Mathematical Analysis of Statistical Design of Experiment and Machine Learning Methods in Identifying Factors Influencing Obesity

Abstract

Introduction: This paper explores a mathematical framework for defining factors influencing obesity by comparing statistical design of experiment and machine learning (ML) approaches.

Methods: A low-calorie program was applied to 100 overweight to morbidly obese patients monitored over 8 visits in 4 months and over. A traditional three-factor experimental design was employed to evaluate the impact of glucose, Alanine aminotransferase (ALT) enzyme, and cholesterol levels on obesity. ML methods (Multiple Linear Regression, Random Forest, Decision Tree Classifier, Gradient Boosting Regressor and XGBoost) were employed to evaluate the impact of glucose, ALT enzyme, cholesterol levels, body mass, blood pressure, and sex on obesity.

Results: The three-factor experiment indicated glucose had the greatest impact on obesity, followed by cholesterol and ALT, particularly significant in females. ML models, with over 90% accuracy and RMSE less than 1.5, corroborated these findings and also highlighted the roles of blood pressure.

Conclusion: Both statistical and ML models aim to understand relationships between variables and predict outcomes, differing in assumptions, flexibility, and interpretability. Statistical methods offer high interpretability and rigorous testing, while ML provides flexibility and robust performance with complex data.