  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.
