Random Sub-sampling Cross Validation for Empirical Correlation Between Heart Rate Variability, Biochemical and Anthropometrics Parameters

According to National Cholesterol Education Program-Adult Treatment Panel III, metabolic syndrome (MS) is a condition characterized by: Dyslipidemia, abdominal obesity, high levels in fasting glucose and arterial hypertension. Studies have explored indexes using dimensional analysis (DA) formed by anthropometric, biochemical and heart rate variability parameters for the diagnosis of MS. The dimensionless numbers made from DA have the capability to manage them as a mathematical functionality; therefore it is possible to relate them, even when the parameters used are not connected. The aim of this work is to find a polynomial equation using as variables two dimensionless numbers designed from anthropometrical and biochemical (π_IS) parameters and from heart rate variability (π_HRV) parameters. A fitting using a parametrical random sub-sampling cross validation (RSV) was performed using as an objective function the least squares method. A database of 40 subjects (25 control subjects and 15 subjects with MS) was employed. The polynomial parameters that best fit the database used correspond to a polynomial of order eight. The RSV substantially improves the adjustment of the polynomial compared to the application of the least squares method only (0.6678 vs. 0.3255). The polynomial relationship between π_IS and π_HRV allows the possibility to determine biochemical and anthropometric variables from heart rate variability parameters. Due to the limited number of subjects in the database used, it is necessary to repeat this methodology in a more extensive database to determine a more general polynomial that can be used with any type of population.