Sample Design for Audit Populations

TL;DR

This paper introduces new statistical tools and models for designing audit samples, specifically for healthcare claim audits, addressing gaps in existing literature with methods for variance estimation, sample size calculation, and optimal stratification.

Contribution

It develops novel estimators and criteria for sample design in audit populations, including a hypergeometric process model and variance estimators under partial error assumptions.

Findings

Tools demonstrated on simulated populations

Improved variance estimation methods

Guidelines for choosing estimation techniques

Abstract

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.