Abstract
The National Health Care Anti-Fraud Association (www.nhcaa.org) states that in 2007 over 4 billion health insurance claims were processed in the United States and that fraud amounted to $68 billion (over 3%) of the total paid $2.26 trillion. Additional overpayments come from billings for unnecessary practice and procedures and errors in billings. It is of vital importance that valid and efficient statistical methods be developed for audits of payments by insurers. The Minimum Sum Method (MSM) is based on simple random sampling. It is a valid statistical method for obtaining a (1 − α)100% confidence level lower estimate (bound) for the total overcharge in a health care payment population whatever the sample size. The MSM lower bound is efficient (not too conservative) when the payments in population are about the same size and each payment is either completely in error (all overcharge) or not in error. It is the purpose of this paper to point out a simple adaptation of MSM that extends its effectiveness to populations where payments vary, to demonstrate the advantage with a small simulation study, and to point out how randomized lower estimates can be used to precisely apportion the risk due to sampling error.