The Minimum Sum Method: A Distribution-Free Sampling Procedure for Medicare Fraud Investigations

Abstract

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.