Rufaidah Ali Rushdi
Department of Pediatrics, Kasr Al-Ainy School of Medicine, Cairo University Cairo, 11562, Arab Republic of Egypt.

Ali Muhammad Rushdi
Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia.

DOI https://dx.doi.org/10.33889/IJMEMS.2018.3.3-016

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Abstract

This paper advocate and demonstrates the utility of the Karnaugh map, as a pictorial manual tool of Boolean algebra, in the exploration of medical problems as exemplified herein by the problem of Fetal Malnutrition (FM). The paper briefly introduces the FM problem, and specifies four metrics or tests used frequently in its study. Clinical data collected about these metrics (as continuous variables or dichotomized versions thereof) are conventionally treated via statistical methods. The Karnaugh map serves as a convenient way for aggregating the set of clinical data available into a pseudo-Boolean function. The map can be used to produce a two-by-two contingency matrix (confusion matrix or frequency matrix) that relates an assessed test or metric to a reference or standard one. Each of these two metrics can be any of the map variables or a function of some or all of these variables. While the map serves in this capacity as a supplement or aid to statistical methods, it is also useful for certain non-statistical methods (specifically Boolean ones). The paper shows how the map entries can be dichotomized via an appropriate threshold for use in Boolean Analysis (BA), which can be conducted despite the lack of a gold standard. The map also implements Qualitative Comparative Analysis (QCA) for the given clinical data. The map variable-handling capability does not pose as a shortcoming for either BA or QCA, since the number of variables involved (not only herein but in other typical medical problems as well) is relatively small. The concepts and methods introduced herein are demonstrated through application to the aforementioned set of clinical data for the FM problem, and can be extended to a wide variety of medical problems.

Keywords- Karnaugh map, Contingency table, Gold standard, Fetal malnutrition, Pseudo-Boolean function, Boolean analysis, Qualitative comparative analysis, Epidemiology, Diagnostic testing.

Citation

Rushdi, R. A., & Rushdi, A. M. (2018). Karnaugh-Map Utility in Medical Studies: The Case of Fetal Malnutrition. International Journal of Mathematical, Engineering and Management Sciences, 3(3), 220-244. https://dx.doi.org/10.33889/IJMEMS.2018.3.3-016.