Sample Design for Audit Populations

We develop several tools for the determination of sample size and design for MediCal audits. This audit setting involves a population of claims for reimbursement by a healthcare provider which need to be reviewed by an auditor to determine the correct amount for each claim. The existing literature regarding sample planning for audits is incomplete and often includes restrictive assumptions. To fill these gaps, we exploit the special relationship between the known claim amounts and the unknown post-audit amounts. We propose a hypergeometric generative process for audit populations which we use to derive estimators of variances needed for sample size determination. We further develop a criterion for choosing between simple expansion and ratio estimation and an efficient method for determining exact optimal strata breakpoints in populations with repeated values. We also derive a variance estimator under a more general "partial error" model than previous researchers have used. These tools apply more generally to audits where an overstated book/claim amount is the primary concern and estimation of the total dollar value of the claim errors is the goal. The sample design methods we develop are illustrated on two simulated audit populations.