Using the Benford’s Law as a First Step to Assess the Quality of the Cancer Registry Data

Abstract

BackgroundBenford’s law states that the distribution of the first digit different from 0 [first significant digit (FSD)] in many collections of numbers is not uniform. The aim of this study is to evaluate whether population-based cancer incidence rates follow Benford’s law, and if this can be used in their data quality check process.MethodsWe sampled 43 population-based cancer registry populations (CRPs) from the Cancer Incidence in 5 Continents-volume X (CI5-X). The distribution of cancer incidence rate FSD was evaluated overall, by sex, and by CRP. Several statistics, including Pearson’s coefficient of correlation and distance measures, were applied to check the adherence to the Benford’s law.ResultsIn the whole dataset (146,590 incidence rates) and for each sex (70,722 male and 75,868 female incidence rates), the FSD distributions were Benford-like. The coefficient of correlation between observed and expected FSD distributions was extremely high (0.999), and the distance measures low. Considering single CRP (from 933 to 7,222 incidence rates), the results were in agreement with the Benford’s law, and only a few CRPs showed possible discrepancies from it.ConclusionThis study demonstrated for the first time that cancer incidence rates follow Benford’s law. This characteristic can be used as a new, simple, and objective tool in data quality evaluation. The analyzed data had been already checked for publication in CI5-X. Therefore, their quality was expected to be good. In fact, only for a few CRPs several statistics were consistent with possible violations.

Ongoing outbreak of COVID-19 in Iran: challenges and signs of concern with under-reporting of prevalence and deaths

“…The probability that a digit, 1, 2,...,9 d = , is a leading number is given by 10 ( ) log (1 (1/ )) P d d =+where numbers with leading digit 1 have the highest probability of appearance and this probability steadily decreases as the starting digit becomes larger. BL is used in a variety of fields such as accounting, trade, and election results to study possible fraud and irregularities with data [28][29][30] and is also frequently used to assess the quality of epidemiological and clinical data [31][32][33].…”

Ongoing outbreak of COVID-19 in Iran: challenges and signs of concern with under-reporting of prevalence and deaths

“…The probability that digit d = 1, 2, ..., 9 is a leading number is given by P (d) = log10(1 + (1/d)) where numbers with leading digit 1 have the highest probability of appearance and this probability steadily decreases as the starting digit becomes larger. Benford's law is used in a variety of different areas to study irregularities in data [Brown, 2005, Durtschi et al, 2004 and is also frequently used in medicine to assess the quality of data [Crocetti andRandi, 2016, Idrovo et al, 2011]. Figure 8a shows the distribution of leading digits in data acquired from Iran, the USA, and the UK compared to the Benford distribution.…”

Benford’s law and geographical information – the example of OpenStreetMap

“…If data are not in accordance with Benford's law while it could be expected to be, this is an indication that the data might be erroneous or even fraudulent. This principle is, e.g., used in the context of taxes (Nigrini 1996, Niskanen and Keloharju 2000, Watrin et al 2008; for accounting data (Durtschi et al 2004, Nigrini andWells 2012); in the context of earnings (Thomas 1989, Skousen et al 2004; for financial data in the Global South (Shi et al 2018); for survey data (Judge and Schechter 2009); and for health-related data (Crocetti and Randi 2016). In addition, Benford's law is used to detect hidden messages in image data (Jolion 2001, Pérez-González et al 2007, Zaharis et al 2011).…”