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

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Abstract

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.