The "first digit law" – A hypothesis on its possible impact on medicine and development aid. (December 2016) - Pollach, Gregor; Brunkhorst, Frank; Mipando, Mwapatsa; Namboya, Felix; Mndolo, Samson; Luiz, Thomas
Abstract: The "first digit law" or "Benford's law" is a mathematical distribution discovered by Simon Newcomb and Frank Benford. It states, that the probability of the leading number d (d ∈ {1, …, 9}) in many natural datasets follows: P (d) = log10 (d + 1) − log10 (d) = log10 (1 + 1/d). It was successfully used through tax authorities and "forensic accounting" in order to detect fraud and other irregularities. Benfords law was almost neglected for its use outside financial accounting. The planning for health care systems in developing countries is extremely dependant on good, valid data. Whether you plan the catchment area for the future district hospitals, the number of health posts, the staff establishment for the central hospital or the drug budget in the Ministry. The "first digit law" can be used in medicine, public health, physiology and development aid to unmask questionable data, to discover unexpected challenges, difficulties in the data collection process, loss through corruption and criminal fraud. Our hypothesis suggests, that the "first digit law" is a cost effective tool, which is easy to use for most people in the medical profession, which does not really needs complicated statistical software and can be used on the spot, even in the resource restricted conditions of developing countries. Several preconditions (like the size of the data set and its reach over more than two dimensions) have to be fulfilled, but then Benfords law can be used by any clinician, physiologist, public health specialist or aid consultant without difficulties and without deeper statistical knowledge in the four steps, we suggest in this article. The consequences will be different depending on the level (local regional, national, continental, international) on which you will use the law. All levels will be enabled to get insight into the validity of the data-challenges for the other levels without the help of trained statisticians or accountants. We believe that the "first digit law" is a vastly underestimated and neglected, but extremely useful tool for the identification of unexpected challenges, supervision and control in various parts of medicine and public health for almost all aspects of development aid.