1. St. Elizabeth Physicians Regional Diabetes Center, Covington, KY 41011, USA
2. College of Medicine, University of Kentucky, Lexington, KY 41011, USA
3. Sanford School of Medicine, University of South Dakota, Sioux Falls, SD 41011, USA
4. Faculty of Medicine, Department of Internal Medicine, Endocrine Unit, Alexandria University, Alexandria, Egypt
5. St. Elizabeth Healthcare, Edgewood, KY 41017, USA
6. Department of Mathematics and Statistics, Northern Kentucky University, Highland Heights, KY 41099, USA