pool of numbers and quantify the amount of possible fraud. You then extrapolate the results of the sample to represent how much fraud is in the total population within a predefined degree of certainty.

For example, let's say you're a state auditor and you receive a vague tip that a contractor is fraudulently inserting erroneous expenses for reimbursement. You determine the contractor submitted 2,500 reimbursement claims to the state. Rather than spend months looking at all 2,500, you decide to look at a statistically valid random sample. You use a statistical sampling tool such as a sample size calculator, Microsoft Excel Data Analysis ToolPak or RAT-STATS to determine if a review of 48 reimbursement claims would give you a figure that when extrapolated to the entire population of 2,500 claims, would have a confidence interval ¹ of 80 percent and a potential error rate ² of +/- 10 percent.

After you complete your initial audit of those 48 files, you can decide if you need to review more. If you didn't find any fraudulent activity, you could justify closing your fraud examination. If you found actionable fraudulent activity, you could review 51 more reimbursement claims — for a total of 99 — to increase your confidence interval to 95 percent.

You can extrapolate that figure to the entire population of 2,500 by reviewing less than 100 of the 2,500 claims. And you can give the actual fraud you found in the claims to a criminal prosecutor. The prosecutor could also use the extrapolated amounts to quantify the crime as relevant in a criminal sentencing. Oversight agencies and victims of the fraud can use the results as court-recognized figures to initiate civil and/or administrative action and recovery.

Fictitious nursing visits

In our Home Care Inc. case, we investigated allegations about the state-mandated records for billing. Nurses working for the company alleged that the agency's owner, Francesca, was instructing and paying them to sign off on visits to home-health patients that never actually occurred.

Nurses also alleged that Francesca knew about the regulation that doctors' orders needed to be in patients' files to substantiate the medical necessity of home-health services. Yet the nurses, under Francesca's direction, said they failed to obtain and maintain those orders and necessary documentation to bill the state for the provided home-health services.

Dozens of our interviews with nurses substantiated both allegations. They stated that Francesca instructed them to sign off on multiple nursing visit forms during visits so the agency could use them for fictitious future visits.

Multiple former directors of nursing at Home Care stated Francesca knew that nurses weren't placing doctors' orders in patients' file to substantiate the medical necessity of their services and justify the visits and billing. Home Care's office staff corroborated that falsification of forms and the failure to have doctors' orders in patients' folders were normal business operations.

After we obtained fraud evidence, the next step was to quantify it. We found 137 home-health patients' folders associated with the allegations surrounding the absence of doctors' orders, which involved years of services and thousands upon thousands of claims.

RAT-STATS to the rescue

We then used the RAT-STATS program — the HHS OIG's Office of Audit Services' primary tool — to generate a statistically valid random sample of 25 patient files among the 137 to examine. We could then extrapolate the results of the sample's examination to represent the entire population with a 90 percent confidence interval and a 16 percent +/- margin of error. (By the way, you can use RAT-STATS in just about any case in which you have a burdensome amount of items to review or audit — not just health care cases.)

An examination of those 25 patient files revealed that legitimate doctors' orders didn't support $42,993 out of $116,144 in claims, which was equivalent to 37 percent of all reviewed claims. When we extrapolated to the entire population, we found a 90 percent confidence interval of $389,043 in state billings that were fraudulent (+/- 16 percent). We also found Home Care Inc. had submitted claims for more than $3,000 in home-health services while the patients were hospitalized and would've been unable to receive these services. We used only a fraction of the time and resources we would've spent if we were to review all the files.

The reckoning

We supplied $46,394 as the fraud amount for criminal prosecution. This was the total fraud calculation of the 25 files we reviewed plus home-health billings while the patient was hospitalized. RAT-STATS extrapolated findings aren't generally acceptable for criminal proceedings in which the burden of proof is higher. However, in civil actions, courts have widely accepted the larger extrapolated amounts.

On Jan. 21, 2014, Francesca, the Home Care Inc. owner, was indicted on one felony count of tampering with evidence, one felony count of Medicaid fraud, one felony count of grand theft by deception and two felony counts of forgery. The state's department of Medicaid suspended Home Care Inc. and suspended the payment of more than $90,000 of pending claims.

We worked with the prosecution to present the RAT-STATS extrapolated findings and our investigation results to defense counsel, which assisted in communicating the extent and proof of the fraud. Francesca pleaded guilty to felony forgery. The court sentenced her to a suspended one-year prison sentence and four years of probation, and ordered her to pay $70,000 in restitution. The state's department of Medicaid terminated Home Care Inc. as a provider, and the business closed. Francesca was also excluded from participating in any federal health care program pursuant to 42 U.S.C. 1128 for a minimum of five years.

RAT-STATS contributed to a successful criminal investigation and ultimate conviction. If the state later decides to pursue civil action and recoveries, it can also use the RAT-STATS results.

Since the Home Care Inc. case, we've successfully used statistical sampling in our fraud examinations. RAT-STATS and other statistical tools aren't shortcuts; they can save valuable time and resources while giving you useable results.

Paul Kolb, CFE, is a special agent supervisor with a state agency that investigates health care fraud. His email address is: Officer_Kolb@yahoo.com. 

Tobey Culler is a fraud analyst with a state agency that investigates health care fraud. His email address is: Culler20@gmail.com.

^{1 Confidence Interval: A group of continuous or discrete adjacent values that is used to estimate a statistical parameter (as a mean or variance) and that tends to include the true value of the parameter a predetermined proportion of the time if the process of finding the group of values is repeated a number of times (Meriam-Webster.com).}

^{2 Potential error rate: Rate of error associated with not analyzing the entire population.}