On stratified sampling and ratio estimation in medicare and medicaid benefit integrity investigations



Billions of dollars are lost each year to Medicare and Medicaid fraud. Using three real payment populations, we consider the operating characteristics of commonly used sampling-and-extrapolation strategies for these audits: simple random sampling using (1) the simple expansion estimator or (2) the ratio estimator; and (3) stratified sampling where the basis of stratification is the payment amount. The achieved confidence level (=rate of under-recoupment) of the lower confidence bound based on the ratio estimator fell far below the government-prescribed 90% level for all three populations in commonly encountered high denial-rate scenarios. For the expansion estimator in simple random sampling, the achieved confidence level depends on the skew of the overpayment population: if it is left skewed, the level will fall below 90%, sometimes far below; if it is right-skewed, it will exceed 90%. In the latter case, careless stratification by payment amount can destroy this conservatism. When there is strong right skew, limited stratification can sometimes preserve the 90% confidence while yielding improvements in overpayment recovery. In any population where 90% under-recoupment is not achieved by extrapolation methods based on the central limit theorem, methods based on sample counts and the hypergeometric distribution (Edwards et al., Health Serv Outcomes Res Methodol 4:241–263, 2005; Gilliland and Feng, Health Serv Outcomes Res Methodol 10:154–164, 2010; Edwards et al., Pennysampling. Technical Report No. 232, Dept. of Statistics, University of South Carolina, Columbia, SC, 2010) should be considered; these mathematically guarantee the 90% confidence level. Regardless of the sampling and extrapolation plan being considered, operating characteristics (under-recoupment rate, overpayment recovery, etc.) should be thoroughly checked in the planning stages with Monte Carlo simulation testing, which we use throughout this paper.


Centers for Medicare and Medicaid Services (CMS) Sampling Auditing Fraud Benefit integrity 


  1. Centers for Medicare and Medicaid Services: Program Integrity Manual Transmittal 114, Change Request 3734. http://www.cms.hhs.gov/transmittals/downloads/R114PI.pdf (2005)
  2. Cochran, W.G.: Sampling Techniques, 3rd edn. Wiley, New York (1977)Google Scholar
  3. Edwards, D., Ward-Besser, G., Lasecki, J., Parker, B., Wieduwilt, K., Wu, F., Moorhead, P.: The minimum sum method: a distribution-free sampling procedure for medicare fraud investigations. Health Serv. Outcomes Res. Methodol. 4, 241–263 (2005)CrossRefGoogle Scholar
  4. Edwards, D., Gilliland, D., Ward-Bessr, G., Lasecki, J.: Pennysampling. Technical Report No. 232, Dept. of Statistics, University of South Carolina, Columbia, SC (2010)Google Scholar
  5. Gilliland, D., Edwards, D.: Using randomized confidence limits to balance risk – an application to Medicare fraud investigations. Statistics and Probability Research Memorandum RM-685, Michigan State University (2010)Google Scholar
  6. Gilliland, D., Feng, W.: An adaptation of the minimum sum method. Health Serv. Outcomes Res. Methodol. 10, 154–164 (2010)Google Scholar
  7. Ignatova, I., Edwards, D.: Probe samples and the minimum sum method for medicare fraud investigations. Health Serv. Outcomes Res. Methodol. 8, 209–221 (2008)CrossRefGoogle Scholar
  8. Mobley, J.: Sample Size Selection for the Minimum Sum Method. Technical Report No. 230. Department of Statistics, University of South Carolina, Columbia (2009)Google Scholar
  9. Neter, J., Loebbecke, J.K.: On the behavior of statistical estimators when sampling accounting populations. J. Am. Stat. Assoc. 72, 501–507 (1977)CrossRefGoogle Scholar
  10. Scheaffer, R.E., Mendenhall, W., Ott, L.: Elementary Survey Sampling, 4th edn. PWS-Kent, Boston (1990)Google Scholar
  11. U.S. Department of Health and Human Services: FY 2007 Agency Financial Report. http://www.hhs.gov/afr/ (2007). Accessed 2008

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of South CarolinaColumbiaUSA

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