Never, once, and repeated illness: a geometric view for insights and interpretations

Ramalingam Shanmugam


Background: Medical/health researchers depend on data evidence for knowledge discovery. At times, data analysis to capture the data evidence is overwhelming and the process becomes too tedious to give up the attempt. A prudent thing to do is to seek out a simpler visual approach to obtain insights. One visual approach is devised in this article to understand what the data are really revealing to either get an insight first or then confirm what is intuitively configured by the medical concepts. This visual approach is geometric concepts based. In specific, triangle is employed in this new and novel approach.  

Methods: A successful treatment of any illness is a consequence of knowledge build-up arising from data mining about the never, once, or repeated episode of a disease incidence in a patient. This article investigates and illustrates a novel and pioneering geometric approach, especially based on the properties of triangle, to extract hidden evidence in the data. New probabilistic expressions are derived utilizing trigonometric relations among the corner points of a triangle. The conceptual contents of this article are versatile enough for different medical/health data analysis.

Results: For illustration here, the medical binomial data in Hopper et al. (Genetic Epidemiology, 1990) on the occurrence of asthma or hay fever among the four groups: (1) monozygotic females (MZF), (2) monozygotic males (MZM), (3) di-zygotic females (DZF), and (4) di-zygotic males (DZM) are considered and triangularly interpreted. The results indicate that the angle in the vertex representing one episode is the largest compared to the other two angles in the vertices representing never or repeated episode of an illness among a random sample of twins from these four groups with respect to getting asthma or hay fever. This geometric finding implies that the event of never and the event of repeated incidence of the illness have farthest Euclidean distance in probability sense. In other words, the never and repeated incidences are not in close proximity as probable.

Conclusions: This geometric view of this article is versatile enough to be useful in other research studies in drug assessment, clinical trial outcomes, business, marketing, finance, economics, engineering and public health whether the data are Poisson or inverse binomial type as well. 


Discrete probability, Likelihood of two or more episodes, Poisson, Binomial, Geometric models

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