U.S. Department of Justice (USDOJ) press release (May 8, 2008): Eleven people have been indicted in $\dots$ a targeted criminal, civil and administrative effort against individuals and health care companies that fraudulently bill the Medicare program. The indictments in the Central District of California resulted from the creation of a multi-agency team of federal, state and local investigators designed specifically to combat Medicare fraud through the use of real-time analysis of Medicare billing data.

USDOJ press release (June 27, 2008): The owners of four Miami-based health care corporations were sentenced and remanded to prison yesterday for their roles in schemes to defraud the Medicare program. Collectively, the three defendants through their companies collected more than $14 million from the Medicare program for unnecessary medicine, durable medical equipment (DME) and home health care services.

USDOJ press release (Oct. 7, 2008): Eight Miami–Dade County residents have been charged in a 16-count indictment for their alleged roles in a Medicare fraud scheme involving fake HIV infusion treatments.

As the above press releases imply, the U.S. Department of Justice (USDOJ) and its Medicare Fraud Strike Force conduct investigations into suspected fraud and abuse of the Medicare system by health care providers. According to published reports, the Strike Force was responsible for almost 25% of the Medicare fraud charges brought nationwide in 2007.

One way in which Medicare fraud occurs is through the use of “upcoding,” which refers to the practice of providers coding Medicare claims at a higher level of care than was actually provided to the patient. For example, suppose a particular kind of claim can be coded at three levels, where Level 1 is a routine office visit, Level 2 is a thorough examination involving advanced diagnostic tests, and Level 3 involves performing minor surgery. The amount of Medicare payment is higher for each increased level of claim. Thus, upcoding would occur if Level 1 services were billed at Level 2 or Level 3 payments or if Level 2 services were billed at Level 3 payment.

The USDOJ relies on sound statistical methods to help identify Medicare fraud. Once the USDOJ has determined that possible upcoding has occurred, it next seeks to further investigate whether it is the result of legitimate practice (perhaps the provider is a specialist giving higher levels of care) or the result of fraudulent action on the part of the provider. To further its investigation, the USDOJ will next ask a statistician to select a sample of the provider’s claims. For example, the statistician might determine that a random sample of 52 claims from the 1,000 claims in question will provide a sufficient sample to estimate the overcharge reliably. The USDOJ then asks a health care expert to audit each of the medical files corresponding to the sampled claims and determine whether the level of care matches the level billed by the provider and, if not, to determine what level should have been billed. Once the audit has been completed, the USDOJ will calculate the overcharge.

In this chapter, we present a recent Medicare fraud case investigated by the USDOJ. Results for the audit of 52 sampled claims, with the amount paid for each claim, the amount disallowed by the auditor, and the amount that should have been paid for each claim, are saved in the MCFRAUD file.* Knowing that a total of $103,500 was paid for the 1,000 claims, the USDOJ wants to use the sample results to extrapolate the overpayment amount to the entire population of 1,000 claims.