Auditing primary diagnostic coding using the First Digit Law of Benford

Bogdan-Vasile Ileanu and Adrian Pana

Journal of Management Analytics, 2026, vol. 13, issue 2, 331-349

Abstract: This research explores the possibility of applying the First Digit Law of Benford (BL1) – a statistical principle stating that in many naturally occurring datasets, the first digit is more likely to be small – in auditing the codification of hospital discharges, using two types of analysis: one involves ten European countries with Organisation for Economic Co-operation and Development (OECD) data plus Romania, grouped by main classes of diseases, and the other applies the technique to the Romanian case through a particular set of 28,000,000 hospitalized events, discharged between 2016 and 2019, grouped by categories. Chi-squared, Sum of Squared Deviances, and Freedman-Watson evaluate the agreement with the Leading Digit Law. Then, our work combines the probability of rejecting Benford Law (BL) and several explanatory variables into a panel binary logit model. The tests applied to the selected OECD countries and Romanian data reveal close conformities by the OECD broad morbidity classes. Particular inquiries applied in the Romanian case show puzzling results. For instance, the disease group with the most years of life lost class and the class with the highest number of discharges fit (BL1). A contrario, the most expensive disease class breaks down the law. Among other interesting results, regression modeling finds that classes with higher cost per episode are more likely to break the BL1, while the share of cases treated in inpatient care for a particular group of diagnostics tends to obey the natural law. We also highlight that anomalies are directly linked with the cost and polarization of cases in university centers and are inversely associated with a possible wider availability of services. Our findings support using this procedure as a primary filter in diagnostic coding audits. The specific set of diagnostics and covariates emphasized here can help the auditor in identifying higher anomaly rates and save time for hospital data mining.

Date: 2026
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DOI: 10.1080/23270012.2026.2639974

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