Abstract:
The history and methodology of contemporary applied mathematics, namely the history and methodology, concerning development of statistical methods applications, is the subject of presented paper. Authors propose the principles, that allow for historian of mathematics to understand clearly, how it is better to research the present, recently founded achievements in case, if the achievements is not completely recognized yet, and what is possible to explore instead of so-called “results” of recently produced applied statistical research. The core of problem is: how to interpret the principles of mathematical models and data fitting, when data satisfy the model by miracle, without logical explanation. The proposed methodology leads toward the new interpretation of key notions of applied mathematics, as randomness, probability, randomization, and finally sets the vision of contemporary applied science that is goes out of the limits of rationalism (including positivism and post-positivism). The proposed vision in the article is called as “theological direction in the philosophy of science”.
This approach is carried out on a specific example from the field of application of statistics in medicine in the study of simple risk score of contrast-induced nephropathy (CIN) after percutaneous coronary intervention (PCI). First on the scientific and popular level, this describes a medical problem, and then discusses approaches to address it.
Source materials for discussion are from the articles in American medical journals about this particular problem (there is a distinct impression that the American Mathematical Statistics, used in medicine, lost the understanding since 1960th). A hard question arises: Is suitable for anything the results of these studies? On the one hand, there are incompetent errors, but on the other – a large number of observations. Nevertheless attempt to use the results of these studies to test data obtained at the Institute of Transplantation is not unsuccessful.
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