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.
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机译：摘要每年因医疗保险和医疗补助欺诈而损失的金钱达数十亿美元。我们使用三个实际的支付总体，考虑了这些审计中常用的抽样和外推策略的操作特征：使用（1）简单扩展估计量或（2）比率估计量的简单随机抽样; （3）分层抽样，其中分层的基础是付款金额。基于比率估计量的较低置信区间的已达到置信度水平（=补偿不足率）在常见的高拒绝率情况下，对所有三个人口而言，远低于政府规定的90％水平。对于简单随机抽样中的扩展估计量，获得的置信度取决于多付人群的偏度：如果偏斜，则该置信度将降至90％以下，有时远低于此;如果右偏，它将超过90％。在后一种情况下，按付款额的粗心分层会破坏这种保守性。当右偏严重时，有限的分层有时可以保留90％的置信度，同时可以改善多付款项的回收率。在任何无法通过基于中心极限定理的外推方法实现不足补偿的人群中，均应采用基于样本数和超几何分布的方法（Edwards等，Health Serv Outcomes Res Methodol 4：241-263，2005; Gilliland和Feng，《卫生服务成果研究方法》，2010年10月：154-164;爱德华兹等人，《竹enny取样》，南卡罗来纳大学，统计局，技术部第232号技术报告，2010年）;这些在数学上保证了90％的置信度。不管考虑采用哪种抽样和外推计划，都应在计划阶段使用蒙特卡洛模拟测试对操作特性（回收率不足，多付款项回收等）进行彻底检查，我们将在本文中通篇使用。
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