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Abstract
Objective Newcomb-Benford’s Law (NBL) proposes a regular distribution for first digits, second digits and digit combinations applicable to many different naturally occurring sources of data. Testing deviations from NBL is used in many datasets as a screening tool for identifying data trustworthiness problems. This study aims to compare public available waiting lists (WL) data from Finland and Spain for testing NBL as an instrument to flag up potential manipulation in WLs.
Design Analysis of the frequency of Finnish and Spanish WLs first digits to determine if their distribution is similar to the pattern documented by NBL. Deviations from the expected first digit frequency were analysed using Pearson’s χ2, mean absolute deviation and Kuiper tests.
Setting/participants Publicly available WL data from Finland and Spain, two countries with universal health insurance and National Health Systems but characterised by different levels of transparency and good governance standards.
Main outcome measures Adjustment of the observed distribution of the numbers reported in Finnish and Spanish WL data to the expected distribution according to NBL.
Results WL data reported by the Finnish health system fits first digit NBL according to all statistical tests used (p=0.6519 in χ2 test). For Spanish data, this hypothesis was rejected in all tests (p<0.0001 in χ2 test).
Conclusions Testing deviations from NBL distribution can be a useful tool to identify problems with WL data trustworthiness and signalling the need for further testing.
- benford-newcomb distribution
- waiting list data
- fabricated data
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Footnotes
Contributors JPD, BGL-V and SP conceptualised and designed the study. JPD and CG-M oversaw data collection and performed the statistical analysis. JPD drafted the manuscript and all coauthors participated equally in the revision and final approval of the manuscript. JPD is the guarantor for the study. All authors had full access to all the data in the study (including statistical analysis, tables and figures) and can take responsibility for the integrity of the data and the accuracy of the data analysis.
Funding This paper forms part of the research funded by Grant ECO2017-83771-C3-2 under the ’National Programme for Research, Development and Innovation to Address the Challenges of Society: National Plan for Scientific Research and Technical Innovation 2017–2020' funded by the Ministry of Economy and Competitiveness of Spain.
Disclaimer The funder had no influence on the conduct of this study or on the drafting of this manuscript.
Competing interests None declared.
Patient consent Not required.
Ethics approval The study, with secondary data available from public sources and no patients as participants, does not require ethics approval according Spanish law and international regulations.
Provenance and peer review Not commissioned; externally peer reviewed.
Data sharing statement The full dataset (Dataset.csv) is available without restrictions in the Appendix.