Confidence limits for estimates of totals from stratified samples, with application to medicare Part B overpayment audits

Abstract

Superpopulation models are proposed that should be appropriate for modelling sample-based audits of Medicare payments and other overpayment situations. Simulations are used to estimate the coverage probabilities of confidence intervals formed using the standard Stratified Expansion and Combined Ratio estimators of the total. Despite severe departures from the usual model of normal deviations, these methods have actual coverage probabilities reasonably close to the nominal level specified by the US government's sampling guidelines. An exception occurs when all claims from a single sampling unit are either completely allowed, or completely denied, and for this situation an alternative is explored. A balanced sampling design is also examined, but shown to make no improvement over ordinary stratified samples used in conjunction with ratio estimates.

Keywords:

• Stratified samples
• ratio estimators stratified expansion estimators
• coverage probability
• audit
• overpayment

Acknowledgements

This work was supported by a contract with First Coast Service Options, Inc, a CMS Medicare Contractor. I am grateful to Dr Ben King for suggesting the examination of Satterthwaite's df with the Combined Ratio Estimator, and to Dr Albert Lee and Dr Clauda Laster for comments.