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.