Towards the insulin resistance and obesity diagnosis: A dimensional analysis approach

Diabetes mellitus and cardiovascular diseases are ailments related to insulin resistance (IR) and obesity. The existing methods for IR and obesity diagnosis are the HOMA-IR and body mass index (BMI), respectively. Those methods have limitations in the diagnosis. The aim of this research is to propose dimensionless indexes that can diagnose subjects with IR and obesity using anthropometrics and biochemical variables (waist circumference, height, weight, systolic blood pressure, diastolic blood pressure and triglycerides). Three dimensionless indexes, designed from the π Vaschy-Buckingham theorem, were assessed using receiver operating characteristic (ROC) curves and a database of 829 subjects. The index π1, constructed with the variables: waist circumference, triglycerides height and weight; obtained a better performance as classifier of IR and obesity, presenting an area under the ROC curve of 0.78, sensitivity of 0.82 and specificity of 0.68 for IR diagnosis, and an area under the ROC curve of 0.68, sensitivity of 0.66 and specificity of 0.65 for obesity diagnosis. The π1 dimensionless index designed in this study is a simple method that allows diagnosing two pathologies from variables that can be collected in a routine medical examination.