Heuristic Search of Cut-Off Points for Clinical Parameters: Defining the Limits of Obesity

We studied the variability of obesity in a sample of 4,164 young Mexicans (17-24 years old) measured through the waist circumference. According to the American Heart Association, obesity is one of the five clinical alterations to define the Metabolic Syndrome (MS); the other four are low levels of HDL cholesterol, and high values of triglycerides, glucose, and blood pressure. It has been proposed a cut-off point of 80 cm for women and 90 cm for men to define a normal or altered value of waist circumference for Mexicans. We assume that the waist circumference in healthy population has a normal distribution, so a monolithic cut-off point is only an upper limit for normal values. The objective of this work is to estimate the subjacent normal distribution of the waist circumference of healthy people, involving in this analysis the other four components of the MS, and approaching the problem as a combinatory one. We defined a combination of cut-off points for the other four components of the MS; if considering a set of 50 cut-off points candidates for each of the five parameters, then results in a searching space of 50

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(more than 300 millions of combinations). Each particular combination of cut-off points (excluding waist circumference) sets a subpopulation in which parameter values fall into normal ranges so defined; then for each subpopulation we calculated the histogram of the waist circumference values. Using a heuristic function involving the symmetry value of the histogram (skewness), we applied a ‘best first search’ on the combination of cut-off points. We found a combination of cut-off point values that generates the more symmetrical histogram, so we propose it as a useful criterion to set cut-off points of MS parameters for Mexicans. Finally, the obtained histogram is proposed as the normal distribution of healthy population, and represents the variability of the waist circumference of non-obese young Mexicans.