Using Benford's Law to Assess Data Integrity in Two Retracted Papers About COVID-19

Background: Two papers about hospitalizations in patients with COVID-19 that were published in the Lancet and the New England Journal of Medicine were retracted soon after being published because the authors were unable to make the data used in the papers available for audit. The possibility that the data were fabricated was raised in the media but no evidence to refute or confirm this speculation has been presented. Methods: We did an analysis of the numeric data in the two papers to assess their conformance with “Benford’s law,” which states that, for a determined set of “natural” numbers, those whose first digit is 1 will appear more frequently (30.1%) than those beginning with other digits, following in order from 2 to 9 (17.6%, 12.5%, 9.7%, 7.9%, 6.7%, 5.8%, 5.1%, and 4.6%, respectively). Conformance with Benford’s law is evidence that data have not been fabricated since it is difficult to “fake” data. Findings: In both retracted papers, there were statistically significant deviations of the numeric data in the papers from Benford’s law. Interpretation: Violation of Benford's law for first digits is not proof of data falsification or fraud. Whether the retracted papers contained fabricated data, data obtained fraudulently, or data that could not be made available for audit will probably never be known. Funding Statement: This research was not funded. Declaration of Interests: Guido Schuepfer, Jacqueline Mauch, and Diana Petitti declare that they have no financial or personal relationships that create a conflict of interest.