The Minimum Sum Method: A Distribution-Free Sampling Procedure for Medicare Fraud Investigations
Random sampling of paid Medicare claims has been a legally acceptable approach for investigating suspicious billing practices by health care providers (e.g. physicians, hospitals, medical equipment and supplies providers, etc.) since 1986. A population of payments made to a given provider during a given time frame is isolated and a probability sample selected for investigation. For each claim or claim detail line, the overpayment is defined to be the amount paid minus the amount that should have been paid, given all evidence collected by the investigator. Current procedures stipulate that, using the probability sample’s observed overpayments, a 90% lower confidence bound for the total overpayment over the entire population is to be used as a recoupment demand to the provider. It is not unusual for these recoupment demands to exceed a million dollars. It is also not unusual for the statistical methods used in sampling and calculating the recoupment demand to be challenged in court.
Though it is quite conservative in most settings, for certain types of overpayment populations the standard method for computing a lower confidence bound on the population total, based on the Central Limit Theorem, can fail badly even at relatively large sample sizes. Here, we develop “nonparametric sampling” inferential methods using simple random samples and the hypergeometric distribution, and study their performance on four real payment populations. These new methods are found to provide more than the nominal coverage probability for lower confidence bounds regardless of sample size, and to be surprisingly efficient relative to the Central Limit Theorem bounds in settings where overpayments are essentially all-or-nothing and where the payment population is relatively homogeneous and well separated from zero. The new methods are especially well-suited for sampling payment populations for providers of motorized wheelchairs, which at the time of this article’s submission was a national crisis. Extensions to stratified random samples and to settings where there are frequent partial overpayments are discussed.
Keywordsmedicare fraud motorized wheelchairs sampling hypergeometric distribution distribution-free procedures lower confidence bounds
Unable to display preview. Download preview PDF.
- 1.CNN, “Wheelchair scams cost Medicare millions,” 2003. Website http://www.cnn.com/2003/HEALTH/11/11/us.wheelchair.ap/
- 2.Casella, G. and Berger, R., Statistical inference, 2nd edn., Duxbury, Pacific Grove, CA, 2002.Google Scholar
- 3.Center for Medicare and Medicaid Services, Program Memorandum Carriers Change Request 1363. Office of the Inspector General, U.S. Dept. of Health and Human Services, 2001.Google Scholar
- 4.Center for Medicare and Medicaid Services, “Medicare Definition of Fraud,” 2003. Website http://cms.hhs.gov/providers/fraud/DEFINI2.ASP
- 5.Cochran, W.G., Sampling techniques, 3rd edn., John Wiley and Sons, New York, 1977.Google Scholar
- 6.HHS Office of the Inspector General, RAT-STATS program, 2003. Website http://www.oig.hhs.gov/organization/oas/ratstat.html
- 7.Health Care Financing Administration, Medicare Carriers Manual, Part B, Part 3, Sampling Guidelines Appendix. Office of the Inspector General, U.S. Dept. of Health and Human Services, 1975.Google Scholar
- 8.Johnson, N. and Kotz, S., Discrete distributions, Houghton-Mifflin, Boston, 1969.Google Scholar
- 9.MSNBC, “Wheelchairs take taxpayers for ride,” 2003. Website http://www.msnbc.msn.com/id/3475857/
- 10.MathSoft, Inc., Splus user’s guide, Data Analysis Products Division, MathSoft, Seattle, WA, 1997.Google Scholar
- 11.National Health Care Antifraud Association, “About health care fraud,” 2003. Website http://www.nhcaa.org/pdf/all_about_hcf.pdf.
- 12.The R Project for Statistical Computing, 2003. Website http://www.r-project.org/.
- 13.SAS Institute, Inc., SAS® user’s guide: Statistics, SAS Institute, Inc., Cary, NC, 1985.Google Scholar
- 14.Scheaffer, R.E., Mendenhall, W., and Ott, L., Elementary survey sampling, 4th ed., Duxbury, 1990.Google Scholar
- 15.Wright, T., Exact confidence bounds when sampling from finite universes, Springer, 1991.Google Scholar